write an equation parallel to y=-5/2x+9 that passes through the point (-4,-1) brainly

Answer:

  a. P = 190t -373,930 . . . . . t=actual year number

  b. P = 6640

Step-by-step explanation:

Given the two points (1991, 4360) and (1999, 5880) on a linear relation between years and moose population, you want a formula for the population (P) and an estimate of the population in 2003.

We can use the point-slope form of the equation for a line to write the formula for moose population. To do that, we need to know the slope of the line.

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1) . . . . . . . . line through points (x1, y1) and (x2, y2)

Using the given point values, we have ...

  m = (5880 -4360)/(1999 -1991) = 1520/8 = 190

The point-slope equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Using the first ordered pair, we can write the equation as ...

  y -4360 = 190(x -1991)

  y = 190x -373,930 . . . . . . . where x is the actual year number

Using P and t for the variables, the formula is ...

  P = 190t -373,930

Using t=2003, the above formula evaluates to ...

  P = 190(2003) -373,930 = 380,570 -373,930

  P = 6,640

The linear model predicts the 2003 population to be 6640 moose.

__

Additional comment

The formula above uses actual year number. The year value can be translated any way you might want. For example, using t = years after 1991, the formula would be ...

  P = 190(t +1991) -373,930

  P = 190t +4360

Then t=12 for year 2003.

Check the picture below.

Answer:

N = 34

Step-by-step explanation:

METHOD I

(hit and trial)

The given two ratios have to be equal.

This means, 24 : N must break down to 12 : 17 after dividing it by some common factor.

The common factor here is 2.

Since,

12 × 2 = 24

17 × 2 = 34

\( \boxed{\mathsf{ \underline{N \: must \: be \: 34}}}\)

(after dividing the first ratio by 2(common factor) we get the second ratio. Meaning that they become equivalent as required by the question).

METHOD II

(mathematical approach)

Ratios can be written in form of fractions as:

\( \boxed{ \mathsf{ \frac{24}{N} = \frac{12}{17} }}\)

Cross multiplying:

\( \implies \mathsf{24 \times 17 = 12 \times N }\)

taking 12 to the denominator:

\( \implies \mathsf{ \frac{24 \times 17 }{12} = N }\)

24 and 12 gets canceled and 2 takes up their spot

(why?

=> 24 ÷ 12 = 2)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{ N = 34 } \)

\( \implies \mathsf{ N = 34} \)

Answer:

$207.20

I hope this can help in any way!

Answer:

G. 245.04cm²

Step-by-step explanation:

The shortest way to solve this problem would be:

total surface area = 2 * π * r² + (2 * π * r) * h

or

total surface area = 2 * π * r * (r + h).

Diameter = 6

Radius = 3

Height = 10

The radius is half the diameter

TSA = Total surface area

TSA = 2 π 3(3+10)

TSA = (2)(3.141593)(3)(3+10)

TSA = (6.283185)(3)(3+10)

TSA = 18.849556(3+10)

TSA = (18.849556)(13)

TSA = 245.044227

TSA = 245.04

Or you could do the longer way, which would be:

Step 1: Find the surface area of the curved part of the cylinder

Surface Area (Curved) = 2 x π x Radius x Height

Step 2: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius²

Step 3: Add the surface are of the curved part to the surface area of the ends

Surface Area (Total) = Surface Area (Curved) + Surface Area (Ends)

For the cylinder in the picture:

A cylinder has a height of 10 and a diameter of 6

Hence, Radius = d/2 = 6/2 = 3 cm

Surface Area (Curved) = 2 x pi x 3 x 10

Surface Area (Curved) = 188.495559

Surface Area (Ends) = 2 x pi x 3²

Surface Area (Ends) = 2 x pi x 25

Surface Area (Ends) = 56.548668

Surface Area (Total) = 245.044227

245.04 is the result of rounding 245.044227 to the nearest hundredth

Answer:

Q1 - 3.7

Q2 - 5.6

Q3- 300.8

Q4 - 1860.9

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

a. ³√50 = 3.68

b.  ³√180 = 5.64

c.  6.7³ = 300.76

d.  12.3³ = 1860.867

Answer:

Suppose Galileo should walk x meters on 15 degree inclined plane, and then he will get the 150 meter altitude and he could perform his experiments with the balls

The relation R on the set (1, 2, 3, 4) can be represented by an arrow diagram and a matrix. The arrow diagram visually depicts the connections between the elements.

