As our scientific and technical knowledge has increased, so has our need for ever-smaller and ever-larger units of measure. The prefixes used to denote some of these units of measure are listed in the table below.
These new units of measure are quickly working their way into our everyday lives. For example, it is quite easy to purchase a 1-terabyte hard drive. One terabyte (TB) is equal to 1012 bytes. As another example, many computers can do multiple operations in 1 nanosecond (ns). One nanosecond is equal to 10−9 s.
In the 1980s, it became possible to measure optical events in nanoseconds and picoseconds. Express 1 ps as a decimal.

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer: 33

Step-by-step explanation: In the problem, you are given the figure with the following:

2x+3 and 3x+12

Method: Lets set this into an equation. Remember that straight lines add up to 180°.

2x+3+3x+12=180°    Combine like terms.

5x+15=180°

5x=165°

x=33°

You can always plug in 33° in the expression that was set to make sure it does give you 180°.

Hope this helps.

Answer:

33

Step-by-step explanation:

The length of the hypotenuse section on the rock-climbing wall at the local park is 3.92 meters

The length of the hypotenuse section is calculated using the following cosine function

cos(14) = adjacent/hypotenuse

Substitute the known values in the above equation, so, we have the following representation

cos(14) = (5 - 1.2)/hypotenuse

This gives

hypotenuse = (5 - 1.2)/cos(14)

Evaluate

hypotenuse = 3.92 meters

Hence, the hypotenuse is 3.92 meters

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Answer: 20 minutes

Step-by-step explanation:

35/14 = x/8

35 x 8 = 280

14x = 280

x = 20

The number of tickets that will be sold is 5560.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Ticket sales for Six Flags White Water totaled $94,520 this summer.

Tickets for the water park cost $17 each.

The number of tickets sold will be = 94520/17 = 5560.

Hence, the number of tickets that will be sold is 5560.

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Answer:

32 and 58

Step-by-step explanation:

Let's set up equations.

The sum of two numbers (x and y) is 90: x + y = 90

The larger number (y) is 6 less than twice the smaller number (x): y = 2x - 6

We have our system of equations:

x + y = 90

y = 2x - 6

Let's use substitution.

Substitute y = 2x - 6 into the first equation.

x + y = 90

x + (2x - 6) = 90

Combine like terms.

x + 2x - 6 = 90

3x - 6 = 90

Add 6 to both sides to isolate x.

3x = 96

Divide both sides by 3 to further isolate x.

x = 32

Now that we know x, let's find y.

Plug in x = 32 into one of our original equations.

y = 2x - 6

y = 2(32) - 6

Multiply.

y = 64 - 6

y = 58

Now we have x = 32, y = 58.

Check your answer by plugging these values into one of our original equations.

x + y = 90

32 + 58 = 90

Add.

90 = 90

Your solution is correct.

Hope this helps!

Answer:

X+2

Step-by-step explanation:

The dog is playing with his chew toy!

Answer:

Explanation

Step-by-step explanation:

In general, dogs can run 15-20 mph

humans can run 6-8 mph

You are significantly slower than the dog,

the fastest human is around 27 miles per hour, unfortunately, even if you were this fast

the fastest dog can run 40 miles per hour as an estimate

even house cats can run at 30 mph maximum if they really wanted,

You have no chance of outrunning this dog, and barely a chance of outsmarting it if that option was available, in conclusion, the dog is chasing you at a speed of around 30 mph about 6-7x more than your own speed with no chance of outrunning it(the dog).

Answer:

Finding b:

57+b = 180     (linear pair)

b = 123

Finding c:

c = 123          (vertical angles are always congruent

Answer:

4

Step-by-step explanation:

You see the hunderth digit has a 8, so you round up. 0.9+0.1=1 so you add 1 to 3, so 3.987 rounded is 4

Answer:

K=-13/3

Step-by-step explanation:

Answer:

- Pulling 50 names from a hat. <-> e. Simple Random

- Asking your 20 closest friends <->  b. Convenience

- Separating all students by grade level, and selecting 10 students from each grade <->  c. Stratified

- Call every 15th phone number on every 5th page of the phone book <->  d. Systematic

- Dividing by population by voting precinct, and sampling everyone in the precints selected <->  a. Cluster

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

- Pulling 50 names from a hat

All options in the hat and pick some of them. So Simpel Rando.

- Pulling 50 names from a hat. <-> e. Simple Random

- Asking your 20 closest friends

Closest friends lead to convenience. so

- Asking your 20 closest friends <->  b. Convenience

- Separating all students by grade level, and selecting 10 students from each grade

Divided the population into groups, and choose some from each group. Stratified.

- Separating all students by grade level, and selecting 10 students from each grade <->  c. Stratified

- Call every 15th phone number on every 5th page of the phone book

Every kth person. Systematic.

- Call every 15th phone number on every 5th page of the phone book <->  d. Systematic

- Dividing by population by voting precinct, and sampling everyone in the precints selected

Division into groups, and choosing everyone from each group. Cluster

- Dividing by population by voting precinct, and sampling everyone in the precints selected <->  a. Cluster

Answer:111

Step-by-step explanation:

1111

Answer:

4% used pastels.

Step-by-step explanation:,,

green is the most

5 isnt blue.green,yello or red

The percentage of the class-preferred pastels will be 25%. The color there has most pastels will be Green. And the number of pastels that are colors other than blue, green, red, or yellow will be 7.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Out of 24 students, 6 preferred to use pastels for their portraits while 4 preferred to use watercolors. Then the percentage of the class preferred pastels will be

P = 6 / 24 x 100

P = 0.25 x 100

P = 25%

Jasmin bought a box of 40 assorted colored pastels, 1/5 are blue, 3/10 are green, 20% are red and 5 are yellow. Then the number of pastels of each color will be

Blue = 1/5 = 8 / 40 = 8

Green = 3/10 = 12 / 40 = 12

Red = 0.2 = 1/5 = 8 / 40 = 8

Yellow = 5

The number of pastels are colors will be

⇒ 40 - 8 - 12 - 8 - 5

⇒ 40 - 33

⇒ 7

The color there has most pastels will be Green. And the number of pastels that are colors other than blue, green, red, or yellow will be 7.

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Answer: The two numbers that multiply to -65 and add to -8 are -13 and 5.

Steps: Here are the steps to find two numbers that multiply to -65 and add to -8:

Write down the equation x * y = -65 where x and y are the two numbers you’re looking for.

Write down the equation x + y = -8.

Solve for one of the variables in one of the equations. For example, solving for x in the second equation gives us x = -8 - y.

Substitute this expression for x into the first equation: (-8 - y) * y = -65.

Solve this quadratic equation for y: -y^2 - 8y + 65 = 0.

Use the quadratic formula to find the values of y: y = (-(-8) +/- sqrt((-8)^2 - 4 * (-1) * 65)) / (2 * (-1)).

This gives us two possible values for y: -13 and 5.

Substitute these values back into one of the original equations to find the corresponding values of x. For example, when y = -13, we have x = -8 - (-13) = 5. When y = 5, we have x = -8 - 5 = -13.

So, the two numbers that multiply to -65 and add to -8 are -13 and 5.

Answer:

60 contain 6 tens

then

60+10

contain

7 tens

the

correct answer

is

7 tens

Answer:

6 tens + 1 ten = 7 tens

Step-by-step explanation:

6 tens = 60

1 ten = 10

7 tens = 70

The required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.

Given that,
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
z = [ x - μ]/σ
Accoding to the question,

= p[z < (170-150)/10] -  p[z < 130-150/10]
= p [z <2] - p [z < -2]
= 0.9772 - 0.0228
= 95.44%

Thus, the required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.

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Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Answer:

39/10

Step-by-step explanation:

.......................

The values are evaluated to give;

h(-3) = 0

h(0) = -9

h(5) = -24

A function can simply be defined as laws, rules or expression that shows the relationship between two variables in an equation.

The variables are termed;

We have the function as;

h(x) = -3x - 9

When the value of x = -3

Substitute the value into the equation

h(-3) = -3(-3) - 9

expand the bracket

h(-3) = 9 - 9

h(-3) = 0

When the value of x = 0

Substitute the value

h(0) = -3(0) - 9

expand the bracket

h(0) = 0 - 9

h(0) = - 9

When x = 5

h(5) = -3(5) - 9

h(5) = -15 - 9

h(5) = -24

Hence, the values are 0, - 9 and -24

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Answer:

6x2+4x-2=0(changing the sign )

Step-by-step explanation:

x=-4+-\(\sqrt\)16+48/12

=-4+-8/12

-4+8/12,-4-8/12

1/3.-1

The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)  

When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials may be easily simplified with the use of factoring.

When a polynomial is factored, its factors are expressed as the polynomial's product. Finding the zeros of the polynomial expression or the values of the variables in the supplied expression are both made possible by factoring polynomials.

Here we have

24x⁶ - 1029y³  

Take 3 as common

=> 3(8x⁶ - 343y³)  

As we know 8 = 2³ and 343 = 7³

=> 3[(2x²)³ - (7y)³]  

From the algebraic identities

Take a = 2x² , b = 7y and apply above formula

=> 3[(2x² - 7x)((2x²)²+(2x²)(7y)+(7y)²)]  

=> 3 [ (2x² - 7x) (4x⁴ +14x²y+49y²)]  

Therefore,

(24x⁶ - 1029y³) = 3 (2x² - 7x) (4x⁴ +14x²y+49y²)  

Therefore,

The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)  

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Answer:

36

Step-by-step explanation:

Step-by-step explanation:

hope this helps, you can ask any questions for clarification

Answer:

The height of 5 books of height 7 cm 5 mm each can be calculated as follows:

Height of one book = 7 cm + 5 mm = 7.5 cm

Height of 5 books = 5 x 7.5 cm = 37.5 cm

Therefore, the total height obtained by stacking 5 books of height 7 cm 5 mm each is 37.5 cm.

The perimeter of the square park is 3 m 20 cm, which can be written as 320 cm.

Tania takes 3 complete rounds of the park, so the total distance traveled by her is:

Total distance = 3 x perimeter

Total distance = 3 x 320 cm

Total distance = 960 cm

Therefore, the total distance traveled by Tania is 960 cm or 9.6 m.

Step-by-step explanation:

Answer:

C

it's the set that will add to 180°

36° + 42° + 102° = 180°

Answer:

Step-by-step explanation:

This is because here,

36° + 42° + 102° = 180°

Hence, a triangle can be made.