6. The news program for KOPE, the local television station, claims to have 40% of the market. A random sample of 500 viewers conducted by an independent testing agency found 192 who claim to watch the

Answer:

The slope is 10/1 so +10

Step-by-step explanation:

Hope this helps !!!

Answer:

10.

Step-by-step explanation:

Picking out 2 convenient points, (3, 30) and (0, 0):

Slope = (30-0)/(3-0)

= 30/3

= 10.

Answer:

12?

Step-by-step explanation:

Answer:The Answer is 10!!!

Step-by-step explanation:

If you plot (1,4) and (-5,-4) on a graph, you can see that you can form a right triangle.

you would count the values on the X-axis and on the Y-axis. The values are 6 and 8 respectively.

You put the values on the second power and add them. So the equation would be 6^2 + 8^2. The answer would be 100.  Because the Pythagorean Theorem is a^2 + b^2= c^2, you would square root would be 10. The distance between the two points is 10.

Answer: 24/m

Step-by-step explanation:

There are m members in the science club.

24 bumper stickers were purchased to be split amongst these m members.

The number of stickers that each member will get is:

= Number of stickers / Number of members

Number of stickers = 24

Number of members = m

The expression is therefore:

= 24/m

The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

The given coordinates on the graph are;

(-3, 0), (0, 3), (2, 4), and (5, 5)

The coordinates of the starting point of the graph = (-3, 0)

Shape of the graph = Extends from point (-3, 0), upwards and to the right

Therefore;

As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.

However, given that the graph is for a square root function, the correct option is option C;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

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To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).

To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.

Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).

To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).

Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.

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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.

To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:

1. τ(mn) = τ(m)τ(n)

2. σ(mn) = σ(m)σ(n)

Let's start with property 1:

1. τ(mn) = τ(m)τ(n)

If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.

Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).

Now let's move on to property 2:

2. σ(mn) = σ(m)σ(n)

Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.

Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.

Hence, we can conclude that σ(mn) = σ(m)σ(n).

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Answer:

180

Step-by-step explanation:

Answer:

149°

Step-by-step explanation:

let the remaining side of the triangle a,

now,

63°+86°+a=180°(sum of angles of a triangle)

149°+a=180°

a=180°-149°

a=51°

again,

x+a=180°(being linear pair)

x+51°=180°

x=180°-51°

•°•x=149°

The sum of the areas of the enclosed regions is 2.004 , and -3.811 the rate at which h changes with respect to x when x = 1.8 .

Given : f(x) = 1 + x + e^x^2 - 2x and g(x) = x^4 - 6.5x^2 + 6x + 2

The graphs of y = f(x) and y = g(x) intersect in the first quadrant at the points (0, 2), (2, 4), and (A, B) = (1.032832, 2.401108).

(a)  the sum of the areas of the enclosed regions is given by

Area =

\(\int\limits^A_0[[g(x) - f (x)] dx +\int\limits^2_A [f(x) - g(x)] dx\)

= 0.997427 +1.006919

= 2.004

(b)  the sum of the volumes of the enclosed regions is given by

Volume = [[ƒ(x) − g(x)]² dx = 1.283

(c) the rate at which h changes with respect to x when x = 1.8

h(x) = f(x) = g(x)

h'(x) = f'(x) - g'(x)

h'(1.8) = f'(1.8) g'(1.8)

          =-3.812 (or -3.811)

Hence , the sum of the areas of the enclosed regions is 2.004 , and -3.811 the rate at which h changes with respect to x when x = 1.8 .

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Answer: 7 times 4

Step-by-step explanation:

Answer:

B. 20%

Step-by-step explanation:

Percentage Error = (Actual Value - Expected Value) / Expected Value * 100

Actual Value = 30

Expected Value = 25

Percentage Error = (30 - 25) / 25 * 100

Percentage Error = (5) / 25 * 100

Percentage Error = 0.2 * 100

Percentage Error = 20

Answer:

distance = independant; time = dependant

Step-by-step explanation:

You are able to change the distance you travel, making it the independant. As you go farther, the time increases, so it is dependant on the distance traveled, therefore it is the dependant.

The firm 4's efficient scale occurs at 4

In this question, we have been given a table of long-run total cost and the quantity.

We need to find the quantity at which the firm 4's efficient scale occurs.

We know that the efficient scale occurs at the quantity of output where average total cost is minimum.

For the firm 4 the average total cost would be,

(210 + 340 + 490 + 660 + 850 + 1060 + 1290) / 7

= 4900 / 7

= 700

This value is clsoe to 660.

Therefore, the firm 4's efficient scale occurs at quantity 4.

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Given question is incomplete.

To answer this question, we'll use the exponential distribution and the concept of the probability density function (pdf). Let X be the time until failure of a single device, with a mean lifetime of 20 months. The exponential distribution has the following pdf:

f(x) = (1/μ) * e^(-x/μ),

where μ is the mean lifetime (20 months in this case).

Now, let's find the probability that the first failure occurs at w months among the 5 independent devices. For this, we need to calculate the probability that none of the other 4 devices fail before w months and that the first device fails at w months.

The probability that a single device does not fail before w months is given by the complementary cumulative distribution function (ccdf) of the exponential distribution:

P(X > w) = e^(-w/μ).