To represent the relation R on the set (1, 2, 3, 4) using an arrow diagram, we draw a directed arrow from each element in the set to the element it is related to. For example, we draw an arrow from 1 to 3 and 4, an arrow from 2 to 1, an arrow from 3 to 2 and 4, and an arrow from 4 to 2. The resulting arrow diagram shows the connections between the elements in the relation.

The matrix representation of a relation uses a table to show the presence or absence of connections between elements. For the relation R on the set (1, 2, 3, 4), we create a 4x4 matrix where the rows and columns correspond to the elements of the set. We fill in the matrix with 1s to indicate that there is a connection between the respective elements and 0s otherwise. In this case, the matrix would be:

| 0 0 1 1 |

| 1 0 0 0 |

| 0 1 0 1 |

| 0 1 0 0 |

In the matrix, a 1 in the i-th row and j-th column indicates that the element i is related to the element j. For example, the entry in the first row and third column is 1, indicating that 1 is related to 3.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Number of times per week is quantitative data. Quantitative data is a numerical measurement that expresses a magnitude, amount, quantity, or degree of something, while qualitative data is non-numerical information. The number of times per week data is quantitative because it involves counting the number of times people visit the park, and this data can be analyzed mathematically.

Therefore, it involves numbers and is measurable in the form of a count, which makes it quantitative data. In the study to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose, frequency data is being collected by researchers. Frequency data consists of counts and statistics that summarize the number of times a particular event occurs in a particular dataset.

Therefore, in this study, the number of times per week is frequency data. In conclusion, the number of times per week data collected in the study is a type of quantitative data Data can be categorized into two main types: qualitative data and quantitative data. Quantitative data can be expressed in numbers, and it is measurable and objective. On the other hand, qualitative data is non-numerical information and descriptive and subjective. The study aimed to determine the age, number of times per week, and duration of resident use of a local park in San Jose. The number of times per week data collected in the study is quantitative data since it involves counting the number of times people visit the park. This data can be analyzed mathematically, and it is measurable in the form of a count. In research studies, frequency data are collected, and it consists of counts and statistics that summarize the number of times a particular event occurs in a particular dataset.

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Answer:

x is 4

Step-by-step explanation:

Step one: Add 12x to both sides-

8x-19+12x=-12x+61+12x

20x-19=61

Step 2: add 19 to both sides

20x -19+19=61+19

20x=80

Step 3: divide both sides by 20

20x/20=80/20

x=4

For the first series, we can use the Limit Comparison Test by comparing it to the series 1/n^2. Specifically, we will take the limit as n approaches infinity of the quotient of the two series:

lim_n->∞ [(n + 7)/(n^3 - 3n + 3)] / (1/n^2)

= lim_n->∞ [(n + 7)/(n^3 - 3n + 3)] * (n^2/1)

= lim_n->∞ [(n^3 + 7n^2)/(n^3 - 3n + 3)]

Since the numerator and denominator both have degree 3, we can apply L'Hopital's rule:

= lim_n->∞ [(3n^2 + 14n)/(3n^2 - 3)]

= lim_n->∞ [3 + 14/n] / [3 - 3/n^2]

= 3/3 = 1

Since the limit is positive and finite, and the series 1/n^2 is known to converge, the original series also converges.

For the second series, we can use the Limit Comparison Test by comparing it to the series 1/n^2. Specifically, we will take the limit as n approaches infinity of the quotient of the two series:

lim_n->∞ [(n^(k-1))/(n^(k+7))] / (1/n^2)

= lim_n->∞ (n^(k-1) * n^2) / (n^(k+7))

= lim_n->∞ n^(k+1) / n^(k+7)

= lim_n->∞ 1/n^6

Since the limit is positive and finite, and the series 1/n^2 is known to converge, the original series also converges.

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a random sample of size is selected from a population and used to calculate a 95% confidence interval for the mean of the population

To produce a new, narrower confidence interval with a smaller margin of error based on the same data, you can take one or more of the following actions:

Increase the sample size: Increasing the sample size will result in a more precise estimate of the population mean. As the sample size increases, the margin of error decreases, leading to a narrower confidence interval.

Decrease the desired level of confidence: The confidence level determines the range of values included in the confidence interval. By lowering the confidence level (e.g., from 95% to 90%), the margin of error decreases, resulting in a narrower confidence interval. However, it's important to note that reducing the confidence level also increases the risk of the estimate being incorrect.

Decrease the variability of the population: The margin of error is influenced by the variability or standard deviation of the population. If the population's variability can be reduced (e.g., through improved control or selection of homogeneous subgroups), the margin of error will decrease, leading to a narrower confidence interval.

