5 aplicaciones de notación científica en la vida cotidiana

Answer:

c. /pi/2

Step-by-step explanation:

\(y = \sin(4x) \\ y = 2\pi \omega\)

Option C ,  pi/2 is the period of the sine function y = sin (4x)

The amplitude of a periodic variable is a measure of its change in a single period.

The amplitude of a non-periodic signal is its magnitude compared with a reference value.

sin4x=sin(4x+4h)

sin(θ+2π)=sinθ , we have  4h=2π ,  h=π/2

or it can be also understood as

The amplitude and period of y = a sin (bx + c ) are a and 2π/b

Here, a = 1 and b = 4.

This sine wave oscillates between the crests at y = 1 and the lowest points at y= -1 periodically, with period π/2 for one full wave.

period of sin(4x) is (1/4)x(period of sin(x))

= (1/4)x(2pi)

= (pi/2) .

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Using a system of equations, it is found that her normal week is of €285.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The first equation, considering the first sentence, is given by:

x + 8y = 375.

The second equation, considering the second sentence, is given by:

x + 4y = 330.

Then the system is:

Multiplying the second equation by -2, the system is:

Adding the equations, we have that her normal week is given by:

x = 660 - 375 = €285.

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The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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The volume of the cardboard box is approximately 13197.402 cubic inches.

The volume of a cardboard box is 216 dm³, we can convert it to the English system of measurements.

1 dm (cubic decimeter) is equivalent to 1 liter.

To convert dm³ to cubic inches, we can use the following conversion factors:

1 dm³ = 61.0237 cubic inches

Using this conversion factor, we can calculate the volume of the box in cubic inches:

The cube carton volume is 216 dm3 and the cube edge value is 6 dm.

The volume of the cube is calculated by dividing the edge values. In other words, volume = edge 3.

To find the edge (side) value, you can solve for the volume formula as follows:

edge 3 = volume.

edge = ∛ volume,

Where ∛ is the cube root.

Applying this formula to the given problem gives edge = ∛(216 dm³).

Edge = 6dm. Therefore, the side (edge) value of the cube is 6dm.

Volume (cubic inches) = 216 dm³ * 61.0237 cubic inches/dm³

= 13197.402 cubic inches

Question :- If the volume of a cubic cardboard box is 216 dm³

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Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

D) The terms in Pattern B are one half the corresponding terms in Pattern A.

Step-by-step explanation:

Pattern A | Pattern B

0 divided by 1/2 = 0

6 divided by 1/2 = 3

12 divided by 1/2 = 6

18 divided by 1/2 = 9

24 divided by 1/2 = 12

Answer/Step-by-step explanation:

2. a. 5y - 3 = -18

Add 3 to both sides

5y - 3 + 3 = -18 + 3

5y = -15

Divide both sides by 5

5y/5 = -15/5

y = -3

b. -3x - 9 = 0

Add 9 to both sides

-3x - 9 + 9 = 0 + 9

-3x = 9

Divide both sides by -3

-3x/-3 = 9/-3

x = -3

c. 4 + 3(z - 8) = -23

Apply the distributive property to open the bracket

4 + 3z - 24 = -23

Add like terms

3z - 20 = -23

Add 20 to both sides

3z - 20 + 20 = - 23 + 20

3z = -3

Divide both sides by 3

3z/3 = -3/3

z = -1

d. 1 - 2(y - 4) = 5

1 - 2y + 8 = 5

-2y + 9 = 5

-2y + 9 - 9 = 5 - 9

-2y = -4

-2y/-2 = -4/-2

y = 2

3. First, find the sum of 3pq + 5p²q² + p³ and p³ - pq

(3pq + 5p²q² + p³) + (p³ - pq)

3pq + 5p²q² + p³ + p³ - pq

Add like terms

= 3pq - pq + 5p²q² + p³ + p³

= 2pq + 5p²q² + 2p³

Next, subtract 2pq + 5p²q² + 2p³ from 3p³ - 2p²q² + 4pq

(3p³ - 2p²q² + 4pq) - (2pq + 5p²q² + 2p³)

Apply distributive property to open the bracket

3p³ - 2p²q² + 4pq - 2pq - 5p²q² - 2p³

Add like terms

3p³ - 2p³ - 2p²q² - 5p²q² + 4pq - 2pq

= p³ - 7p²q² + 2pq

4. Perimeter of the rectangle = sum of all its sides

Perimeter = 2(L + B)

L = (5x - y)

B = 2(x + y)

Perimeter = 2[(5x - y) + 2(x + y)]

Perimeter = 2[5x - y + 2x + 2y]

Add like terms

Perimeter = 2(7x + y)

Substitute x = 1 and y = 2 into the equation

Perimeter = 2(7(1) + 2)

Perimeter = 2(7 + 2)

Perimeter = 2(9)

Perimeter = 18 units

5. First let's find the quotient to justify if the value we get is greater than or less than 2.25

7⅙ ÷ 3⅛

Convert to improper fraction

43/6 ÷ 25/8

Change the operation sign to multiplication and turn the fraction by the left upside down.