Since the devices are independent, the probability that all 4 devices do not fail before w months is:

P(All 4 devices survive > w) = (e^(-w/μ))^4.

Now, the probability that the first device fails at w months is given by the pdf of the exponential distribution:

P(X = w) = (1/μ) * e^(-w/μ).

Finally, we multiply the two probabilities to find the chance that the first failure occurs at w months:

P(First failure at w) = P(All 4 devices survive > w) * P(X = w)
= (e^(-w/μ))^4 * (1/μ) * e^(-w/μ)
= (1/20) * e^(-5w/20).

Thus, the chance that the first failure will occur at w months is given by the expression (1/20) * e^(-5w/20).

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The approximate length of ab is 12.2 feet

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the other two sides' lengths.

It can be written as c2 = a2 + b2 where c is the hypotenuse's length and a and b are the other two sides' lengths. Pythagoras, a Greek mathematician, is credited with discovering the theorem, which bears his name.

The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, can be used to estimate the length of AB (the hypotenuse).

The distances along the room's 11-foot and 13-foot sides serve as the two shorter sides in this situation, while AB serves as the hypotenuse. AB is around the following length:

√(11^2 + 13^2 + 10^2) = √(146) = 12.2 feet

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The equation of the line found is:

y = 3x + 1.

Since the rate of change is always the same, that is, when x changes by 1, y always changed by the same value, this is a linear equation.

Linear equation:

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables, A and B are coefficients, and C is a constant.

The equation of a line is given by:

y = mx + b

In which:

m is the slope, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

From the table, when x =0 and y =1 , thus b = 1.

When x = and y = 1 . When x =1 and y = 4 , when x = 2 and y =7  , and so on. That is, when x changes by 1, y changes by 3, and the slope is m = 3.

The equation of the line is:

    y = 3x + 1.

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Step-by-step explanation:

A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.

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Answer:

The youngest daughter is 10

The area of the triangle with vertices (0,0),(4,2),(2,6) is 16 square units.The determinant method is one of the most straightforward methods to find the area of a triangle.

Let's utilize calculus to find the area of the triangle with the given vertices (0,0),(4,2),(2,6).

We can use the determinant of a matrix method to solve the problem. The matrix is of the form $A=\begin{bmatrix}x_1&x_2&x_3\\y_1&y_2&y_3\\1&1&1\end{bmatrix}$,

where $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ are the vertices of the triangle.

So, for this specific triangle, the matrix is $A=\begin{bmatrix}0&4&2\\0&2&6\\1&1&1\end{bmatrix}$, which means $A=\left|\begin{matrix}0&4&2\\0&2&6\\1&1&1\end

{matrix}\right|=\left| \begin{matrix} 4&2\\2&6 \end{matrix} \right|-\left| \begin{matrix}

0&2\\0&6 \end{matrix} \right|+\left| \begin{matrix} 0&4\\0&2 \end{matrix} \

right|=16-0+0=16$.

Therefore, the area of the triangle with vertices (0,0),(4,2),(2,6) is 16 square units.The determinant method is one of the most straightforward methods to find the area of a triangle.

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The probability of picking each kind of card is 1/4 or 0.25.

There are four kinds of cards in a standard deck of 52 cards: hearts, diamonds, clubs, and spades. Each kind has 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

To find the probability of picking a card of each kind, we can use the following formula:

Probability = Number of favorable outcomes / Total number of outcomes

Probability of picking a heart:

There are 13 hearts in the deck, so the number of favorable outcomes is 13. The total number of outcomes is 52, since there are 52 cards in the deck. Therefore, the probability of picking a heart is:

Probability of picking a heart = 13/52

Probability of picking a heart = 1/4

Probability of picking a diamond:

There are 13 diamonds in the deck, so the number of favorable outcomes is 13. The total number of outcomes is still 52, since we haven't replaced the card that we picked earlier. Therefore, the probability of picking a diamond is:

Probability of picking a diamond = 13/52

Probability of picking a diamond = 1/4

Probability of picking a club:

There are 13 clubs in the deck, so the number of favorable outcomes is 13. The total number of outcomes is still 52. Therefore, the probability of picking a club is:

Probability of picking a club = 13/52

Probability of picking a club = 1/4

Probability of picking a spade:

There are 13 spades in the deck, so the number of favorable outcomes is 13. The total number of outcomes is still 52. Therefore, the probability of picking a spade is:

Probability of picking a spade = 13/52

Probability of picking a spade = 1/4

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.

α = 0.05

μ = 2

If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.

This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.

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Answer:

+4√5

Step-by-step explanation:

Note that this is a right triangle.  Therefore, the lengths of the three sides are related through the Pythagorean Theorem:  a^2 + b^2 = c^2, where c is the length of the hypotenuse.  

Thus, x^2 + 19^2 = 21^2, or, after solving this for x^2,

x^2 = 441 - 361 = 80

x is therefore +√80, or +4√5.

Answer:

a) y = 11x

b) y = $660

Step-by-step explanation:

a) For 10 people is $110, so simply divide.

110/10 = $11 per person.

y = 11x

b) So using that, substitute 60 for x.

y = 11(60)

y = $660

Answer:

D - Triangle 1, triangle 3, and triangle 4