Write the equation of the line that goes through the points: (2, -3) and (-4, -12).

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Having tested the hypothesis, we can conclude   that there is sufficient evidence to support the   claim that the true proportion of days with a tornado during peak season isgreater than 1%.

Hypothesis  -

Significance level  -  α = 0.05

Test statistic  -

z  = (p - p0)/ √(p0(1 - p0) /n)

where  -

Calculations  -

z = (0.44 - 0.01) / √(0.01 * 0.99   /50)

= 8.014

Decision rule  -

Reject H0 if z > zα = 1.645.

Conclusion -

Since z = 8.014 > 1.645, we reject H0 and conclude that there is sufficient evidence to support the claim that the true proportion of days with a tornado during peak season is greater than 1%.

p-value  -

The p-value   is the probability ofobtaining a test statistic as extreme as or more extreme than the   one that was actually observed, assuming that H0 is true.

In this case,the p-value is <0.0001, which is   very small. This means that the probability of   obtaining a result as extreme as the one that we observed bychance alone is very small.

Therefore,   we can reject H0 with ahigh degree of confidence.

Interpretation  -

We can   conclude that there is more than a 95% chance that the true proportion of days with a tornado during peak season   is greater than 1%.

Excel  -

The following Excel code can be used to calculate the test statistic and p-value  -

=NORMDIST(8.014, 0, 1, 1)

The output of this code is 0.000026, which is the p-value.

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Answer:

The set D has 5 elements - 3, 6, 9, 12, and 15, all of which are multiples of 3.

Answer: 40

Step-by-step explanation:

150 / 30 = 5

8 x 5 = 40

40 of 150 students is equivalent to 8 of 30 students.

Solved  equation x=80 and z=2, y=40

An element, feature, οr factοr that is liable tο vary οr change

If y varies directly as x and inversely as the square οf z, we can write the fοllοwing prοpοrtiοnality:

y ∝ x/z²

where ∝ denοtes prοpοrtiοnality cοnstant.

Tο find the value οf ∝, we can use the given values οf y, x, and z:

y = ∝ x/z²

28 = ∝ (63)/(3)²

∝ = 28 * (3)² / (63)

∝ = 4/3

Nοw we can use this value οf ∝ tο find y when x=80 and z=2:

y = ∝ x/z²

y = (4/3) * (80)/(2)²

y = 40

Therefοre, when x=80 and z=2, y=40.

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Answer:

Im pretty sure its B

Step-by-step explanation:

The ratio to be used to find sink is A. JL : JK

The sine of an angle is the ratio of perpendicular to its hypotenuse.

Mathematically,

Sine of an angle = Perpendicluar/Hypotenuse

Now, it is given that a △JKL.

To find sine K we need to find the hypotenuse and Perpendicular of the triangle.

Since, Sine of an angle = Perpendicluar/Hypotenuse

So, sin K = Perpendicluar/Hypotenuse

Since K is the angle given so opposite of the angle K must be the perpendicular.

So, Perpendicular of the △JKL = JL

So, Hypotenuse of △JKL = JK or KL.

Since from the given option, it can be concluded that JK is the hypotenuse of △JKL.

Therefore, sin K = JL/JK

Thus, the ratio to be used to find sink is A. JL : JK

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The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

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Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

Step-by-step explanation:

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

-9/5 is the slope

Step-by-step explanation:

5-(-4)=9

1-6=-5

use an equation to write each fraction or product as a multiple of a unit fraction

3/4

A unit fraction is a fraction of the form 1/n where n is a positive integer. So to write these fractions as multiples of a unit fraction, just pull out the numerator as the multiplier.

2/4 = 2 * (1/4)

4/6 = 4 * (1/6)

3/4 = 3 * (1/4)

Answer:

y = - 25x + 800

Step-by-step explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 650 ) and (x₂, y₂ ) = (8, 600 )

m = \(\frac{600-650}{8-6}\) = \(\frac{-50}{2}\) = - 25 , then

y = - 25x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 650 )

650 = - 25(6) + c = - 150 + c ( add 150 to both sides )

800 = c

y = - 25x + 800 ← linear equation

From the given question,

The employees in the one country is, 12900 and it is the 24.2% of the total employee.

So,

Suppose x is the total number of the employees in the company.

Then,

then,

Hence, the value of total employess is 53,306.

The distance travelled by the particle is 15

\(v(t) = \frac{t ds}{dt} = 2t - 2\)

\(ds = v(t) dt\)

\(\implies ds(t) = (2t-2)dt\)

\(\implies s = \int\limit_0^5 (2t-2) \, dt\)

\(s = \left(t^2 - 2t \right)_2^5 = 25 - 10 - 4 + 4\)

\(\therefore s = 15\)

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Answer:

14w

Step-by-step explanation:

Hope this helps

Answer:

the number 27 is a composite

Step-by-step explanation:

Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors

Answer:

The number 27 is composite.

The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

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Answer:

Ken is planting vegetables in his garden. He has 20 seeds. Determine whether 20 is prime or composite number. If it is composite, list all of the ways Ken can arrange the seeds in even rows.

Answer:

change your pfp and ill give u the answer

Step-by-step explanation:

Answer:

x = 17.5 degrees

Step-by-step explanation:

So with this, it gives you the angle measure and the terms for that angle measure for Angle EDC. Since these are equal, set them equal to each other.

2x+10 = 45

Move over the 10

2x = 35

Divide by 2

x = 17.5 degrees

That's all.

Answer:

should be complementary angles

Answer would be shifted up

Step-by-step explanation:

hence the +9 you would be going up 9 units :)

Number of People who knows the Code are 6401

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of People who kows the Code be x

Number of Peoplee who do not know the Code be y

According to the Question:

x + y = 7338 ----------(i)

2x + 5y = 17487 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 14676 ---------(iii)

Substracting Equation (iii) from Equation (ii)

3y = 2811

y = 937

This means x = 6401

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Answer:

Deepak have taken 5 days leave from the start of the work.