43/6 × 8/25

= (43 × 8)/(6 × 25)

= (43 × 4)/(3 × 25)

= 172/75

≈ 2.29

Therefore, the quotient of 7⅙ ÷ 3⅛ is greater than 2.25

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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The derivatives of sin(x) follow a simple pattern:

f(x) = sin(x)

f '(x) = cos(x)

f ''(x) = - sin(x)

f '''(x) = - cos(x)

f ''''(x) = sin(x)

and so on. 96 is a multiple of 4, so

f ⁽⁹⁶⁾(x) = sin(x)

Answer:

x = 14

Step-by-step explanation:

Figure A to Figure B = 1:3.5 = 1/3.5

Therefore:

Side length of figure A to side length of figure B = 1/3.5

Thus:

4/x = 1/3.5

Cross multiply

x*1 = 3.5*4

x = 14

Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Write down the percent divided by 100 like this:

25% = 25/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As 25 is an integer, we don't have numbers after the decimal point. So, we just go to step 3

(or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(25,100) = 25. So,

(25÷25)/(100÷25) = 1/4 when reduced to the simplest

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

The measure of trapezoid's opposite angle is 135°. The solution has been obtained by using properties of trapezoid.

What is a trapezoid?

Four sides make up the quadrilateral of a trapezoid, two of which are parallel while the other two are not. It is also referred to as a trapezium. A closed, four-sided form or figure known as a trapezoid has its own perimeter and can enclose an area.

We are given that one base angle is equal to 45°

We know that in a trapezoid

Base angle + Opposite angle = 180°

Using this, we get

⇒45° + Opposite angle = 180°

⇒Opposite angle = 180° - 45°

⇒Opposite angle = 135°

Hence, the measure of trapezoid's opposite angle is 135°.

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Random error is the variation in a statistic from sample to sample due to chance. It is the difference between a sample statistic and the true population parameter that it is estimating.

Good sampling techniques help to reduce the amount of random error in a sample by reducing the variability of the sample results.

Random error is the variability of a statistic from sample to sample due to chance. It occurs when a statistic from a sample does not accurately reflect the true population parameter it is attempting to estimate. Random error can be minimized through the use of good sampling techniques, such as randomization and stratification, as these help to reduce the variability of results from sample to sample. Good sampling techniques also help to ensure that the sample is representative of the population, thus reducing the amount of random error.

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The time that the ball traveled is given as follows:

1.5 seconds.

The quadratic function determining the ball's height after t seconds is given as follows:

H(t) = -16t² + 24t.

The roots of the quadratic function in this problem are given as follows:

-16t² + 24t = 0.

16t² - 24t = 0

8t(2t - 3) = 0.

Hence we apply the factor theorem as follows:

Hence the time is given as follows:

1.5 - 0 = 1.5 seconds.

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Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

Answer:

Unless there is more information to this question, 3 degrees per hour, for 10 hours, after the 10th hour it will have risen 3*10 degrees, so 30 degrees

Answer:

30

Step-by-step explanation:

You can do 3×10 directly, or you can solve it like this to avoid error

Hour Degree

1 +3

2 +6

3 +9

4 +12

5 +15

6 +18

7 +21

8 +24

9 +27

10 +30

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The minimum allowable value of slope for tree A is 0.052 and rte slope of the zip line is 0.043 in tree B.

The horizontal distance from starting tree is 135 feet. Therefore, the slope of the zipline will be:

= 7/135 = 0.052

The horizontal distance from starting tree for tree B is 160 feet. Therefore, the slope of the zipline will be:

= 7/160

= 0.043

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer: 40

Step-by-step explanation:

150 / 30 = 5

8 x 5 = 40

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

Answer:

= 0.25 g/cm3

Step-by-step explanation:

this is called density the grams per volume.

density = mass

               volume

             =   120g

                480cm3

  = 0.25 g/cm3

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Answer:

60

Step-by-step explanation:

3/2t-16=4/3t-6

       +16      +16

3/2t=4/3t+10

      -4/3t

(t/6)6/1= 10(6/1)

t=60

Answer:

\(t=60\)

Step-by-step explanation:

To get both variables on one side, do the opposite of their current form and move them over (I'm not sure how else to explain this, so I'm just going to show you).

\(\frac{3}{2} t-16=\frac{4}{3} t-6\)

You see that the \(\frac{4}{3} t\) is positive, so you subtract it. The same goes for the -16 (do the opposite). You would add the -16 to the other side.

You need to do the opposite of them because only one number exists. If you move it, you need to cancel it out so that there is always only one of that number. (so when you add the -16 to the other side, the one on the left cancels out, but the same value (16) is still present on the right side and is added).

\(\frac{3}{2} t-\frac{4}{3} t=-6+16\)

Now you have this after moving like terms to their coinciding sides (you could do this any way, btw. It doesn't matter what order you add everything, so long as you get t on one side and by itself).

\(\frac{9}{6} t-\frac{8}{6}t =-6+16\\\frac{1}{6} t=10\\(\frac{6}{1} )(\frac{1}{6} t)=(\frac{6}{1} )(10)\\t=60\)

** Everything you do on one side, you need to do on the other side. This is a very important rule (and it goes hand in hand with the idea that there can only be one of each value, unless the exact same value appeared on both sides in the given equation).

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

5.9(86)

Step-by-step explanation:

The slope of the line is -1/2.

The equation of a line is given by:

y = mx + c

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

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the given line is in the point-slope form:

y - 3 = -1/2 (x - 2)

We can rewrite this equation in slope-intercept form,

y = mx + b,

Solving for y:

y - 3 = -1/2(x - 2)

y - 3 = (-1/2)x + 1

y = (-1/2)x + 4

Comparing this equation to the slope-intercept form,

We can see that the slope (m) of the line is -1/2.

Therefore,

Slope = -1/2

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