Complete the sequence
8,27,64,125,.........
Just next letter

Answer: 2/3

Step-by-step explanation: As you can see, the denominators are different so we need to find a common denominator to add these 2 fractions.

We find the common denominator by finding

the common multiple for these 2 denominators.

Multiples of 10

1 x 10 = 10

2 x 10 = 20

3 x 10 = 30

Multiples of 15

1 x 15 = 15

2 x 15 = 30

As you can see, we have a common multiple of 30.

To get 30 in the denominator of 2/10, multiply top and bottom by 3.

To get 30 in the denominator of 7/15, multiply top and bottom by 2.

So we have 6/30 + 14/30 which is 20/30.

20/30 can be reduced to 2/3.

Answer:

1). 114.29 km per hour

2). 93.24 km per hour

Step-by-step explanation:

Question (1)

Umar drove his taxi in two parts;

1). Ipoh to Tapah

2). Tapah to Kuala Lumpur

Since, the formula to calculate the average speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

Total distance from Ipoh to Tapah = 60 km

Average speed to cover this distance = 100 km per h

Time taken to cover this distance = [tex]\frac{\text{Distance covered}}{\text{Speed}}[/tex]

                                                            = [tex]\frac{60}{100}[/tex]

                                                            = 0.6 hours

Total distance from Ipoh to Kuala Lumpur = 220 km per h

Average speed from Ipoh to Kuala Lumpur = 110 km per h

Time taken to cover the distance = [tex]\frac{220}{110}[/tex] = 2 hours

Distance from Tapah to Kuala lumpur = 220 - 60

                                                               = 160 km

Time taken to travel from Tapah to Kuala Lumpur = 2 - 0.6

                                                                                   = 1.4 hours

Average speed from Tapah to Kuala Lumpur = [tex]\frac{160}{1.4}[/tex]

                                                                           = 114. 29 km per hour

Question (2).

Speed achieved by the leopard = 25.9 meter per sec.

Since, 25.9 meter = [tex]\frac{25.9}{1000}[/tex] km

                              = 0.0259 km

1 second = [tex]\frac{1}{3600}[/tex] hour

Therefore 25.9 meter per second = [tex]\frac{0.0259}{\frac{1}{3600} }[/tex]

                                                        = 0.0259 × 3600

                                                        = 93.24 km per hour

Write it out as an equation:

(48 /(5+(11-8))) -7

Simplify:

(48/(5+3))-7

(48/8)-7

6-7 = -1

The answer is -1

The length a spring stretches when subjected to the given load is required.

The spring is stretched by 18 inches.

F = Force

k = Spring constant

x = Stretched length

[tex]F=50\ \text{lbf}[/tex]

[tex]x=5\ \text{inch}[/tex]

Hooke's law is given by

[tex]F=kx\\\Rightarrow 50=k5\\\Rightarrow k=\dfrac{50}{5}\\\Rightarrow k=10\ \text{lbf/inch}[/tex]

[tex]F=180\ \text{lbf}[/tex]

For the required spring

[tex]F=kx\\\Rightarrow x=\dfrac{F}{k}\\\Rightarrow x=\dfrac{180}{10}\\\Rightarrow x=18\ \text{inches}[/tex]

Learn more about Hooke's law:

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Answer: The answer is B

Step-by-step explanation:

Part A

Her steps were

[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]

Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.

The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]

=======================================================

Part B

Here's what she should have written

[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]

If you want to convert that improper fraction to a mixed number, then you could do something like this

[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]

Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.

Answer:

Step-by-step explanation:

Draw a triangle and label the sides (picture below):

● the length is 2x+2

● and the width or the height is 6x

The perimeter of a rectangle is the sum of the sides

● P = 2x+2 + 6x + 2x+2 + 6x

Isolate the similar terms

● P = (2x+2x+6x+6x) + (2+2)

● P = 16x + 4

The perimeter of the window of lengths 2x+2 and 6x is 16x + 4

The formula for calculating the perimeter of a rectangle is expressed as:

[tex]P=2(L+W)[/tex] where:

L is the length of the rectangular stained glass window.

