Given the table of values, determine the the constant of proportionality, then write the equation of the proportion.

The slope of the linear equation that passes through the two given points is 1/7.

A general linear equation can be written in the slope-intercept form as:

y = a*x + b

Where the coefficients are:

a: the slope.

b: the y-intercept.

If a line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is equal to:

a = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that the line passes through (-10, -9) and (-3, -8), then the slope of this linear equation will be:

a = (-8 + 9)/(-3 + 10) = 1/7

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The ladder would reach a distance of 6 feet up the wall.

This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:

/hyp/^2 = /opp/^2 + /adj/^2

In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.

So that, let the height of the ladder on the wall be represented by t. Then;

10^2 = t^2 + 8^2

100 = t^2 + 64

t^2 = 100 -64

     = 36

t = (36)^1/2

t = 6 feet

Thus the ladder is placed 6 feet up the vertical wall.

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Answer:y=1.19x

Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.

Answer: 15

Step-by-step explanation: In ΔNOP,

m

∠

N

=

(

9

x

+

8

)

∘

m∠N=(9x+8)

∘

,

m

∠

O

=

(

4

x

+

13

)

∘

m∠O=(4x+13)

∘

, and

m

∠

P

=

(

2

x

−

6

)

∘

m∠P=(2x−6)

∘

. Find

m

∠

N

.

m∠N

The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The cost to transport an item varies between two shipping providers. The price charged by Company A is $6.50 plus $0.35 per pound. Charges from Company B are $7.25 plus $0.25 per pound.

Let 'p' be the number of pounds and 'T' be the total cost of shipping. Then the equations are given as,

T = 0.35p + 6.50

T = 0.25p + 7.25

If the total cost of shipping the packages is to be the same. Then the number of pounds is given as,

0.35p + 6.50 = 0.25p + 7.25

0.35p - 0.25p = 7.25 - 6.50

0.10p = 0.75

p = 7.50 pounds

The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.

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The number of positive two-digit integers that are multiples of 5 and 7 are 2

In mathematics, multiples are the results of multiplying an integer by a given number.

The multiples of 5 and 7 within 10 to 100 are

35 and 70

multiples of 5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

multiples of 7: 7 14 21 28 35 42 49 56 63 70 77 84 91 98

The common numbers are 2 which are 35 and 70

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The equation which correctly represents the explicit formula for the nth term of the given sequence is; a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.

As evident in the task content; the given sequence is a geometric sequence and the common ratio of the sequence can be determined as;

r = 3 / 9 = 9 / 27 = 1 / 3.

On this note, since the common ratio of the consecutive terms of the sequence is; 1/3 it follows that the required explicit formula which represents the nth term , a (n) is;

a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.

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it's infinitely many bc the equations have the same line

Answer:

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

Step-by-step explanation:

How many solutions does the following system have?

y = -2x – 4

y = 3x + 3

Solution:

Given y = -2x – 4

y = 3x + 3

Rewriting to the general form

-2x – y – 4 = 0

3x – y + 3 = 0

Comparing the coefficients,

(a1/a2) = -⅔

(b1/b2) = -1/-1 = 1

(a1/a2) ≠ (b1/b2)

Hence, this system of equations will have only one

Answer: 35

Step-by-step explanation:

: i took this quiz before :)

10 equally sized slices of the spinner's 250 results. 25 times were made by Diane's dial. 12 spins are for 208.33333333333334 .

12 spins are for 208.33333333333334, 5 spins are worth 500, and 8 spins are worth 312.5. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. In this case, the probability is 18.

If you spin three times and fall on red (or any other colour), the likelihood is 3/30. The likelihood that the spinner will land on an even number is 5/10. The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it.

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The mean is lower than the mode which is lower than the median.

A skewed curve is a type of statistical distribution in which the data is unevenly distributed. It is often referred to as an asymmetric distribution, meaning that the two halves of the curve look different. Skewed curves can be either positively or negatively skewed, depending on which direction the data points are shifted. Positively skewed curves tend to have a long tail to the right, while negatively skewed curves have a long tail to the left. This type of distribution is commonly seen in real-world data, such as income or wealth distributions.

A negatively skewed curve is characterized by a tail on the negative side of the graph. This means that the data points have a higher probability of being lower than the mean. As such, the mean is lower than the mode, which is lower than the median. The mean is the arithmetic average of all of the data points, the mode is the most frequent value, and the median is the midpoint of the data points.

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On solving the provided question, we can say that - the answer of the following sequence 1.9, 3x , 8x will be 13.78x

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

sequence 1.9, 3x , 8x

answer is = 13.78x

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Answer:

n0p = 120°

Step-by-step explanation:

m0n + n0p = 180°

60° + n0p = 180°

n0p = 120°

Answer:

The common difference is 4.

Step-by-step explanation:

270 mins - 10 laps

xmins -5 laps

(cross multiply)

270*5=10x

10x=1350

x= 1350/10

x=135 mins

All values that are NOT in the domain of 9 are 5 /11 at x=9, where function  h=7.

All real numbers x, with the exception of those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.

h(x)=x-2\sg(x)=(x-4)(x+2)

Suppose x = 9 and h(9) = 9-2 and g(9) = (9-4) (9+2) =5 /11

Because it is impossible to divide by zero while h is in the denominator, there will always be an issue anytime h = 7. After solving them, we discover that x cannot be either -2 or 5. So, the answer to part B would be x-5/11.or 5/11 are examples of x values that are beyond the domain.

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This probability does not support the Trump/Farage claim that 60% of all immigrants are male.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes, and how likely they are.

The probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found using the binomial probability formula, which calculates the probability of a specific number of successes (male immigrants) in a fixed number of trials (sample size) with a fixed probability of success (p = 0.60).

Using the binomial formula, the probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found by summing the probabilities of obtaining 257 males, 256 males, 255 males, etc. up to 0 males.

Using a binomial calculator, we can find that the probability of obtaining 257 or fewer males in a sample of 583 immigrants is about 0.04.

This probability is quite low, which suggests that it is unlikely to obtain 257 or fewer males in a sample of 583 immigrants if the proportion of male immigrants is actually 60%.

Therefore, this probability does not support the Trump/Farage claim that 60% of all immigrants are male.

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The largest prime number that divides the quantity is the largest prime number less than 5.5e+22.

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.

We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.

0! = 1

1! = 1

2! = 2

3! = 6

...

50! = 30414093201713378043612608166064768844377641568960512000000000000

Now we can write the expression as

(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)

We can notice that the number is very large, and it's impractical to factorize it using traditional methods.

We can use the property that if n is not divisible by a prime number p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.

The next step would be to check if the remaining number is divisible by any prime numbers.

Since it's impractical to check for all the prime numbers, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)

Which is approximately 5.5e+22.

Therefore, the largest prime number that divides the quantity is the largest prime number less than 5.5e+22.

It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.

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The speed of Mark riding the bike is 16 miles/hour. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.

Speed tells us how quickly or slowly an object is moving. While distance, as the name suggests, refers to the amount of space between two points, time refers to the period of time separating two events.

Given,

Distance travelled= 6 miles

time taken = 30 minute =0.5 hour

[tex]speed = distance/time\\speed=8/0.5\\speed= 16 miles/hour[/tex]

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The distance between two points A and B is 5 units.

The total cost of Jess Norton is $995.85 and the total cost of Olive Baker is $678 .

What is total cost ?

The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost = (Average Fixed Cost x Average Variable Cost) x Units Produced is the formula.

In economics, total cost is the total of all expenses a company incurs to produce a particular level of output.

The average cost, or the typical sum of money required to create a unit, can be determined using the cost function. The average cost function is A(x)=C(x)x, where x > 0 and C is the constant. Calculating the average cost per unit requires dividing the total cost by the quantity of units produced.

 2 one hundred dollar bills = 2 x $100

                                                   = $200                

 Total deposits = 2 one hundred dollar bills + Checks

                                = $200 + $474.85 + $321

                                = $995.85          

 Checks amount = $100 x 4

                                   = $400                  

 12 for $7.5

       = 12 x $7.5

       = $90                  

 Six 20-dollar bills = 6 x $20

                                     = $120                  

 Five 10-dollar bills = 5 x $10

                                      = $50                  

 Eighteen 1-dollar bills = 18 x $1

                                            = $18                

 Total deposits = $400 + $90 + $120 + $50 + $18

                                = $678

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Answer:

m∠A=126°

Step-by-step explanation:

Supplementary means that they add up to 180°.

Therefore we can do 180-54 to get 126° for the m∠A.

Hope this helped! :)

Answer:

[tex]5 \sqrt{3} [/tex]

Step-by-step explanation:

Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.

Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

5√3

Decimal Form:

8.66025403…

The conditions for inference are: The customers who are surveyed are chosen independently at random, so we can assume that the survey results are independent.

The amount of grams or mole equivalents of solute present in a solution that contains one liter is what is referred to as normalcy according to the accepted definition. The amount of moles of reactive units in a compound is what we mean when we say it is equal.

The conditions for inference are met.

However, to conclude that more than 50% of customers who dine at his restaurant would rate the food as excellent, we need to conduct a statistical test such as a one-sample proportion test or a confidence interval. The manager would need to compare the proportion of the customers who rated the food as excellent from the survey with the proportion of customers who would rate the food as excellent. This would allow to see if the data provides convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent.

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The 8.4 inches length of g and the 79° and 25° measures of the angles ∠G and ∠E, using the law of sines, indicates that the length of the side  EG = f is about 8,3 inches.

The law of sines states that the ratio of the sine of an interior angle of a triangle to the length of the opposite side to the angle is the same for the three sides and angles in a triangle.

Mathematically, the law of sines can be presented as follows;

[tex]\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]

Where;

a, b, and c are the length of each of the sides of the triangle, and ∠A, ∠B, and ∠C are the measure of each of the interior angles of the triangle.

The details of the triangle ΔEFG, specifying the side g as the side opposite the angle ∠G, and the side f as the side opposite the ∠F we get;

The length of EF = g = 8.4 inches

Length of EG = f

The angle sum property of a triangle indicates that we get;

∠E + ∠F + ∠G = 180°

∠F = 180° - (∠E  + ∠G)

∠F = 180° - (25°  + 79°) = 76°

According to the law of sines, we get;

8.4/(sin(79°) = f/(sin(76°))

f = (sin(76°)) × 8.4/(sin(79°) ≈ 8.3

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The corresponding element in the range when 7 is an element  in the domain is f(7)=33

Step-by-step explanation:

Given that the 7 is an element in the domain of f(x)

The function f is defined by f(x)=6x-18/2

To find the corresponding element in the range:

That is put x=7 in the given function f(x)

Therefore f(x) becomes

f(7) = 6(7)-18/2

      =42-18/2

      =42-9

      =33

Therefore corresponding element in the range when 7 is an element  in the domain is f(7)=33

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Answer:

8u - 20

Step-by-step explanation: