Write an equation of the line in slope-intercept form. Pls help me

Answer:

50mb

Step-by-step explanation:

So start with what you have 300/150 = 2 so each song took up 2mb of space, so 25 songs would take up 25x2= 50mb

The number of megabytes taken up by 25 songs is 50 megabytes.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

150 songs = 300 megabytes

1 song = 300 /150 megabytes

1 song = 2 megabytes ______(1)

Now,

Multiply 25 on both sides of (1).

25 songs = 25 x 2 megabytes

25 songs = 50 megabytes

Thus,

25 songs will take 50 megabytes.

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The value of the inequality expression 2x ≤ 5 is (oo, 2.5]

How to evaluate the inequality expression?

The inequality expression is given as

2x ≤ 5

The above inequality expression is an inequality with only one variable

So, it means that we can solve it by dividing both sides of the inequality by 2

Solving further, we have

Divide both sides of the inequality by 2

2x/2 ≤ 5/2

Evaluate the quotient

x ≤ 5/2

Evaluate the other quotient

x ≤ 2.5

Express as interval notation

(oo, 2.5]

Hence, the solution is (oo, 2.5]

See attachment for the graph

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Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

\(w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\\)

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

--------------------

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

--------------------

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

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

--------------------

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

Answer: 57769.8 in²

Let A be the area of the shaded region

We have a relation that can help us calculate its area

A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle

A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²

Answer:

818.4

Step-by-step explanation:

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

Answer:

the last one

Step-by-step explanation:

__________________

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:

13.8 minutes

Step-by-step explanation:

5000/6= 833/60

Answer: $16137.07

Step-by-step explanation:

A = p(1+r/n)^nt

A= 4600(1+0.16/4)^4x8

A= 16137.07

The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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Answer: The answer is (x-5)^2

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

99.9453% of matter in the ore is neither diamond or copper

Step-by-step explanation:

First add  0.0297 and 0.025

0.0297+0.025=0.0547

Now subtract 0.0547 from 100

100-0.0547=99.9453

99.9453% of matter in the ore is neither diamond or copper

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The probability that there will be less than 4 defects in batch = 0.58

We need to find the probability that there will be less than 4 defects in batch.

Let us assume that x represents the number of defects in a batch and P(x) represents the probability of x number of  defects in a batch.

The probability that there will be less than 4 defects in batch.

i.e., P(x < 4) = P(x = 2) + P(x = 3)

Substitute values P(x = 2) = 0.35 and P(x = 3) = 0.23 in above equation we get,

P(x < 4) = 0.35 + 0.23

P(x < 4) = 0.58

Therefore, the required probability is 0.58

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Find the complete question below.

Answer:

b.8

Step-by-step explanation:

2/3 = x/12

8/12 = x/12

x = 8

Answer:

8

Step-by-step explanation:

65.29/8.23≈7.933

7.933 rounds to 8

The required coordinate of B' is B' = (4, -5), across the y-axis after reflection. Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them.

here,
Given that a point B (-4, -5) is reflected across the y-axis, the Coordinate of image B' is to be determined.

Since the coordinate is reflected across the y-axis,
The equation of trasformation is given as,
(x , y) ⇒ (-x , y)

So, the image of B,

B' = (-(-4), -5)

B' = (4, -5)

Thus, the required coordinate of B' is B' = (4, -5), across the y-axis after reflection. Option A is correct.

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Answer:

\(d=\dfrac{t^2}{a}\)

Step-by-step explanation:

The time  in seconds, required for an object accelerating at a constant rate of a meters/second to travel a distance of d meters is given by this  equation.

t = va

We need to find the expression for d in terms of t and a.

As velocity = distance/time

\(t=\dfrac{d}{t}a\\\\t^2=da\\\\d=\dfrac{t^2}{a}\)

So, the distance d is \(\dfrac{t^2}{a}\).

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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9514 1404 393

Answer:

  a5 = 48

Step-by-step explanation:

To find the 5th term, put 5 where n is in the formula and do the arithmetic.

  \(a_5=3(-2)^{5-1}=3(-2)^4=3(16)\\\\\boxed{a_5=48}\)

Answer:

the answer is

a5=48

Step-by-step explanation:

:)))

Answer:

k=3.5, and y=3.5x is the equation of the line

Step-by-step explanation:

y and x are proportional means that y = kx for some constant k.

Thus, when y=7 and x=2, we have that 7 = k * 2, so that k = 7/2 = 3.5,

and the equation of the line is y = 3.5x

The probability that either event will occur to the nearest hundredth would be = 0.9

To calculate the probability of the given events, the sample space should be generated and followed by the probability of each sample space generated.

That is;

P(A) = 14/18 = 0.78

P(B) = 10/18 = 0.56

P(A and B) = 0.78×0.56 = 0.4368

Therefore ;

P(A or B)= 0.78+0.56-0.4368

= 1.34- 0.4368

= 0.9

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9514 1404 393

Answer:

  4/5 acre

Step-by-step explanation:

We assume your allocations are ...

  goats: 3/5 acre

  pigs: 1/5 acre

  llamas: 2/5 acre

2 acres is 10/5 acres, so the remaining area is ...

  10/5 -3/5 -1/5 -2/5 = (10 -3 -1 -2)/5 = 4/5

4/5 acre is allocated to horses.

Answer:

(AUB)UC=2,3,4,5,6,7,8,9

put all these numbers inside curly bracket

Step-by-step explanation: