Actividad 1.1
Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que
la función
definida a continuación sea diferenciable en t = 2, luego construya su gráfica.
at +b, sit < 2
f(t) = {2t2 – 1, si 2 st
1​

Answer:

42

Step-by-step explanation:

7/8 = x / 48

We need to get a common denominator

Multiply the left side by 6

7/8 *6/6 = x/48

42/48 = x/48

Since the denominators are equal, the numerators must be equal

42 =x

Answer:

42

Step-by-step explanation:

7/8=42/48

Cross products: 7(48)=8x

Answer:

B. 3x+15 / 4x+10

Step-by-step explanation:

[tex]\frac{3x+}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex]  -> multiply by the reciprocal

[tex]\frac{3x}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex]  -> reduce the expression

[tex]\frac{3}{2x+5}[/tex] X [tex]\frac{x+5}{2}[/tex] -> multiply the fractions

[tex]\frac{3(x+5)}{2(2x+5)}[/tex]       -> remove parenthesis

and you get:

[tex]\frac{3x+15}{4x+10}[/tex]

-Hope this helps :)

Answer:

C.

Step-by-step explanation:

Step 1: Multiply jar weights

12(10) = 120 oz

Step 2: Convert lbs to oz

16 + 14 = 30 oz

Step 3: Add weights

150 oz

Step 4: Convert to lbs

150/16 = 75/8 = 9.375 lbs

9.375 lbs = 9 lbs 6 oz

Answer:

1.03 × 10-1

3.1 × 10-2

2.01 × 10-3

2.32 × 10-4

4.2 × 10-5

Step-by-step explanation:

Hope this helps you!

Answer:

1.03 × 10-1

3.1 × 10-2

2.01 × 10-3

2.32 × 10-4

4.2 × 10-5

Step-by-step explanation:

Answer:

2.99

Step-by-step explanation:

99.99 - 97 = 2.99

The percentage change to 2 decimal places when a price of 97 is increased to 99.99 is 3.08%

What is percentage change?

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.

percentage change formula = [tex]\frac{final value - initial value }{Initial value}[/tex]× 100

According to the given question

We have

initial value = 97

final value = 99.99

therefore,

⇒percentage change = [tex]\frac{99.99-97}{97}[/tex]× 100

⇒percentage change = [tex]\frac{2.99}{97}[/tex]×100

⇒percentage change = 0.0308×100=3.0824

⇒percentage change = 3.08%

Hence, the percentage change to 2 decimal places when a price of 97 increased to 99.99 is 3.08%.

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Answer:

Greatest number = 9867

Smallest number = 1027

Step-by-step explanation:

Greatest number:

- - - 7

In order to form the greatest number, we should simply put the greatest available digit at the thousands place, the second greatest at the hundreds place and the third greatest at the tens place (which would be 9, 8, and 6 respectively).

9867

Smallest number:

- - - 7

In order to form the greatest number, we should simply put the lowest available digit at the thousands place (excluding zero since a number can't start with a zero), put zero at the hundreds place and the third lowest at the tens place (which would be 1, 0, and 2 respectively).

1027

Answer:

y= -3.7x+100.94

Step-by-step explanation:

Generally this type of problems is solved by using a calculator or a spreadsheet. Now, getting the final equation depends on the model of calculator you are using, so I will suggest you look for the instructions on your calculator's instruction manual. I'll provide indications for using excel.

So first you need to input the table on an excel sheet. You can input them just the same way they were given to you. (See attached picture)

Once you inputed them, you can highlight them and go to the insert tab. There you can pick the scattering plot option. Once the scatterplot is graphed, you can right-click on the graph and a menu should appear. Pick the option add tendency line. Choose the line option and below, you can mark the option present equation on the graph and present the value of R. And that will be it! Excel will automatically provide you with the equation of the regression line you need.

Most scientific calculators nowaday can provide you with the equation, you just need to input the data and they will return the slope and y-intercept of the line.

There are other formulas you can use to find this regression by hand, but they are generally used in statistics courses.

Answer:

39

Step-by-step explanation:

Angle AQC, AQB and BQC are 120deg. (360/3=120). Therefore, Angle BZC, CXA and AYB are 60deg. Because, angle BZC is half of angle BQC. same for the other three angles. As, all 3 angles are 60deg, it is an equilateral triangle. So, YZ is 13 therefore as all 3 sides are equal its 13*3=39.

The solution is: 39 is the perimeter of XYZ.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

Angle AQC, AQB and BQC are 120deg.

(360/3=120).

Therefore, Angle BZC, CXA and AYB are 60deg.

Because, angle BZC is half of angle BQC.

same for the other three angles.

As, all 3 angles are 60deg, it is an equilateral triangle.

So, YZ is 13

therefore as all 3 sides are equal

its 13*3=39.

Hence, 39 is the perimeter of XYZ.

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Answer:

187 ft/s

Step-by-step explanation:

Given in the y direction:

v₀ = 0 ft/s

Δy = 75 ft

a = 32 ft/s²

Find: t

Δy = v₀ t + ½ at²

(75 ft) = (0 ft/s) t + ½ (32 ft/s²) t²

t = 2.165 s

Given in the x direction:

Δx = 480 ft

a = 0 ft/s²

t = 2.165 s

Find: v₀

Δx = v₀ t + ½ at²

(480 ft) = v₀ (2.165 s) + ½ (32 ft/s²) (2.165 s)²

v₀ = 187 ft/s

Answer:

Total number of T-shirts= 200

Cost per T-shirt (without shipping ) = $2.80

Shipping cost per t-shirt ; 5% of a T-shirt = 0.05 *2.80 = $0.14

Total cost of T-shirt (shipping included) = 2.80 +0.14 = $2.94

Markup = 150% of total cost = 1.50 * 2.94 = $4.41

To get the price at which Michelle will sell each T-shirt , add total cost  to the markup; 2.94 +4.41 = 7.35.

Therefore, selling price will be $7.35

Answer:

a.) dx3x² + 2

Use the properties of integrals

That's

integral 3x² + integral 2

= 3x^2+1/3 + 2x + c

= 3x³/3 + 2x + c

= x³ + 2x + C

where C is the constant of integration

b.) x³ + 2x

Use the properties of integrals

That's

integral x³ + integral 2x

= x^3+1/4 + 2x^1+1/2

= x⁴/4 + 2x²/2 + c

= x⁴/4 + x² + C

c.) dx6x 5 + 5

Use the properties of integrals

That's

integral 6x^5 + integral 5

= 6x^5+1/6 + 5x

= 6x^6/6 + 5x

= x^6 + 5x + C

d.) x^6 + 5x

integral x^6 + integral 5x

= x^6+1/7 + 5x^1+1/2

= x^7/7 + 5/2x² + C

Hope this helps

Answer:

On average, students in the 4th period Did more chin-ups than students in the 2nd period.

Answer:

$2,160 is what he need for both daughters for 1 year

Step-by-step explanation:

90 x 2 = 180

180 x 12 = 2,160

Dominic need to budget a total of 2160 for a year of gymnastics for both daughters.

Multiplication is one of the basic mathematical operations which includes a number added repeatedly to times of the other number. The final answer is called the product of the numbers.

Multiplication is usually denoted as '×' sign.

a × b indicates that a is added repeatedly upto b times.

Cost for the gymnastics per month per child = 90

In order to find the cost per month for both daughters, we need to multiply 90 with 2.

Cost for the gymnastics per month for 2 daughters = 2 × 90 = 180

To find the total cost for an year, we need to multiply 180 with 12.

Total cost for the year = 180 × 12 = 2160

Hence the total budget for Dominic to send both the daughter in a year is 260.

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Answer:

4/7

Step-by-step explanation:

The numbers 7 or odd are 1, 3, 5, and 7.

4 numbers out of 7.

P(7 or odd) = 4/7

x+-2*2-3x-7

x+4-3x-7

x+1.x-7

x.x-7

2x-7

Answer:

The picture on the bottom right.

Step-by-step explanation:

There are eight compartments and seven of it is shaded and the other one five of the eight compartments are shaped.

I hope this helps :)

Answer:

see below

Step-by-step explanation:

9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank

We are replacing 9 with 10 minus something

9 = 10 -1

9 x 8 = (10 x 8) - ( 1 x 8)

           80 - 8

             72

Answer: Part 1: 1/52 Part 2: 15/26 Part 3: 1/26

Step-by-step explanation:

A ace of hearts is only 1 card

a 8 or a diamond a 8 is a 4/52 chance and a diamond is a 26 / 52 chance

26 + 4 = 30

30/52 simplifies to 15/26

A red 7 has a 4/52 chance for a 7 and half of that for a red card so 2/52 then 1/26

Answer:

7. f⁻⁻¹(x)=x-3                 11. f⁻⁻¹(x)= 2x/(1-x)

Step-by-step explanation:

to find the inverse of an expression:

1. change f(x) to y.

2. switch the x and y values.

3. solve to find y.

So....                                                              

7.) f(x)=x+3                              11.) f(x)=  x/(x+2)

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

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

f⁻⁻¹(x)=x-3                                       f⁻⁻¹(x)= 2x/(1-x)

Answer:

The y-coordinate is -4.5

Step-by-step explanation:

Point has x-coordinate -3 and y-coordinate -4.5.

Answer:

the y-coordinate is  -4.5

Step-by-step explanation:

the x-coordinate is -3

the y-coordinate is in between -4 and -5. from here one can assume it is half way unless there is information that has not been stated.

In between -4 and -5 is -4.5 so the y-coordinate is -4.5

the coordinate of point 7 is ( -3, -4.5)

Answer:

A. System of equations:

[tex]3.2C+3P=48.5\\C+P=15.5[/tex]

B. 5.5 pounds of peanut butter fudge were sold.

Step-by-step explanation:

Given:

Cost of chocolate fudge = $3.20

Cost of peanut butter fudge = $3.00

Total pounds sold = 15.5

Total gross profit = $48.50

C is the number of pounds of chocolate fudge sold.

P is the number of pounds of peanut butter fudge sold.

To find:

System of equations and number of pounds of peanut butter fudge sold = ?

Solution:

As per given conditions:

1. [tex]C+P=15.5[/tex]

Gross profit from Chocolate fudge: [tex]3.20 \times C[/tex]

Gross profit from Peanut Butter fudge: [tex]3.00 \times P[/tex]

Total gross profit = [tex]3.20C+3.00P = 48.50[/tex]

So, the system of equations is:

[tex]3.2C+3P=48.5\\C+P=15.5[/tex]

2. To find P.

Let us solve the equations.

Multiply 2nd equation with 3 and subtracting from 1st equation:

[tex]0.2C = 48.5- 3 \times 15.5\\\Rightarrow 0.2C = 48.5- 46.5\\\Rightarrow C = 10\ pounds[/tex]

Putting in 2nd equation:

[tex]10+P=15.5\\\Rightarrow P =5.5\ pounds[/tex]

So, the answer is:

5.5 pounds of peanut butter fudge were sold.

Answer:

2•2•2•3

24 has factors 2 and 12

12 has factors 2 and 6

6 has factors 2 and 3

Answer: a) 2401  b) 840 c)343  d)343  e) 686

Step-by-step explanation:

a) Total are 7 letters

There are 4 possible places in 4-letter word for each of 7 letter.

So total amount of the words is

7*7*7*7= 2401

b) No letter can be repeated mens that in 1st place can stay any of 7 letters,

in 2-nd place- any of 6 letters

in 3-rd place- any of 5 letters

in 4-th place any of 4 letters

Total amount of words is

7*6*5*4=840

c)  It is not written if the letters can be repeated. Assume that they can.

1st place occupied by letter A. So at 2-nd, 3-rd and 4th places can stay any of 7 letters

Total amount of words is

1*7*7*7=343

d) Similar case like c). At 1-st ,2-nd, 3-rd can stay any of 7 letters, and at 4th place the letter C (1 letter). Total amount of words is

7*7*7*1=343

e) There are 2 vowels A and E.  

So at 1st place can stay any of 7 letters, at 2-nd place -any of 2 letters, at 3-rd place- any of 7 letters and at 4th place any of 7 letters. Total amount of words is

7*2*7*7=686

The total number of 4-letter words possible is 2401

The total number of 4-letter words possible with no letter repeated is 840

The total number of 4-letter words possible with the first letter being A is  343

The total number of 4-letter words possible with the letter C at the end is 294.

The total number of 4-letter words possible with the second letter being a vowel is 1029.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

(a) No condition is imposed:

There are 7 choices for the first letter, 7 choices for the second letter, 7 choices for the third letter, and 7 choices for the fourth letter.

The total number of 4-letter words possible.

7 × 7 × 7 × 7 = 2401

(b) No letter can be repeated in a word:

For the first letter, there are 7 choices.
For the second letter, there are only 6 choices left (since we cannot repeat the first letter). Similarly, for the third letter, there are only 5 choices left, and for the fourth letter, there are only 4 choices left.

The total number of 4-letter words possible with no letter repeated.

7 × 6 × 5 × 4 = 840

(c) Each word must begin with the letter A:

For the first letter, there is only 1 choice (the letter A). For the second letter, there are 7 choices (since any letter can be used).

For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.

The total number of 4-letter words is possible with the first letter being A.

1 × 7 × 7 × 7 = 343

(d) The letter C must be at the end:

For the fourth letter, there is only 1 choice (the letter C).

For the first letter, there are 7 choices (since any letter can be used).

For the second letter, there are 7 choices, and for the third letter, there are 6 choices (since the letter C cannot be used).

The total number of 4-letter words possible with the letter C at the end.

7 × 7 × 6 × 1 = 294

(e) The second letter must be a vowel:

For the first letter, there are 7 choices (since any letter can be used). For the second letter, there are 3 choices (the vowels A, E, and I).

For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.

The total number of 4-letter words possible with the second letter being a vowel.

7 × 3 × 7 × 7 = 1029

Thus,

The total number of 4-letter words possible is 2401

The total number of 4-letter words possible with no letter repeated is 840

The total number of 4-letter words possible with the first letter being A is  343

The total number of 4-letter words possible with the letter C at the end is 294.

The total number of 4-letter words possible with the second letter being a vowel is 1029.

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Answer:

4159277

Step-by-step explanation:

156218 and 8162336

Add the two numbers and divide by 2

(156218 + 8162336)/2 =

8318554/2=

4159277

Answer:

4159277

Step-by-step explanation:

156218+8162336

=8318554

8318554 divided by 2 = 4159277

you add both numbers and divide by how many you added

Answer:

x=9

Step-by-step explanation:

for this sort of a problem, I would set up a proportion

5/25=x/45

multiply both sides by 25 and 45

45*5=x*25

225=25x

x=9

Answer:

1/7

Step-by-step explanation:

y=-7X

The slope of this line is -7

Perpendicular lines have slopes that multiply to -1

-7 * m = -1

Divide each side by -7

m = -1 / -7

m = 1/7

The slope of the perpendicular line is 1/7

Answer:

1/7

Step-by-step explanation:

Perpendicular slope can be calculated by take the opposite/negative reciprocal of the given slope. This means multiply the given slope by -1 (so if it is negative it becomes positive and if it is positive then becomes negative) and then flip the numerator and denominator.

So -7 is the slope of the given equation (y = mx + b where is m is slope and b is the y-intercept).

to find perpendicular slope..

Step 1. Multiple -7 by -1 = 7

Step 2. Flip 7/1 to 1/7

Answer: 1/7 is perpendicular slope

Answer:

Step-by-step explanation:

1) Point estimate is the difference between the sample means. Therefore,

A point estimate for the difference between the mean purchases of the users of the two credit cards is = 140 - 125 = $15

2) Margin of error = z√(σ²/n1 + σ2²/n2)

Where

z is the z score from the 95% confidence level. From the normal distribution table, z = 1.96

s1 and s2 are standard deviation for both customers respectively.

Standard deviation = √variance

σ1 = √100 = 10

σ2 = √641 = 25.32

Margin of error = 1.96√(10²/64 + 25.32²/49 = 7.5

At 95% confidence, the margin of error is 7.5

3) The confidence interval for the difference of two population means is expressed as point estimate ± margin of error

Confidence interval = 15 ± 7.5

The upper boundary for the confidence interval is

15 - 7.5 = 7.5

The lower boundary for the confidence interval is

15 + 7.5 = 22.5

A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is $7.5 to $22.5

4) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)

z = (x1 - x2)/(√σ1²/n2 + σ2²/n2)

z = (140 - 125)/√10²/64 + 25.32²/49

z = 1.02

The test statistic for an alpha of .05 is 1.02

Answer:

150 km

Step-by-step explanation:

1 liter ............ 40 km

15/4 liter .........x km

x = 15/4×40/1 = 600/4 = 150 km

Answer:

dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)

Step-by-step explanation:

x² / (x + y) = y² + 7

x² = (x + y) (y² + 7)

Take derivative of both sides with respect to x.  Use power rule, product rule, and chain rule.

2x = (x + y) (2y dy/dx) + (y² + 7) (1 + dy/dx)

Simplify.

2x = (2xy + 2y²) dy/dx + y² + y² dy/dx + 7 + 7 dy/dx

2x = (2xy + 3y² + 7) dy/dx + y² + 7

2x − y² − 7 = (2xy + 3y² + 7) dy/dx

dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)