3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3: Defining Mathematics - in your study guide and provide the
differences between the three views used to outline the mathematics consideration.
(10)

Answer: the answer is use ur ai in Brainly, it helped me a lot

Step-by-step explanation:

Answer:

(fog)(x) = -4x^3 + 7.

Step-by-step explanation:

We can think of (f o g)(x) as f(g(x)).  This shows that we plug in the entire g(x) function for x in f(x) and simplify:

f(x^3) = -4(x^3) + 7

f(x^3) = -4x^3 + 7

Thus, (f o g)(x) = -4x^3 + 7

The equation of the red graph is g(x) = f(x) - 5

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

The functions f(x) and g(x)

Where, we have

f(x) = -x

i.e.. the parent equation of the function

From the graph, we can see that

The function is shifted down by 5 units

This means that

g(x) = f(x) - 5

This means that the equation of the red graph is g(x) = f(x) - 5

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The approximate average speed of the cab is 50 km/h.

To find the approximate average speed of the cab, we can use the formula:

Average Speed = Total Distance / Total Time

Given that the initial odometer reading is 369 km and the final reading is 469 km, the total distance covered by the cab is:

Total Distance = Final Odometer Reading - Initial Odometer Reading

Total Distance = 469 km - 369 km

Total Distance = 100 Km.

The cab traveled for 2 hours, so the total time is:

Total Time = 2 hours

Now, we can substitute the values into the average speed formula:

Average Speed = Total Distance / Total Time

Average Speed = 100 km / 2 hours

Average Speed = 50 km/h

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The value of x in the diagram given in the question is 6

From the question given above, the following data were obtained:

The value of x can be obtained using cos ratio.

Cos θ = Adjacent / Hypotenuse

Cos 60 = 3 / x

Cross multiply

x × Cos 60 = 3

Divide both sides by Cos 60

x = 3 / Cos 60

= 3 / 0.5

= 6

Thus, the value of x is 6

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Answer:

Percent error is calculated using the formula:

   Percent Error = ( |Predicted Value - Actual Value| / Actual Value ) * 100%

Plugging in Brianna's prediction and the actual number of puppies sold:

   Percent Error = ( |16 - 9| / 9 ) * 100%

The absolute value of (16 - 9) is 7, so the calculation becomes:

   Percent Error = ( 7 / 9 ) * 100%

This is approximately 77.78%, which is Brianna's percent error in her prediction.

Answer:

a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.

For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.

For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.

For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.

For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.

For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.

For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.

b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.

c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).

To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).

d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.

Step-by-step explanation:

The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.

To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:

The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.

We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.

The data are dependent because the education level depends on whether the employee is a man or a woman.

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Answer:

Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:

```

cost_per_gb * G <= budget

```

where:

* cost_per_gb is the cost of data per gigabyte, which is $10 in this case

* G is the number of gigabytes of data

* budget is your budget, which is $130 in this case

To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:

```

G <= budget / cost_per_gb

```

We can then plug in the values for cost_per_gb and budget to get:

```

G <= 130 / 10

```

```

G <= 13

```

This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.

Here is a table that shows the cost of data for different amounts of data:

```

| Amount of data (G) | Cost (\$) |

|---|---|

| 1 | 10 |

| 2 | 20 |

| 3 | 30 |

| ... | ... |

| 13 | 130 |

| 14 | 140 |

| ... | ... |

```

Step-by-step explanation:

Answer:

Step-by-step explanation:

n=30

r=12

Plug into formula

you get:

1.7 in²

Answer: 8/9

Step-by-step explanation:

64/72            Divide both the top and bottom by 8

8/9

Answer:

H= [4 -1

      4 0]

Step-by-step explanation:

Answer:h equals 12

Step-by-step explanation:

Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1

0.225 can be expressed as the fraction  1/200.

To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).

Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.

Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).

Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).

Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).

Therefore, 0.225 can be expressed as the fraction 1/200.

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Answer:

incorrect

Step-by-step explanation:

as 7 * 6 = 42 and r is 10

so 6r3 is incorrect

and 7 * 7 = 49 and r is 3

so 7r3 is correct

Step-by-step explanation:

Let Peter's present age be "p" and his father's age be "x"

So, p = x-24 ;

5 years from now,

Peter's age will be (x-24) + 5 = x-19

His father's age will be x+5.

It is given that 3(x-19)= x+5.

3x - 57 = x + 5 => 2x = 62.

On solving, his father's present age (x) is 31.

So Peter's present age is (p) is x - 24 = 31 - 24 = 7.

Now going in the reverse oder to check the answer.

Peter's present is 7.

5 years from now, it will be 12.

His father's age is 31.

5 years from now, his age will be 36 (which is 3x12).

Hence , the answer to the given problem is 7

Answer:

It's 18.37

Step-by-step explanation:

I'm smart trust me.

Answer:

Least to greatest:

√143

4π

√79 + √63

Step-by-step explanation:

√79 + √63 = 16.82

4π = 12.57

√143 = 11.96

Step-by-step explanation:

a probability is always the ratio of

desired cases / totally possible cases.

so, in this case it is the

area of the triangle / area of the circle.

as everything of the triangle is also a part of the circle.

and so, that fraction of the area of the whole circle that is the area of the triangle in refutation to the area of the whole circle is the probability that a random point inside the circle would be also inside the triangle.

the area of a right-angled triangle is

leg1 × leg2 / 2

in our case

12 × 12 / 2 = 72 units²

the area of a circle is

pi × r²

in our case that is

pi × 12² = 144pi units²

the requested probability is

P = 72 / 144pi = 1/2pi = 0.159154943... ≈ 0.16

Answer:

Let's denote the height of the triangle as "h" inches.

According to the given information, the base of the triangle is 3 inches more than two times the height. Therefore, the base can be expressed as (2h + 3) inches.

The formula to calculate the area of a triangle is:

Area = (1/2) * base * height

Substituting the given values, we have:

7 = (1/2) * (2h + 3) * h

To simplify the equation, let's remove the fraction by multiplying both sides by 2:

14 = (2h + 3) * h

Expanding the right side of the equation:

14 = 2h^2 + 3h

Rearranging the equation to bring all terms to one side:

2h^2 + 3h - 14 = 0

Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:

h = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values are:

a = 2

b = 3

c = -14

Substituting these values into the quadratic formula:

h = (-3 ± √(3^2 - 4 * 2 * -14)) / (2 * 2)

Simplifying:

h = (-3 ± √(9 + 112)) / 4

h = (-3 ± √121) / 4

Taking the square root:

h = (-3 ± 11) / 4

This gives us two possible solutions for the height: h = 2 or h = -14/4 = -3.5.

Since a negative height doesn't make sense in this context, we discard the negative solution.

Therefore, the height of the triangle is h = 2 inches.

To find the base, we substitute this value back into the expression for the base:

base = 2h + 3

base = 2(2) + 3

base = 4 + 3

base = 7 inches

Hence, the base of the triangle is 7 inches and the height is 2 inches.

Step-by-step explanation:

-The answer for the height is 5.5 units.

-The base of the triangle is aproximately 2.5454 units.

To answer this problem, you have to set an equation with the information you're given. If you do it correctly, it should look like this:

7=1/2(3+2h)

-Now, you have to solve for h:

7=1.5+h

7-1.5=h

5.5=h

-Now that you have the height, you plug it in into the triangle area formula to solve for the base:

7=1/2(b)5.5

7=2.75b

7/2.75=b

b≈2.5454

-To make sure that the corresponding values for the base and height are correct, we plug the values in and this time we are going to solve for a(AREA):

A(triangle)=1/2(2.5454)(5.5)

A=1/2(13.9997)

A=6.99985 square units

-We round the result to the nearest whole number and we get our 7, which is the given value they gave us.

The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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Answer:

reflex angle

Step-by-step explanation:

the angle of 192 degrees is called a reflex angle

Answer:

bob

Step-by-step explanation:

The length of the segment AD found using the triangle proportionality theorem is the option (B)

(B) = 4 1/2

The triangle proportionality theorem states that if a line drawn parallel to a side of a triangle, intersecting the other two points at two distinct point, then it will divide the two sides intersected in the same ratio.

The arrow markings indicates that the segment DE and ACV are parallel, therefore, according to the triangle proportionality theorem, we get;

8/12 = 3/AD

AD/3 = 12/8

AD = 3 × (12/8) = 4.5

AD = 4 1/2

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Jerry's error is that he incorrectly assumes that the measure of angle ABC is equal to the sum of the measures of angles A and C. Hence Statement B is answer.

This is not true because angle ABC is an inscribed angle, which means its measure is half the measure of the intercepted arc.

In this case, the intercepted arc is AC. Since angle A measures 135 degrees and angle C measures 119 degrees, the sum of their measures is 254 degrees. However, angle ABC is not equal to 254 degrees.

To find the measure of angle ABC, we need to find the measure of arc AC. Since arcs A and C are equal in measure, we can find the measure of arc AC by subtracting angle A's measure (135 degrees) from the full circle measure (360 degrees).

Therefore, the measure of arc AC is 360 - 135 = 225 degrees. Since angle ABC is an inscribed angle, its measure is half the measure of arc AC, which is 225/2 = 112.5 degrees.

Hence Statement B is answer.

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The ray or segment that is a chord is (d) segment FC

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

The circle

By definition, a chord is a straight line that joins points of the circle without passing through the center

The ray that has the above properties is ray FC

Hence, the segments that is a chord is (d) FC

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