Why is -x < 3 equivalent to x>-3? Explain.​

Answer:

The population was 3040 people in 8 years.

Step-by-step explanation:

find unit rate;

3800/10 = 380

380 x 8 = 3040

Answer:

The formula for radioactive decay is:

N = N₀ * (1/2)^(t/T)

where:

N₀ = initial amount

N = remaining amount

t = time elapsed

T = half-life

Let's plug in the given values:

N₀ = 20 g

N = 15 g

T = 1620 years

15 = 20 * (1/2)^(t/1620)

Dividing both sides by 20:

0.75 = (1/2)^(t/1620)

Taking the logarithm base 1/2 of both sides:

log(0.75) = t/1620 * log(1/2)

Solving for t:

t = log(0.75) / log(1/2) * 1620

t ≈ 623 years

Therefore, it will take approximately 623 years for a 20 g sample of Radium to decay to 15 g.

Step-by-step explanation:

Using the normal distribution, it is found that the z-scores are:

a) z = -1.5

b) z = 1.9

c) z = 0

In normal distribution with mean 'μ' and the standard deviation 'σ', the z-score of a measure X is given by:

z = x-μ/σ

It measures how many standard deviations the measure is from the mean, either above the mean(positive z-score), or below(negative z-score).

For first blank: 1.5 standard deviations below the mean, hence z = -1.5.

For second blank: 1.9 standard deviations below the mean, hence z = 1.9.

For third blank: The mean is 0 standard deviations from itself, hence z = 0.

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

$5.16

Step-by-step explanation:

3.00 times 0.72 is 2.16. Because it's a markup that means you add. 3.00 plus 2.16 is 5.16.

Answer:

13

Step-by-step explanation:

Computers=6

Printers=7

Now,

=6+7

=13

Answer:

cos 23 = x/7.8

Step-by-step explanation:

Answer:

The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.

Step-by-step explanation:

brainliest???

Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

Vertical angles are angles opposite to each other where two lines cross.

When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.

These pair of angles are congruent which means they have the same angle measure.

Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

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The probability that a worker selected at random makes between $300 and $350 is 0.1359 Or 13.6%.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Given, Weekly wages at a certain factory are normally distributed.

Mean(\(\overline{x}\)) = 400, S.D(\(\sigma\)) = 50.

Now, Since the wages are normally distributed we know,

\(z = \frac{x - \overline{x}}{\sigma}\).

Therefore,

z = (300 - 400)/50.

z = - 2.

And

z = (350 - 400)/2.

z = - 1.

Now, from the z-table,

P(z ≤ - 2) = 0.0228 and P(z ≤ - 1) = 0.1587.

Combining the two we have P( - 2 ≤ z ≤ - 1) =  0.1587 - 0.0228.

P( - 2 ≤ z ≤ - 1) = 0.1359.

As a result, the likelihood that a randomly chosen employee will earn between $300 and $350 is 0.1359, or 13.6%.

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-√144 ÷ 3 ? -π

Replacing √144 = 12:

-12 ÷ 3 ? -π

-4 < -π

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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Answer:

Slope = 2

Step-by-step explanation:

Rise/run = 2/1 = 2. You can also use slope formula m = (y2-y1)/(x2-x1)

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

-13x^2+8x-3

Step-by-step explanation:

Answer:

-13x2 + 8x - 3

Step-by-step explanation:

Djduhdbevzhzjsvvsyshavahsysjsjsj

Answer:

it is rational

Step-by-step explanation:

it is rational because the number ends

Answer:

It is rational.

Step-by-step explanation:

Answer:

Substitute values first

Answer:

Probability is 0.831727

Step-by-step explanation:

The probability can be calculated as below

There are multiple scenarios

Scanerio 1

0 occurance & No damage = 1 - 0.2 - 0.03 - 0.001 = 0.769

Scanerio 2

1 occurance & No damage = 0.2 x ( 1 - 0.7 ) = 0.06

Scanerio 3

2 occurance & No damage = 0.03 x ( 1 - 0.7 )^2 = 0.0027

Scanerio 4

3 occurance & No damage = 0.001 x ( 1 - 0.7 )^3 = 0.000027

P(structure will not suffer any damage) = Scanerio 1 + Scanerio 2 + Scanerio 3 + Scanerio 4 = 0.769 + 0.06 + 0.0027 + 0.000027 = 0.831727

Answer:

6 cookies

Step-by-step explanation:

himself + 6 friend = 7

(17+25)/7

= 42/7

= 6

Each friende get:

6 cookies

Answer:

6 cookies each person

Step-by-step explanation:

(17+25=42)

Answer:

69

Step-by-step explanation:

xvusvsuvtuvqYSQY

Third row:

The balance stays the same as the previous row ($337.52).

We have 12 days between 9/7 and 9/18, so we can calculate the product/sum as:

NOTE: the product/sum will be used to calculate the average balance for the month.

Fifth row:

The balance stays the same as the previous row ($399.78).

We have 11 days between 9/20 and 9/30.

Then, the product/sum is:

Total:

The total product/sum is:

Average daily balance:

We can take the total product/sum and divide by the total amount of days.

Finance charge:

New balance:

The new balance is $404.41.

Answer:

True

Step-by-step explanation:

To compare the two speeds, we can calculate the speed of each in miles per hour (mph) and then compare them.

22 miles in 20 minutes = (22/20) miles per minute = 1.1 miles per minute

To convert to mph, we can multiply by 60 to get:

1.1 x 60 = 66 mph

38 miles in 30 minutes = (38/30) miles per minute = 1.27 miles per minute

To convert to mph, we can multiply by 60 to get:

1.27 x 60 = 76.2 mph

Therefore, 38 miles in 30 minutes is faster than 22 miles in 20 minutes, as 76.2 mph is greater than 66 mph.

In other words, the statement "22 miles in 20 minutes is less than 38 miles in 30 minutes" is true.

Answer:

41

Step-by-step explanation:

Answer:

70/100= 0.7= 70%

70%

Step-by-step explanation:

At least twice means it could be   2  3  4  5  6  7  or  8 heads

 there is 8 chances of having only one TAIL

there are   2^8 outcomes = 256 outcomes possible

     take away the EIGHT with one tail

                  248 out of 256 have at least 2 heads

248/256 = 31/32

( Let me know if this is incorrect and I will re-evaluate !)

Answer:

\(\frac{247}{256}\)

Pre-requisite Knowledge:

Permutations and Combinations

Elementary Probability

Step-by-step explanation:

Total number of outcomes (Cardinality of the sample space) = \(2^{8}\)  

P(at least 2 heads show up) = 1 - [ P(no Head) + P(exactly 1 Head) ]

\(= 1-\frac{C(8,0)+C(8,1)}{2^8}\\\\=1-\frac{1+8}{256}\\\\ =1-\frac{9}{256}\\\\= \frac{247}{256}\)

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

Answer:

A. 18x + 15

Step-by-step explanation:

For this problem, we will simply simplify the given expression:

5(4x + 3) - 2x

= 5*4x + 5*3 - 2x

= 20x + 15 - 2x

= 20x - 2x + 15

= 18x + 15

Cheers

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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