true or false (and state why): if a sample from a population is large, a histogram of the values in the sample will be approximately normal, even if the population is not normal.

The height of a man with a z-score of 0 is 69 inches.

The average height of adult men = 69.0 inches, Standard deviation of adult men = 2.8 inches to find the Z-score the following formula is used:

z = (x- μ)/σ where z is the z-score, x is the value to be standardized, μ is mean and σ is the standard deviation.

To find the height of a man with a z-score of Standardized value(z) = 0

z = (x - μ)/σ

0 = (x - 69)/2.8

x = 69 + 0 (2.8)

x = 69 inches.

Therefore, the height of a man with a z-score of 0 is 69 inches.

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The effect on the surface area is best described by the statement "the surface area is multiplied by 1/4." The correct option is D.

Given that the radius of a right cone is 5 ft and the slant height is 9 ft. If the radius and slant height of the cone are both multiplied by 1/2, then the new radius of the cone will be:5 × (1/2) = 2.5 ft

New slant height of the cone will be:9 × (1/2) = 4.5 ft. The surface area of a cone can be given by the formula:

S = πrl + πr²   Where r is the radius of the base, l is the slant height of the cone, and π is a constant (3.14). The surface area of the original cone can be calculated as:

S1 = π × 5 × 9 + π × 5² = 141.37 ft².  Now, if we multiply the radius and slant height by 1/2, the new surface area of the cone will be:S2 = π × 2.5 × 4.5 + π × 2.5² = 17.67 ft².  

Therefore, the ratio of the new surface area to the original surface area will be:S2/S1 = 17.67/141.37 = 0.125Thus, the new surface area is 1/8th (0.125) of the original surface area or multiplied by 1/8th (1/2 × 1/4). So, the surface area is multiplied by 1/4.

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[tex]10 + 9 + 2 + 4 = 25[/tex] possible outcomes

[tex]25 - 4 = 21[/tex] outcomes that are not green

[tex]\dfrac{21}{25}[/tex] chance that you don’t choose green

[tex]\frac{21}{25}=\bold{84\%}[/tex]

As per the given probability, the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes is either one or two hurricanes, depending on which sequence is more likely to occur.

The probability of the DD sequence is 0.4 x 0.4 = 0.16. This means that there is a 16% chance that the home will experience damage in both the first and second hurricanes.

The probability of the DN sequence is 0.4 x 0.6 = 0.24. This means that there is a 24% chance that the home will experience damage in the first hurricane but not in the second hurricane.

The probability of the ND sequence is 0.6 x 0.4 = 0.24. This means that there is a 24% chance that the home will not experience damage in the first hurricane but will experience damage in the second hurricane.

To determine the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes, we need to consider which sequence is most likely to occur.

In this case, the DN and ND sequences have the same probability, which means that there are two possible modes: one and two hurricanes.

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Answer:

Step-by-step explanation:

Setting A=45, we see that it is not true. However, you might find the following revealing:

sin2(45+A)=(sin45cosA+cos45sinA)2=12(1+2cosAsinA)

sin2(45−A)=(sin45cosA−cos45sinA)2=12(1−2cosAsinA)

Now, stare.

The equation of the line parallel to y = (1/3)x + 4 and passing through (-6, 1) is y = (1/3)x + 3.

To find the equation of a line parallel to y = (1/3)x + 4 and pass through the point (-6, 1), we can use the fact that parallel lines have the same slope. The slope of the given line is 1/3, so the slope of the parallel line must also be 1/3.

Now we have the slope (m = 1/3) and a point on the line (-6, 1), so we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Plugging in the values, we get:

y - 1 = (1/3)(x - (-6))

Simplifying, we get:

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

Adding 1 to both sides, we get the final equation:

y = (1/3)x + 3

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Simplified form of the expression 8 ( 3 + 4 ) using the Distributive Property of Multiplication over Addition is 56

To apply the Distributive Property of Multiplication over Addition, you need to multiply the number outside the parentheses by each term inside the parentheses and then add the products together.

In this case, the number outside the parentheses is 8, and the terms inside the parentheses are 3 and 4. So, you can apply the distributive property as follows:

8 ( 3 + 4 ) = 8 × 3 + 8 × 4

Multiply the numbers

= 24 + 32

Add the numbers

= 56

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The pieces are reassembled into a triangulation of the original polygon.

In a proof by strong induction, the inductive hypothesis is a statement that assumes the desired property is true for all cases up to some fixed size, and then uses that assumption to prove that the property is also true for the next case.

For the proof that every simple polygon with at least three sides can be triangulated, the inductive hypothesis would be something like,

"Assume that every simple polygon with up to k sides can be triangulated for some fixed k >= 3."

In other words, we are assuming that the property is true for all polygons with up to k sides, where k is some fixed number greater than or equal to 3.

The proof then proceeds by showing that if the property is true for all polygons with up to k sides, then it must also be true for polygons with k+1 sides. This usually involves breaking the (k+1)-sided polygon into smaller pieces (using a diagonal), each of which has fewer sides and can therefore be triangulated by the inductive hypothesis. Finally, the pieces are reassembled into a triangulation of the original polygon.

By completing this proof, we have shown that the property is true for all simple polygons with at least three sides.

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To locate the stations and draw cirradius cles on the map of California, follow these steps:

1. Identify the city stations on the map: Find the city stations indicated on the map, such as San Francisco, Los Angeles, and San Diego.

2. Use a compass: Set your compass to the scale provided on the map.

For example, if the scale says 1 inch = 100 km, adjust your compass accordingly.

3. Determine the distance from the epicenter: Based on the information provided, determine the distance from each city station to the epicenter. If it is not provided, refer to additional resources or data.

4. Draw the circles: Place the compass point on each city station and draw a circle with a corresponding to the distance determined in

step 3. Ensure the radius is in scale with the map.

5. Identify the epicenter: The point where all the circles intersect is the approximate location of the epicenter.

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The value of the trigonometric function for the given ratio are Sin X= 12/20. Cos L = 16/34. Tan X = 12/16. Tan Z = 16/12. Tan L = 30/16. Cos M = 16/34.

The fundamental six functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulae, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

Using the relationship of a right triangle and different trigonometric identities we have the values of the following as:

Sin X= opposite side to X / Hypotenuse = 12/20.

Cos L = adjacent side to L / Hypotenuse = 16/34.

Tan X = Opposite side to X / adjacent side to X = 12/16.

Tan Z = Opposite side to Z / adjacent side to Z = 16/12.

Tan L = 30/16.

Cos M = 16/34.

Hence, the value of the trigonometric function for the given ratio are Sin X= 12/20. Cos L = 16/34. Tan X = 12/16. Tan Z = 16/12. Tan L = 30/16. Cos M = 16/34.

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Answer:

Mark ate 3.3 times the square inches of pizza than Joannie ate.

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr (where r is the radius). If the circumference of a small pizza is 12π inches, then its radius is:

[tex]\implies \sf Radius_{small\;pizza}=\dfrac{circumference}{2\pi}=\dfrac{12\pi}{2\pi}=6\;inches[/tex]

The formula for the area of a circle is A = πr² (where r is the radius).

Therefore, the area of a small pizza is:

[tex]\implies \sf Area_{small\;pizza}=\pi \cdot 6^2=36\pi \; in^2[/tex]

If the small pizzas are cut into 6 congruent pieces, the area of one slice of small pizza is:

[tex]\begin{aligned}\implies \sf Area_{small\;slice}&=\sf \dfrac{Area_{small\;pizza}}{6}\\\\&=\dfrac{36 \pi}{6}\\\\&=6 \pi \; \sf in^2\end{aligned}[/tex]

Therefore, the area of one slice of small pizza is 6π square inches.

[tex]\hrulefill[/tex]

The diameter of a circle is twice its radius.

If the diameter of a large pizza is 16 inches then its radius is:

[tex]\implies \sf Radius_{large\;pizza}=\dfrac{diameter}{2}=\dfrac{16}{2}=8\;inches[/tex]

The formula for the area of a circle is A = πr² (where r is the radius).

Therefore, the area of a large pizza is:

[tex]\implies \sf Area_{large\;pizza}=\pi \cdot 8^2=64 \pi \; in^2[/tex]

If the large pizzas are cut into 8 congruent pieces, the area of one slice of large pizza is:

[tex]\begin{aligned}\implies \sf Area_{large\;slice}&=\sf \dfrac{Area_{large\;pizza}}{8}\\\\&=\dfrac{64 \pi}{8}\\\\&=8 \pi \; \sf in^2\end{aligned}[/tex]

Therefore, the area of one slice of large pizza is 8π square inches.

[tex]\hrulefill[/tex]

If Joannie eats 2 slices of small pizza, the square inches of pizza she ate is:

[tex]\implies \sf Joannie=2 \times 6 \pi = 12 \pi\;in^2[/tex]

If Mark eats 5 slices of large pizza, the square inches of pizza he ate is:

[tex]\implies \sf Mark =5 \times 8 \pi = 40\pi\;in^2[/tex]

To calculate how many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate, divide the area Mark ate by the area Joannie ate:

[tex]\implies \sf \dfrac{40 \pi}{12 \pi} = \dfrac{10}{3}=3.3\;(nearest\;tenth)[/tex]

Therefore, Mark ate 3.3 times the square inches of pizza than Joannie ate.

The probability that at least 5 have eliminated jobs during the last year is  0.002965.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

n = 9

p = probability of businesses have eliminated jobs = 0.13

X = Number of  businesses have eliminated jobs ~

Binomial( n= 9 , p = 0.13)

[tex]P(X \geq 5)[/tex]

[tex]P(X \geq 5) = 1-P( X < 5)[/tex]

[tex]P(X \geq 5) = 1-P( X \leq 4)[/tex]

Use following Excel command:

=1-BINOM.DIST(x, n, p, cumulative)

=1-BINOM.DIST(4,9,0.13,TRUE)

=0.0029649

=0.002965

Thus

[tex]\mathbf{{P(X \geq 5) =0.002965}}[/tex].

Therefore, probability that at least 5 have eliminated jobs during the last year is  0.002965.

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Complete question';

Job Elimination in the past year, 13% of businesses have eliminated jobs. If 9 businesses are selected at random, find the probability that at least 5 have eliminated jobs during the last year. Round the answer to at least four decimal places P(at least 5 have eliminated jobs during the last year) X

Answer:

See below.

Step-by-step explanation:

The volume of the box is given by the expression.

V(x) = x^3 - 2x^2 - 15x

To find the possible dimensions of the box, we need to solve for the values of x that make the volume positive. A box with negative volume is not physically meaningful.

Setting V(x) > 0, we get.

x^3 - 2x^2 - 15x > 0

Factorizing the left-hand side, we get.

x(x^2 - 2x - 15) > 0

Now, we can find the values of x that make each factor positive.

For x > 0, both factors are positive.

For x^2 - 2x - 15 > 0, we can factor it as (x - 5)(x + 3) > 0. This inequality is true when x < -3 or x > 5.

Therefore, the possible dimensions of the box are.

x > 0 and x < -3, or

x > 0 and x > 5.

However, we need to remember that the dimensions of a physical box must be positive. Therefore, the only valid solution is,

x > 0 and x > 5.

So the possible dimensions of the box are.

Length, width, and height > 5 units.

Answer:

Factor the polynomial.

x

(

x

−

5

)

(

x

+

3

Step-by-step explanation:

Therefore , the solution of the given problem of probability comes out to be there are 54,540,000 different security number combinations.

A procedure's criteria-based systems' main objective is to ascertain the likelihood that an assertion is accurate or that a particular event will take place. Chance can be represented by any number range between 0 and 1, where 0 is commonly used to indicate the possibility of something may be and 1 is usually employed to indicate a degree of confidence. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

The alphabet consists of 26 characters, and 5 of them are vowels.

(A, E, I, O, U).

Consequently, there are 21 vowels available for the second letter.

Any one of the 26 letters can be used as the first word.

Therefore, there are 21 options for the second character and 26 options for the first letter.

Consequently, there are 9 options for the first number.

There are 10 options for each of the last three numbers since they can be any of the digits from 0 to 9.

Consequently, there are a total of the following protection codes:

=> 26 x 21 x 9 x 10 x 10 x 10 = 54,540,000

Thus, there are 54,540,000 different security number combinations.

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Answer:

7cm to square centimeters is  2.6458 centimeters

Step-by-step explanation:

352.74 empty calories did miya consume on this 1-day menu.

Hence option d. 352.74 empty calories is correct.

According to the my plate analysis report, how many empty calories did Miya consume on this 1-day menu.

Empty calories refer to those calories that are devoid of any nutrient and provide only energy.

Miya's 1-day menu needs to be analyzed to determine the empty calories count.

The options provided are:

a. 793.34 empty calories

b. 693.74 empty calories

c. 593.54 empty calories

d. 352.74 empty calories.

Let us understand the concept of empty calories in detail.

Empty calories refer to the calories provided by foods that contain little to no nutrients, like vitamins and minerals. Common sources of empty calories are sugary snacks and alcohol.

Though these foods provide energy, they lack the essential vitamins, minerals, and fiber that the body requires for optimal health.

Therefore, empty calories should be limited in the diet.

To determine the empty calories consumed by Miya, we need to know the nutrient content of her 1-day menu.

Once the nutrient content is known, we can subtract the total calories from empty calories to determine the number of calories that are not empty.

Let us assume that Miya's total calorie intake for the day is 1500 calories. Out of this, the my plate analysis report says that empty calories should not exceed 362 calories.

Therefore, the non-empty calories will be: 1500 - 362 = 1138 calories

From this, we can determine the correct option.

Let us substitute the values given in the options :

a. 793.34 empty calories: 1500 - 793.34 = 706.66

non-empty calories, which is less than 1138.

Therefore, this option is incorrect.

b. 693.74 empty calories: 1500 - 693.74 = 806.26 non-empty calories, which is less than 1138.

Therefore, this option is incorrect.

c. 593.54 empty calories: 1500 - 593.54 = 906.46 non-empty calories, which is less than 1138.

Therefore, this option is incorrect.

d. 352.74 empty calories: 1500 - 352.74 = 1147.26 non-empty calories, which is greater than 1138.

Therefore, this option is the correct answer.

So, the number of empty calories consumed by Miya on this 1-day menu is 352.74 empty calories.

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Isabella's net worth is $2,725.

We know that the net worth is nothing but a measure of an individual's financial standing at a given point in time.

Here, to calculate the net worth, we need to add up all of the assets and subtract all of her liabilities:

We can see that,

Assets

Car worth: $16,700

Savings account: $4,950

So, the total assets worth:

$16,700 + $4,950 = $21,650

Now liabilities:

Credit card balance: $925

And the rent for the remainder of the lease:

$1,500 x 12 = $18,000 for year

So, the total liabilities would be:

$925 + $18,000 = $18,925

Hence her net worth would be:

21,650 - 18,925 = 2,725 dollars

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The number line :0-------------4-------------10 represents the solution to the equation.

What Is an integer?

An integer is a whole number that can be positive, negative, or zero. In other words, integers are numbers that can be written without fractions or decimals.

Examples of integers are: -3, -2, -1, 0, 1, 2, 3, and so on.

The equation 4p = 16 represents the number of baseball cards owned by Phillip, where p is the number of baseball cards owned by him.

To solve for p, we can divide both sides of the equation by 4:

4p/4 = 16/4

p = 4

Therefore, Phillip owns 4 baseball cards.

Now we need to represent this solution on a number line. We can draw a number line with 0 on the left and 10 on the right, marking every integer in between. Then we can place a dot at the point corresponding to the number 4, which represents the number of baseball cards owned by Phillip.

Therefore the number line :

0-------------4-------------10

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The person can get 3 fives, 2 sixes, and 1 two in 336 ways.

To find the number of ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die, we can use the formula for combinations with repetition:

[tex]C(n + k - 1, k) = C(6 + 3 - 1, 3) * C(3 + 2 - 1, 2) * C(1 + 1 - 1, 1)[/tex]

where n is the number of possible outcomes (in this case, 6), k is the number of choices to make (in this case, 3 for fives, 2 for sixes, and 1 for twos), and C(n + k - 1, k) represents the number of combinations with repetition.

Using this formula, we can calculate:

[tex]C(8, 3) * C(4, 2) * C(1, 1) = 56 * 6 * 1 = 336[/tex]

Therefore, there are 336 ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die.

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The critical value of z for each hypothesis  test is 2.326

In this question, we are asked to use Excel to find the critical value of z for each hypothesis test. We are given a 2 percent level of significance for a two-tailed test. To find the critical value, we can use the NORM.S.INV function in Excel. The syntax for this function is =NORM.S.INV(probability).

We can enter the probability as 1 - (alpha / 2) for a two-tailed test, where alpha is the level of significance. We can then round the result to three decimal places.

To find the critical value for a 2 percent level of significance, two-tailed test, we can follow these steps:

Step 1: Calculate the value of alpha

Alpha = 2% = 0.02

Step 2: Calculate

1 - (alpha / 2)1 - (alpha / 2)

= 1 - (0.02 / 2)

= 0.99

Step 3: Use the NORM.S.INV function in Excel=NORM.S.INV(0.99)

This gives us a critical value of z = 2.326.

Therefore, the critical value of z for the hypothesis test with a 2 percent level of significance and a two-tailed test is 2.326.

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The required number of multiplications using a single composite transformation matrix for k transformations of n points is n × k.

In computer graphics, composite transformation matrices are used to transform points and shapes. These matrices are created by combining multiple transformations into a single matrix, allowing for efficient processing of large amounts of data. The number of multiplications required to perform a composite transformation depends on the number of points being transformed and the number of transformations being applied.

If there are n points and k transformations, then the required number of multiplications is n × k.

This is because each point needs to be multiplied by the composite transformation matrix k times.

Therefore, the total number of multiplications is n × k.

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Answer:

16.5 units square

Step-by-step explanation:

The area of a triangle is 1/2bh

To find the base and heights

We use the formula above

Using the formula for my x.-axis I got 11

From 14 - 3

And for the y-axis, I got 3

From 8-5

Then using the formula 1/2bh

The area of the triangle is 1/2 ×11×3

=16.5

The option that describes the probability distribution is option (A) The mean is greater than the median, and the majority of the data points are to the left of the mean.

To find the mean of the probability distribution, we can use the formula:

mean = Σ(xi × pi)

where xi is the value of the random variable and pi is the corresponding probability.

Using this formula, we get:

mean = (1 × 0.75) + (2 × 0.1) + (3 × 0.1) + (4 × 0.05) + (5 × 0)

= 0.75 + 0.2 + 0.15 + 0.2

= 1.3

To find the median, we need to arrange the values in increasing order of x and then find the middle value.

Arranging the values in increasing order of x, we get:

x = 1, 2, 3, 4, 5

p(x) = 0.75, 0.1, 0.1, 0.05, 0

The median is the middle value, which is 3 in this case.

Therefore, the mean is 1.3 and the median is 3.

Since the mean is greater than the median, we can eliminate options C and D.

To determine whether the majority of the data points are to the left or right of the mean, we can examine the shape of the distribution.

Since the probability of x=1 is much higher than the other values, the distribution is skewed to the left. This means that the majority of the data points are to the left of the mean.

Therefore, the correct option is (A) The mean is greater than the median, and the majority of the data points are to the left of the mean.

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The given question is incomplete, the complete question is:

Which of the following describes the probability distribution below?

A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.

B.) The mean is greater than the median, and the majority of the data points are to the right of the mean.

C.) The median is greater than the mean, and the majority of the data points are to the left of the mean.

D.) The median is greater than the mean, and the majority of the data points are to the right of the mean.

If 250 is divided in the ratio 3:7, then 75 is the smaller part. To find the smaller part of 250 divided in the ratio 3:7, you need to first find the total number of parts that the ratio represents.

The total number of parts in the ratio of 3:7 is 3+7=10.

Next, you need to find the value of one part.

To do this, divide the total amount by the total number of parts:

250 ÷ 10 = 25

This means that one part of the ratio is equal to 25.

To find the smaller part, you need to multiply the value of one part (25) by the ratio of 3/10 (which represents the smaller part of the total).

So the smaller part is:

3/10 x 250 = 75

Therefore, the smaller part of 250 divided in the ratio of 3:7 is 75.

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Correct question:

If 250 is divided in the ratio 3:7, what is the smaller part?