W is the width of the rectangle stained glass window

Given the following

L = (2x +2) inches

W = 6x inches

Substitute the given values into the formula as shown:

[tex]P = 2(2x+2+6x)\\P=2(2x+6x+2)\\P=2(8x+2)\\P=2(8x)+2(2)\\P=16x+4[/tex]

Hence the perimeter of the window is 16x + 4

Learn more here: https://brainly.com/question/10452031

Answer:

1) 120

2) E (Z) = 12 and Variance of Z = 90

a) 5 liters

Step-by-step explanation:

1. We can find this by suing combinations.

Here n= 10 and r= 3 so n C r

= 10 C 3= 120

2. E(X) = 8 and E(Y) = 3

Z = 2X - 3Y +5

E(Z ) = 2 E (X) - 3(E)(Y) +5   ( applying property for mean)

       = 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12

V(X) = 9 and V(Y) = 6.

V(Z) = E(Z )²-  V(X) *V(Y)   (applying property for Variance for two variables )

        = 144- 54= 90

3. 55 liters contain adulterated milk in 7: 4.

So it contains 4/ 11*55= 20 liters of water

But we want to make it a ratio of 7:6

the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water

So 25- 20 = 5 liters must be added to make it a ratio of 7:6

Answer:

Step-by-step explanation:

[tex]\left|2x-11\right|<3\\\mathrm{Apply\:absolute\:rule}:\quad \\\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a\\\\-3<2x-11<3\\\\2x-11>-3\quad \mathrm{and}\quad \:2x-11<3\\\\2x-11>-3\quad :\quad x>4\\\\2x-11<3\quad :\quad x<7\\\\x>4\quad \mathrm{and}\quad \:x<7\\\\4<x<7[/tex]

Answer:

The number of people in one session that will spend within two standard deviations below the mean and one standard deviations above the mean time on Facespace is 394 people

Step-by-step explanation:

The given information are;

The mean time spent of Facespace, μ = 30 minutes

The standard deviation of the time spent daily, σ = 6 minutes

The number of people in one sitting, n = 2900 people

The time spent two standard deviations below the mean = 30 - 12 = 18 minutes

The time spent one standard deviations above the mean = 30 + 6 = 36 minutes

The Z-score values are;

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

Which gives;

For x = 30

[tex]Z=\dfrac{36-30 }{6 } = 1[/tex]

For x = 18

[tex]Z=\dfrac{18-30 }{6 } = -2[/tex]

From the z-score table, we have;

P(Z > -2) = 1 - 0.02275 = 0.97725

P(Z < 1) = 0.84134

Therefore, the probability P(-2 < Z < 1) = 0.97725  - 0.84134 = 0.13591

Given that there are 2900 are on in one sitting, the number of them that will lie within two standard deviations below the mean and one standard deviations above the mean = 2900 × 0.13591 = 394.139 which is approximately 394 people.

Answer:

66

Step-by-step explanation:

The figure of triangle JKL is attached. JA = 9, AL = 10, and CK = 14.

According to two tangent theorem, the tangent to a circle that meets at the same point is equal to each other. Therefore:

AJ = BJ, AL = CL, CK = BK.

Since AJ = 9, BJ = AJ = 9

AL = 10, CL = AL = 10

CK = 14, BK = CK = 14.

Therefore the lengths of the triangle sides are:

JL = AJ + AL = 9 + 10 = 19

JK = BJ + BK = 9 + 14 = 23

KL = CL + CK = 14 + 10 = 24

The perimeter of the triangle is the sum of all its sides, it is given as:

Perimeter = JL + JK + KL = 19 + 23 + 24 = 66

Answer:

A

Step-by-step explanation:

We can plug in all of the x and y values to check if the point is a solution to the inequality.

Point A: x = 1, y = 7

7 > |1| + 5

7 > 1 + 5

7 > 6

This is a true statement, which means that this point is a solution to the inequality. We don't have to check any more points since we have found our answer.

Answer:

$1.80

Step-by-step explanation:

2/3x = 1.2

x = 1.2 / (2/3)

x = 1.2 * (3/2)

x = 1.80

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 3

▹ Step-by-Step Explanation

[tex]\frac{9}{150} \\\\150/3 = 50\\9/3 = 3\\\\x = 3[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

[tex] q = 2(3r + 8) [/tex]

Step-by-step explanation:

There are two variables, q and r in the expression given. To make r the independent variable, it simply means, make q the subject of the formula, so that variable q would be dependent on variable r. As r changes, q changes also.

Thus,

[tex] q - 10 = 6(r + 1) [/tex]

Open the parenthesis

[tex] q - 10 = 6r + 6 [/tex]

Add 10 to both sides

[tex] q - 10 + 10 = 6r + 6 + 10 [/tex]

[tex] q = 6r + 16 [/tex]

[tex] q = 2(3r + 8) [/tex]

Answer:

A

Step-by-step explanation:

The quotient is  5x³ -5x² + 2x -2.

Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1." This division method requires less human calculation effort than the lengthy division method.

Given:

(5[tex]x^4[/tex] – 3x² + 4) ÷ (x + 1)

So, the division is

                       (x+1) |  (5[tex]x^4[/tex] – 3x² + 4) | 5x³ -5x² + 2x -2

                                   5[tex]x^4[/tex] + 5x³

                               ___________

                                          -5x³ - 3x²

                                          -5x³ - 5x²  

                                       ____________

                                                    2x² + 4    

                                                    2x² + 2x      

                                              ____________

                                                              4 - 2x      

                                                              -2 - 2x

                                                             _______

                                                                    6

Hence, the quotient is  5x³ -5x² + 2x -2.

Learn more about Synthetic Division here:

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Answer:

The constant of proportionality is 11

Step-by-step explanation:

Since the proportionality is given by:

y = r x   (with "r" the constant of proportionality)

and according to the table:

22 = r (2)

then r = 22/2 = 11

Answer:

31.6666666 miles / gallon

Step-by-step explanation:

Take the miles and divide by the gallons

95 miles / 3 gallons

31.6666666 miles / gallon

Answer:

Step-by-step explanation:

Solving trig equations are just like solving "regular" equations. Let's get to it. First and foremost we are going to make a "u" substitution. You'll use that all the time in calculus, if you choose to go that route. Let

[tex]sin^2 \theta=u^2[/tex] and sinθ = u. Making the substitution, the equation becomes:

[tex]2u^2-u-1=0[/tex]

That looks like something that can be factored, right? If you throw it into the quadratic formula you get the factors:

(u - 1)(2u + 1) = 0

By the Zero Product Property, either u - 1 = 0 or 2u + 1 = 0, so we will solve those, but not until after we back-substitute!

Putting sinθ back in for u:

sinθ - 1 = 0 so

sinθ = 1 and in the other equation:

2sinθ + 1 = 0 so

2sinθ = -1 and

[tex]sin\theta=-\frac{1}{2}[/tex]

Get out the unit circle and look to where the sinθ has a value of 1. There's only one place in your interval, and it's at 90 degrees.

Now look to where the sinθ has a value of -1/2. There are 2 places within your interval, and those are at 210° and 330°. Now you're done!

Answer:

work is pictured and shown

Answer:

I'm pretty sure 8 is the correct answer

Step-by-step explanation:

(-1)^(3/7)  x 128^(3/7)

-1 x 128^3/7

128^(3/7) = 8

= 8

Answer:

1/2

Step-by-step explanation:

First die rolled 5

Second die can roll 1, 2, 3, 4, 5, 6

Only if the second die rolls 4, 5, 6 will the sum be greater than 8.

p(sum > 8) = 3/6 = 1/2

Answer: 1/2

Step-by-step explanation:

First die rolled 5

Second die can roll 1, 2, 3, 4, 5, 6

Only if the second die rolls 4, 5, 6 will the sum be greater than 8.

p(sum > 8) = 3/6 = 1/2

Answer:

Around 1.6 cm per month

Step-by-step explanation:

We can set up a proportion to find how much the hair grows per month. It's important to note that there are 12 months in a year, so we can represent a year as 12 months.

[tex]\frac{19}{12} = \frac{x}{1}[/tex]

We can now cross multiply:

[tex]19\cdot1=19\\\\19\div12=1.58\overline{33}[/tex]

1.58333... rounds to 1.6.

Hope this helped!

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

in we have x = 11

put the value of x in equation

[tex]b(11) = \sqrt{3} (11) + 3[/tex]

[tex]b(11) = 11 \sqrt{3} + 3[/tex]

so x = 11√3

Hope it helps

Answer:

x = 12.6 degrees

Step-by-step explanation:

Using the property of alternate interior angles, we can say that m<A is equivalent to m<E.

m<A = m<E

63 = 5x

12.6 = x

So, x = 12.6 degrees

Cheers.

Answer:

it's b :)

Step-by-step explanation:

A number line which represents the solution set for the given inequality is: option B.

A number line refers to a type of graph with a graduated straight line which contains numerical values (both positive and negative numbers) that are placed at equal intervals along its length.

Next, we would solve the given inequality:

-½x ≥ 4

-x ≥ 4 × 2

x ≤ -8.

Therefore, a number line which represents the solution set for the given inequality is a number line from -10 to 10 in increments of 2 with a point at -8 and a bold line starts at -8 while pointing to the left.

Read more on number line here: brainly.com/question/24644930

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Answer:

x=1

Step-by-step explanation:

subtract 38 from both sides:

7x=7

divide both sides by 7 to isolate x:

x=1

HOPE THIS HELPS!!!! :)

Answer:

Integers include whole numbers. However, whole numbers are the list of positive integers, INCLUDING 0. A whole number cannot be negative.

Step-by-step explanation:

Answer and Step-by-step explanation:

True

Whole Numbers       { 0, 1, 2, 3, 4, . . . }  

Counting Numbers  { 1, 2, 3, 4, . . . }  

Integers                    { . . . −4, −3, −2, −1, 0, 1, 2, 3, 4, . . . }

when its a positive integers, say "positive integers"

(note: zero isn't positive or negative):

Integers are a whole numbers, but they also include negative numbers.

But still no fractions allowed!

Integers = { . . . , −4, −3, −2, −1, 0, 1, 2, 3, 4, . . . }

Negative Integers = { . . . , −4, −3, −2, −1 }

Positive Integers = { 1, 2, 3, 4, . . . }

Non-Negative Integers = { 0, 1, 2, 3, 4, . . . } (it includes zero you see)

hope it helps.

Answer:

False

Step-by-step explanation:

Required

State if the product of rational numbers and integer is an integer

The statement is false and the proof is as follows

Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;

Take for instance: 0.2, 0.5, 2.25, etc.

When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;

1. It can result to an integer:

For instance;

[tex]0.2 * 5 = 1[/tex]

[tex]0.5 * 4 = 2[/tex]

[tex]2.25 * 8 = 18[/tex]

2. It can result in a decimal number

For instance;

[tex]0.2 * 3 = 0.6[/tex]

[tex]0.5 * 5 = 2.5[/tex]

[tex]2.25 * 7 = 15.75[/tex]

From (1) above, we understand that the product can result in an integer.

Hence, the statement is false

Answer:

1

Step-by-step explanation:

1^3

This is 1 multiplied by itself 3 times

1*1*1

1