It's crucial to consider that these actions have limitations and potential trade-offs. Increasing the sample size may require additional resources, time, and effort. Lowering the confidence level reduces the level of certainty in the estimate. Reducing population variability may not always be feasible or controllable.

In conclusion, to produce a narrower confidence interval with a smaller margin of error, you can increase the sample size, decrease the desired level of confidence, or decrease the variability of the population. However, these actions should be carefully considered based on the specific context and constraints of the study.

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Riley's mistake in step 2 of her homework was canceling out the x term in both the numerator and denominator of the second fraction. This cancellation is incorrect because the terms x and x-3 are not the same and cannot be simplified or canceled out.

To illustrate the correct simplification, let's evaluate the given expression:

\($$\frac{x}{x^2-5x+6} \cdot \frac{1}{\frac{x}{x-3}}$$\)

First, we simplify the denominator in the second fraction by multiplying by the reciprocal:

\($$\frac{x}{x^2-5x+6} \cdot \frac{x-3}{x}$$\)

Next, we notice that the x terms in the numerator and denominator of the second fraction can be canceled out:

\($$\frac{1}{\frac{1}{x-3}}$$\)

Further simplification can be done by multiplying the fraction in the denominator by its reciprocal:

\($$1 \cdot \frac{x-3}{1} = x-3$$\)

Hence, the correct simplification of the expression is x-3. Riley's mistake was canceling out the x terms in the second fraction, which led to an incorrect simplification.

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Answer:

56 +136 add the rest

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

Answer:

A, B and E

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use Pythagorean theorem to find the length of the square.

Length of the square = a

a² +a² = diagonal²

2a² = 12²

2a² = 144

a² = 144 ÷ 2

a² = 72

\(a =\sqrt{72}\\\\ = \sqrt{2*2*2*3*3}\\\\ = 2*3\sqrt{2}\\\\a = 6\sqrt{2}\\\\\\\\Perimeter= 4a\\\\ = 4*6\sqrt{2}\\\\= 24\sqrt{2} cm\)

Answer:

600

Step-by-step explanation:

We have to find the number of calories that 6 pounds is.

1 pound = 3500 calories

6 pounds = 6 * 3500 = 21000 calories

In 5 weeks we have 35 days. Let us divide 21000 by 35 to find how many calories that is per day:

21000 / 35 = 600

The number of calories must therefore be decreased by 600 every day.

The expression equivalent to \((x + 3)/(x^2 - 2x - 3)\)divided by \((x^2 + 2x - 3)/(x + 1)\) is option (d) x + 3/(x + 1).

To simplify the given expression, we need to divide the numerator of the first fraction by the denominator of the second fraction and vice versa.

The expression \((x + 3)/(x^2 - 2x - 3)\) divided by \((x^2 + 2x - 3)/(x + 1)\) can be rewritten as\((x + 3)/(x^2 - 2x - 3)\)multiplied by\((x + 1)/(x^2 + 2x - 3).\)

Now, let's simplify the individual fractions:

The numerator (x + 3) and denominator \((x^2 + 2x - 3)\))in the first fraction cannot be further simplified.

The numerator (x + 1) and denominator\((x^2 + 2x - 3)\) in the second fraction can also not be simplified.

When we multiply the fractions, the resulting expression is (x + 3)(x + \(1)/(x^2 - 2x - 3)(x^2 + 2x - 3).\)

By multiplying the numerator and denominator, we get \((x^2 + 4x + 3)/(x^4 - 4x^2 + 9).\)

However, this expression is not equivalent to any of the given options. It seems that none of the provided options match the simplified expression.

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Answer: 76 degrees

Step-by-step explanation:

Because the measure of an inscribed angle is half the measure of the central angle (where both angles intercept the same arc), the measure of angle U is 38(2)=76 degrees.

Answer:

50

Step-by-step explanation:

3745 divided by 75 = 49.93

Round to 50

Hope this helped :)

Step-by-step explanation:

I have done this one thing and i m confused weather i shall regret or let it be it or what ,... can anyone advice ?

The quotient from the division of 55 by 5 is 11

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

In this problem, when 55 is divided by 5, the answer is 11.

The quotient after the division is 11

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Answer:

the answer is 225

Step-by-step explanation:

\( \frac{300 \times 25}{100} = 75\)

this is the amount of discount

so remove it from the original price

300 - 75 = 225

which is the price after the 25% discount

hope this helps