what is the equation of the line that is perpendicular to y =- 2/3 x + 4 and passes through (-2, -2)

Answer:

a

  \( P = 0\)  OR  \( P = 135\)

b

\(P > 0\) and \( P < 135 \)

OR

\(P > 0\) and \( P < 135 \)

c

Generally the carrying capacity is can be defined as the highest amount of population and environment can support for an unlimited duration or time period

d

\( P = 67.5 \)

Step-by-step explanation:

From the question we are told that

The population model is \(\frac{dP}{dt} = 0.2P(1 - \frac{P}{135} )\)

Generally at equilibrium

\(\frac{dP}{dt} = 0 \)

So

\(0.2P = 0\)

=> \( P = 0\)

Or

\((1 - \frac{P}{135} ) = 0 \)

=> \( P = 135\)

Thus at equilibrium P = 0 or P = 135

Generally when the population is increasing we have that

\(\frac{dP}{dt} > 0 \)

So

\(0.2P > 0\)

=> \(P > 0\)

and

\((1 - \frac{P}{135} ) > 0 \)

\( P < 135 \)

Now when the first value of P i.e \(P< 0\) for \(\frac{dP}{dt} > 0 \)

\( P_2 > 135 \)

So when population increasing the values of P are

\(P > 0\) and \( P < 135 \)

OR

\(P > 0\) and \( P < 135 \)

So to obtain initial values of P where the population converge to the carrying capacity as \(t \to [\infty]\)

The rate equation can be represented as

\(\frac{dP}{dt} = \frac{1}{5}P (1 - \frac{P}{135} )\)

So we will differentiate the equation again we have that

\(\frac{d^2 P}{dt^2} = \frac{(1 - \frac{P}{135} )}{5} - \frac{P}{675}\)

Now as  \(t \to [\infty]\)

\(\frac{d^2 P}{dt^2} \to 0 \)

So

   \( \frac{(1 - \frac{P}{135} )}{5}  - \frac{P}{675} = 0\)      

=>    \( \frac{(1 - \frac{P}{135} )}{5}   =  \frac{P}{675}\)

=> \( P = 67.5 \)

The scientific notation of 827,129,000,000,000,000,000,000,000 can be expressed below

Count the number backward until you each the last number . The number of steps which is 26 becomes the exponential value.

The polynomial  n² + 6n - 1 can be factored as,

(n + 3 + √10)(n - 3 + √10)(3n - 2).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A product of two polynomials (n² + 6n - 1)(3n - 2).

Now, The quadratic expression n² + 6n - 1 can be factored as,

n² + 6n - 1.

[- 6 ± √(36 + 4)]/2.

= [- 6 ± √40]/2.

= [- 6 ± 2√10]/2.

= - 3 ± √10.

Therefore, (n² + 6n - 1)(3n - 2)

= (n + 3 + √10)(n - 3 + √10)(3n - 2).

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Answer:

The angle ACX equals 51 degrees. The angle ACB equals 129 degrees.

Step-by-step explanation:

21 + 30 + y = 180

y = 129

129 + x =180

x = 51

Answer:

1

Step-by-step explanation:

Hello, please consider the following.

First, we develop and move everything to the left side, then we solve the equation, using the discriminant.

Finally, we get the expression of the two solutions and we can conclude.

\((x+1)(x+2)=(x+3)\\\\<=> x^2+3x+2-x-3=0\\\\<=>x^2+2x-1=0\\\\\Delta=b^2-4ac=4+4=8\\\\x_1=\dfrac{-2-\sqrt{8}}{2}=\dfrac{-2-2\sqrt{2}}{2}=-1-\sqrt{2}\\\\x_2=\dfrac{-2+\sqrt{8}}{2}=-1+\sqrt{2}\)

So, m=-1 and n = 2

m+n = -1 + 2 = 1

Thank you

The value of m + n is 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

(x + 1)(x + 2) = x + 3

x² + 2x + x + 2 = x + 3

x² + 3x + 2 - x - 3 = 0

x² + 2x - 1 = 0

This is in the form of ax² + bx + c = 0

a = 1, b = 2, and c = -1

Now,

Using the determinant.

x = -b ± √(b² - 4ac) / 2a

x = -2 ± √(4 + 4) / 2

x = (-2 ± 2√2) / 2

x = (-1 ± √2)

x = -1 + √2

x = -1 - √2

Now,

The solutions can be written in the form of (m + √n) and (m - √n).

This means,

m + √n = -1 + √2

m - √n = -1 - √2

m = -1 and n = 2

Now,

m + n

= -1 + 2

= 1

Thus,

m + n is 1.

