Find the slope and y intercept of 2y +8 = 6x + 4

Answer:

-4

Step-by-step explanation:

The correct statement is option a) The height of the terrain can measure between 2 meters and 10 meters.

Let the base of the triangular piece of land be x meters. Then, the height of the triangular plot is (x+2) meters.

The area of a triangle is given by the formula: A = (1/2)bh, where b is the base and h is the height.

Substituting the given values:

A = (1/2)x(x+2)

Simplifying:

A = (1/2)(x² + 2x)

Since the area is less than 40 m², write:

(1/2)(x² + 2x) < 40

Multiplying both sides by 2:

x² + 2x < 80

Rearranging and factorizing:

x² + 2x - 80 < 0

(x+10)(x-8) < 0

The roots of the quadratic equation are -10 and 8. Since the coefficient of x² is positive, the parabola opens upwards and is negative in between the roots. Therefore, the inequality is true when -10 < x < 8.

However, x cannot be negative, so the base of the triangular terrain is between 0 and 8 meters.

Substituting the values in the expression for the height, the height is between 2 and 10 meters.

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Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

Using the formula for the margin of error, it is found that a smaller confidence interval would be obtained as follow:

D. Increase the sample size to 64.

It is given by the following formula:

\(M = z\frac{s}{\sqrt{n}}\)

In which:

For a smaller interval, we need to decrease the margin of error, which is possible increasing the sample size, hence option D is correct.

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The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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The dark areas and the union symbol on the number line stand for x < 3 or x > 8 respectively.

We must plot the points x = 3 and x = 8 and shade the necessary areas in order to graph the compound inequality x 3 or x > 8 on a number line.

In order to represent all values of x less than 3, we first plot an open circle at 3 and shade the area immediately to its left:

<---|====]--->

  3    8

Finally, to represent all values of x larger than 8, we plot another open circle at 8 and shade the area to its right:

<---|====]---|--->

  3    8   8

Finally, to show that the solution encompasses all values of x greater than or equal to 3, we combine the two coloured zones together with the union symbol "∪":

<---|====]---|--->

  3    8   8

   (x<3)  (x>8)

Solution: The dark areas and the union symbol on the number line denote x 3 or x > 8 respectively.

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Answer:

(9, 2)

Step-by-step explanation:

The segment has a length of 12, so to split it in a 3:1 ratio, you need the point to split it into a segment with a length of 9 and a segment with a length of 3.

The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.

There would be two walls with 10 x 16 dimensions so the area is :

= 2 x 10 x 16

= 320 square feet

Two walls with 20 x 10 dimensions :

= 2 x 20 x 10

= 400 square feet

The total area is :

= 400 + 320

= 720 square feet

One gallon of paint can cover 400 square feet so the number of gallons needed is:

= 720 / 400

= 1. 8 gallons

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Full question is:

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.

The probability that:

First, check if it is appropriate to use the normal approximation to the binomial distribution. The rule of thumb is that this approximation is reasonable if both np and n(1-p) are greater than 5. In this case, p = 0.83 (probability of failure), n = 70 (number of trials).

So,

np = 700.83 = 58.1,

n(1-p) = 700.17 = 11.9.

Both quantities are larger than 5, so use the normal approximation.

Convert this to a problem involving a normal distribution. The mean of this distribution is np = 58.1 and the standard deviation is √(np(1-p)) = √(700.830.17) = 6.35.

(a) within 2 years 47 or more fall:

This corresponds to a Z-score of (47.5 - 58.1) / 6.35 = -1.67. The probability that a standard normal variable is greater than -1.67 is 0.9525.

So the probability that 47 or more products fail is approximately 0.9525.

(b) within 2 years 58 or fewer fail:

This corresponds to a Z-score of (58.5 - 58.1) / 6.35 = 0.063. The probability that a standard normal variable is less than 0.063 is 0.5250.

So the probability that 58 or fewer products fail is approximately 0.5250.

(c) within 2 years 15 or more succeed:

Since the probability of success is 1-p, this is equivalent to fewer than (70 - 15 = 55) failing. This corresponds to a Z-score of (54.5 - 58.1) / 6.35 = -0.567.

The probability that a standard normal variable is greater than -0.567 is 0.7151.

So the probability that 15 or more products succeed is approximately 0.7151.

(d) within 2 years fewer than 10 succeed:

This is equivalent to more than (70 - 10 = 60) failing. This corresponds to a Z-score of (60.5 - 58.1) / 6.35 = 0.377.

The probability that a standard normal variable is less than 0.377 is 0.6478.

However, since we want more than 60 failing, the probability that the variable is greater than 0.377, which is 1 - 0.6478 = 0.3522.

So the probability that fewer than 10 products succeed is approximately 0.3522.

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer: 92 and 94

Step-by-step explanation:

x = first number

x + 2 = second number

x + x + 2 = 186

simplify

2x + 2 = 186

subtract 2 from both sides

2x = 184

divide both sides by 2

x = 92

92 + 2 = 94

The numbers are 92 and 94.

Make sure you read through the problem carefully so that you recognize that we are dealing with consecutive even integers here.

Any 2 consecutive even integers can be represented as x + x + 2.

So we can represent our integers as follows.

X ⇒ first integer

X + 2 ⇒ second integer

Since their sum is 168, our equation reads x + x + 2 = 186.

Simplifying on the left side gives us 2x + 2 = 186.

Now subtract 2 from both sides to get 2x = 184.

Now divide both sides by 2 and we find that x = 92.

If x = 92, then x + 2 will be 92 + 2 or 94.

So our two consecutive integers are 92 and 94.

Answer:

10

Step-by-step explanation:

For an odd number of values, the median is the middle value when you write the values in ascending order.

5, 7, 9, 10, 16, 17, 20

The median is 10.

The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).

The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.

We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .

Factorization by grouping:

We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.

This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)

Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).

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Answer: 12.9

Step-by-step explanation: Divide 39.99 by 31.00 you'll get 1.29, but you slide the decimal over and get 12.9

Point J represents the ordered pair (-4, 6) the correct option is B.

We have to determine

Which point represents the ordered pair (-4, 6)?

An ordered pair is often used to represent a point on a coordinate plane or the solution to an equation in two variables.

The point that represents the ordered pair are as follows;

Hence, point J represents the ordered pair (-4, 6).

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Answer:

6:25 A.M.

Step-by-step explanation:

To solve this, we need to subtract the amount of time it takes her to get to the art museum altogether. To calculate this easier, first add 60 + 45 + 15 = 120. 120 minutes = 2 hours, so it takes her 2 hours to get to the museum starting from her house. Now subtract those 2 hours from the time 8:25 and we get 6:25. So, the latest time Francesca can leave her house is 6:25 A.M.

14 of the machine that cost $150 was sold and 8 of the machine that cost $225 was sold.

To solve this problem, we would write a system of linear equations.

We can proceed to write our equations now.

\(x + y = 22...equation(i)\\150x + 225y = 3900...equation(ii)\)

From equation 1

\(x+ y = 22\\x = 22 - y...equation (iii)\)

put equation (iii) into (ii)

\(150x + 225y =3900\\x = 22-y\\150(22-y)+225y=3900\\3300-150y+225y=3900\\3300+75y=3900\\75y=3900-3300\\75y=600\\75y/75=600/75\\y=8\)

Since we know the number of y, we can simply substitute it into equation (i) and solve.

\(x + y = 22\\x + 8 = 22\\x = 22-8\\x = 14\)

From the calculations above, 14 of the machine that cost $150 was sold and 8 of the machine that cost $255 was sold.

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Answer:

0.0548

Step-by-step explanation:

Given that:

Mean (m) life expactancy of product = 14 years

Standard deviation (σ) = 2.5 years

Probability of buying a product which will last more than 18 years ;

x = 18 years

Using empirical formula:

Zscore = (x - mean) / standard deviation

Zscore = (18 - 14) / 2.5

Zscore = 4 /2.5

Zscore = 1.6

Hence ;

P(Z > 1.6)

P(Z > 1.6) = 1 - P(Z < 1.6)

P(Z < 1.6) = 0.9452

P(Z > 1.6) = 1 - 0.9452

P(Z > 1.6) = 0.0548

Hence, probability = 0.0548 OR 5.48%

Answer:

15

Step-by-step explanation:

2 1/2 = 5/2 = 15/6

Answer:

0.43ᵣ = 0.1 + 0.33ᵣ = 1/10 + 1/3 = 3/30 + 10/30 = 13/30

The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

x = 0.43333......

Multiply the equation by 10 on both sides, then we have

10x = 10 × 0.43333......

10x = 4.33333......                        ...1

Multiply the equation by 100 on both sides, then we have

100x = 100 × 0.43333......

100x = 43.33333......                     ...2

Subtract equation 1 from equation 2, then we have

100x - 10x = 43.3333.... - 4.3333.....

90x = 39

x = 39 / 90

x = 13 / 30

The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.

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Answer:

Unclear.

To find the perimeter you need all three sides of the triangle. You have only given two.

All you need to do is add up all three sides and you have your perimeter.

Formula: P=a+b+c

Answer:

Unknown unless you give the amount of cm for the last side

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Add 5 + 4 which equals 9

Answer:

i) 3/8

ii) -2

Step-by-step explanation:

i) 1/2*3/2/(1/2+3/2)

3/4/2

3/4*1/2

3/8.

ii) 1/2+3/2 / 1/3-3/2

2/-1

-2.

Hope this helps :)

The model predicts that there are approximately 0.012456 (71/5700) restaurants per capita in the year 2016

To determine the number of restaurants per capita, we need to divide the number of restaurants (R) by the population (p). Given that R = 6t + 35 and p = 200t + 4500, we can substitute these values into the equation for restaurants per capita.

Restaurants per capita = R / p

Substituting the given equations, we get:

Restaurants per capita = \((6t + 35) / (200t + 4500)\)

To find the number of restaurants per capita for the year 2016, we need to calculate the value of t for that year. Since t represents years after 2010, in 2016, t would be 6 (2016 - 2010 = 6).

Restaurants per capita (2016) = \((6 * 6 + 35) / (200 * 6 + 4500)\)

= \((36 + 35) / (1200 + 4500)\)

= 71 / 5700

This means that, on average, there is roughly one restaurant for every 80 people in the town. Please note that this prediction is based on the given growth equations and assumes a linear relationship between population and the number of restaurants.

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