Answer: c

Step-by-step explanation:

The number of solutions on the graph is zero.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

to determine the number of solutions:

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

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Answer:

[tex]\huge\boxed{\sf 160 \ km}[/tex]

Step-by-step explanation:

Given that,

50 liters = 400 km

Using unitary method.

50/50 liter = 400/50 km

1 liter = 8 km

1 × 20 liter = 8 × 20 km

[tex]\rule[225]{225}{2}[/tex]

The area beyond the z-score in the tail for a z-score of .63 is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63.

To understand this concept, it is important to first have a basic understanding of the z-score and the normal distribution. A z-score is the number of standard deviations away from the mean of a normal distribution. It is also referred to as a standard score. It is a measure of how far a sample is from the mean. For a given sample, the higher the z-score, the farther away it is from the mean.

When looking at the normal distribution, the area of the tail is the area beyond the z-score. This means that the area of the tail is the area of the distribution that is beyond the z-score of the given sample. In other words, it is the area of the distribution that is farther away from the mean than the z-score. For example, for a z-score of .63, the area of the tail is the area of the distribution that is farther away from the mean that .63 standard deviations.

When finding the area beyond the z-score, it is important to understand that it is divided into two parts, the area in the left tail and the area in the right tail. The area in the left tail is the area beyond the z-score in the direction of the negative standard deviations. This means that it is the area of the distribution that is farther away from the mean than the negative z-score. The area in the right tail is the area beyond the z-score in the direction of the positive standard deviations. This means that it is the area of the distribution that is farther away from the mean than the positive z-score.

For the given z-score of .63, the area beyond the z-score in the tail is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63. This area is divided into the areas in the left tail of -.2643 and the area in the right tail of 0.2357.

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The height of the bat signal is about 214.12 feet.

To find the height of the bat signal from Batman's position, we can use trigonometry.

The angle of elevation is the angle between the line of sight and the horizontal plane.

Using sine, we can set up the following equation:

sin(42) = height / 320

Solving for the height, we get:

height = 320 * sin(42)

Using a calculator, we can calculate the height to be approximately 214.12 feet.

Therefore, the height of the bat signal is about 214.12 feet.

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The value of k such that the solution set of the system is empty is any value of k that is not equal to 4.

A mathematical statement that expresses the equivalence of two numbers or expressions is known as an equation. It has two sides, the left-hand side (LHS) and the right-hand side (RHS), which are equal and are divided by the equal symbol (=). Variables, constants, and mathematical operations like addition, subtraction, multiplication, and division can all be found in an equation.

To find the value of k such that the solution set of the system of equations X + 2y = 5 and 2x + ky = 3 is the empty set (i.e., the intersection of their solution sets is the empty set), we can use the determinant of the coefficient matrix.

The coefficient matrix for the system is:

| 1 2 |

| 2 k |

The determinant of this matrix is:

[tex]det(| 1 2 |[/tex]

| 2 k |) = (1)(k) - (2)(2) = k - 4

For the solution set of the system to be empty, the determinant must be non-zero, since a zero determinant would indicate that the coefficient matrix is singular and therefore the system has no unique solution.

So, we need to solve the equation k - 4 ≠ 0 for k:

k - 4 ≠ 0

k ≠ 4

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Answer:

1.6.1) Inversely proportional

1.6.2) 0.6h

1.6.3) 120km

Step-by-step explanation:

1.6.1)

Inversely proportional relationships are in the form of [tex]y=k/x[/tex]

[tex]y=time=t[/tex]

[tex]x=speed=v[/tex]

If we the relationship is inversely proportional, [tex]k[/tex] must be constant for all values.

[tex]yx=k[/tex]

So we just have to check the value of [tex]yx[/tex] in all cases.

[tex]20*3=60\\50*1.2=60\\80*0.75=60[/tex]

Hence relation is inversely proportional.

1.6.2)

[tex]k=60, x=100, y=k/x\\[/tex]

∴[tex]y=60/100[/tex] ⇒[tex]y=0.6[/tex]

1.6.3)

Distance formula:

[tex]v=s/t\\v*t=s\\s=(20*3) + (50*1.2)\\s=60 + 60\\s=120[/tex]