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Answer:

-3,-9

Hope this helps

Answer:

(-3,-9)

Step-by-step explanation:

X goes first then Y, since they are both negative they go backwards on the graph

The z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

The sample scores are given as:

2, 3, 5, 5, 6.

Calculate the mean and the standard deviation using a statistical calculator.

From the statistical calculator, we have:

\(\bar x = 4.2\) --- mean

\(\sigma_x = 1.64\) --- standard deviation

The z-score is then calculated using

\(z= \frac{x - \bar x}{\sigma}\)

Where:

x = 2, 3, 5, 5, 6.

So, we have:

\(z_1= \frac{2 - 4.2}{1.64} = -1.34\)

\(z_2= \frac{3 - 4.2}{1.64} = -0.73\)

\(z_3= \frac{5 - 4.2}{1.64} = 0.48\)

\(z_4= \frac{5 - 4.2}{1.64} = 0.48\)

\(z_5= \frac{6 - 4.2}{1.64} = 1.10\)

Hence, the z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

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Answer: 24

Yes (x-2) is a factor. There is a remainder.

Step-by-step explanation:

2³-8•2²+14•2-4

8-8•4+14•2-4

0•4+14•2-4

0+14•2-4

14•2-4

28-4

24

Hope this helps if so plz mark me brainly

3/5 are black. To rewrite the fraction with a denominator of 100. Find how many thieves the denominator 5 goes into 100:

100/5 = 20

Multiply both the numerator and denominator by 20:

3/5 = 60/100

Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

The mean absolute deviation of Robin's scores is 5.2.

The mean absolute deviation (MAD) is the mean (average) distance between each data value and the mean of the data set.

To determine the MAD, we subtract the mean of the data set from each data value and sum the absolute values obtained.

Then we divide the sum of the absolute values by the number of the data values to determine the mean absolute deviation.

Robin's Scores   Distance from the Mean

99                              8

108                             1

102                             5

107                             0

119                             12

Sum =                      26

Number of Data Values = 5

The mean = 107 since 107 - 107 = 0

Mean Absolute Deviation (MAD) = 26/5 = 5.2

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Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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Answer:it’s 25:99

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.033

Answer:

-(2×3)×(5+3-8-(3×3))

-(6)×(5+3-8-9)

-6×-9

54

Answer:

The correct answer is 54

Option D

Step-by-step explanation:

All you really need to do is replace the n for 3 when you do so you will get

-2(3)(5+3-8-3(3)) = 54

The () represents multiplication.

Anywas hope this helped!

Answer:

8n - 7 = 5

Step-by-step explanation:

number  -  n

product of 8 and a number    -    8n

Seven less than the product of 8 and a number  -    8n - 7.

Seven less than the product of 8 and a number is equal to 5.

8n - 7 = 5

Answer:

8n-7=5

you can do this

i cand do explaination

For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

   Events                                         Nearest thousand

As given in the question,

Rules to round of nearest thousand are:

Check the near by hundred digit :

Given is the actual ticket rates of the different events tickets sales ,round off to the nearest thousand is given by:

 Events                                         Nearest thousand

Therefore, For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

   Events                                         Nearest thousand

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Answer:

Large number from two numbers = 1,440

Step-by-step explanation:

Given:

Ratio of two numbers = 9 : 2

Smaller number from two numbers = 320

Find:

Large number from two numbers

Computation:

Large number from two numbers / Smaller number from two numbers = Ratio of two numbers

Large number from two numbers / 320 = 9 / 2

Large number from two numbers = 2,880 / 2

Large number from two numbers = 1,440

The actual perimeter of triangle will be 1.3m

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. The perimeter is the whole side covered by the all sides.

The sum of all angle of triangle = 180

The blueprint for a new house includes a triangular-shaped room in the attic.

If the blueprint was made using a scale factor of 12

centimeter = 1 meter

The perimeter will be 9cm

12/9 = 1.3m

So the actual perimeter will be 1.3m.

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Answer:

3 cm

Step-by-step explanation:

One quater of 12 is 3, and you find this out by diving 12 by 4, giving the answer of 3

12 ÷ 4 = 3

Answer:

\(\frac{3}{5} +\frac{1}{5} =\frac{4}{5}\)

Step-by-step explanation:

The denominator doesn't really matter here. You just have to add the numerators and then put the denominator back on again. The numerators are 3 and 1 and if you add 3 and 1 you will get 4. Now you have to put the denominator back on to the bottom of the numerator. So, if you but 5 on the bottom of 4 it will be \(\frac{4}{5}\).

Firms must select a mix of inputs that minimizes the total cost of producing a given quantity of output in order to solve the cost minimization optimization problem.

The final dollar spent on any given input should produce the same marginal physical product at the optimal choice.

The fact that both variable costs and fixed costs are a component of the total costs is a similarity between the two. The manner in which they alter with production is the primary distinction. By definition, fixed costs are unaffected by production levels in the short term because they are "fixed."

A manufacturing facility's annual lease, for instance, is a fixed cost because it is the same regardless of how many units are produced. Variable costs, on the other hand, fluctuate with production levels. Take into account the manufacturing facility's costs for labor and materials; the more is created, the more work and material are expected to be utilized underway.

The variable cost per unit is assumed to remain constant in the above calculation. Because the total fixed costs never change, fixed costs per unit decrease with output quantity in contrast to variable costs. However, the same constant fixed cost is distributed across a larger and larger quantity of output as production increases; consequently, the fixed cost decreases per unit.

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Answer:

50 days are needed to make $2500.

Step-by-step explanation:

Number of tons per day:

One ton equals 2000 pounds, as the problem states as a hint.

The company collects 200 pounds per day.

1 ton - 2000 pounds

x tons - 200 pounds

2000x = 200

x = 200/2000

x = 0.1

0.1 tons per day.

A recycling company makes $500 per ton of aluminum scrap collected.

0.1*500 = $50 per day.

How many days are needed to make $2500?

1 day - $50

x days - $2500

50x = 2500

x = 250/5

x = 50

50 days are needed to make $2500.

The solution of the given equation  y ==2x² - 24r – 56​ :

(6 , -128)

Graph technology aids in the discovery of unknown links in data that cannot be detected or examined using traditional methods. When the broad term graph is introduced as both a topic, it frequently blurs three distinct topics: graph theory, graph analytics, and graph data management.

Graphs and charts are useful visual tools because they deliver information quickly and readily. It is hardly surprising, then, that graphs are widely utilized in print and electronic media. Data can be easier understood when displayed as a graph rather than a table since the graph can illustrate a pattern or comparison.

y =2x² - 24x – 56​

Solving for :

Parabola equation in polynomial form

ax² + bx + c  for x = -b/(2a)

a = 2

b = -24

c = -56.

on solving we get

= -(- 24)/2* 2

= 6

The value of x = 6

putting the value of x to get y:

2x² - 24x – 56​

2(6)² - 24(6) – 56​

-128

the value of y = -128.

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Answer:

7%

Step-by-step explanation:

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

x=35 hope it helps see ☜☆☞

Using relations in a right triangle, it is found that the length of AC is of 14 cm.

The relations in a right triangle are given as follows:

Researching this problem on the internet, we have that:

Hence the hypotenuse is found as follows:

sin(A) = 48/h

0.96 = 48/h

h = 48/0.96

h = 50 cm.

The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:

\(x^2 + 48^2 = 50^2\)

\(x^2 = \sqrt{50^2 - 48^2}\)

x = 14 cm.

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We want to find two values: the number of pieces sold at the original price and the number of pieces sold at the reduced price. Let's name those quantities:

x: number of pieces sold at the original price

y: number of pieces sold at the reduced price

First equation

We know that they sold 95 pieces. Then,

x + y = 95

Second equation

Each piece sold at the original price costs $14.50.

The earnings due to these pieces is given by the product of the number of them, x , and their cost:

14.50x

Each piece sold at the reduced price costs $12.50:

$14.50-$2.00 = $12.50

The earnings due to these pieces is given by the product of the number of them, y, and their cost:

12.50y

Then, the total earning is:

14.50x + 12.50y

We know that they took in $1237.50, then

14.50x + 12.50y = 1237.50

Then, the equations we are going to use are:

x + y = 95

14.50x + 12.50y = 1237.50

Using the equations we want to obtain an equation with just y unkown so we can find its value.

To do so we add each side of both equations, but first we convert the first so the result is an equation with just the y unkown:

Converting the first equation:

x + y = 95

↓ multiplying -14.50 both sides

-14.50(x + y) = -14.50 · 95

-14.50x - 14.50y = -1377.50

Then, the equations we are going to use are:

x + y = 95

14.50x + 12.50y = 1237.50

↓

-14.50x - 14.50y = -1377.50

14.50x + 12.50y = 1237.50

Now we add both sides of the two equations:

-14.50x - 14.50y = -1377.50

14.50x + 12.50y = 1237.50

__________________________

0x - 2.50y = -140

↓

- 2.50y = -140

Now we can find y, taking -2.50 to the right side of the equation

- 2.50y = -140

↓

- 2.50y/(-2.50) = -140/(-2.50)

y= -140/(-2.50)

y = 56

Then, the number of pieces sold at the reduced price is 56.

Since there were sold 95 pieces, then:

x = 95 - 56 = 39

x=39

Then, the number of pieces sold at the original price is 39.

Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)