7.1 x 10-^2 in scientific notation

Answer: 200cm

Calculation: 15cm times 8=120

20cm times 4= 80

Add 120+80= 200cm

1.

  a. m=0-6/5-4

      m=-6/1

      m=-6

  b. m=-10+4/-2+3

      m=-6/1

      m=-6

2.

  a. y=3x+2

  b. y=-x+4

#3 is below.

The probabilities for this problem are given as follows:

A probability is calculated as the number of desired outcomes divided by the number of total outcomes.

For this problem, we have that out of 400 moviegoers, 74 are adults who prefer comedies, hence:

P(C ∩ D) = 74/400 = 0.185.

The number of adults is given by: 2 + 48 + 19 + 74 = 143.

The number of non-adults who prefer comedies is: 24 + 64 = 88.

Hence:

P(C ∩ D) = (143 + 88)/400 = 0.5775.

The complete text for this problem is given by:

"Suppose we randomly select one of these survey participants. Let C be the event that the participant is an adult. Let D be the event that the participant prefers comedies.

Complete the statements.

P(C ∩ D) =

P(C ∪ D) =

"

Additionally, the table showing the observations is given at the end of the answer.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The point at (-3, 4) is at a distance of 5 units from the point (0, 0).

For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:

distance = √( (x₁ - x₂)² + (y₁ - y₂)²)

In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:

distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5

The distance is 5 units.

Learn more about distances between points:

https://brainly.com/question/7243416

#SPJ1

Answer:

happy to help, but c and d are not included in your question

Step-by-step explanation:

Given

(4*10^10)(9*10^-5)

= 36 * 10^10 - 5

= 36 * 10^5

= 3.6 * 10^6

Hope it will help :)

Explanation:

We use the distribution property to multiply the outer 9 with each term inside

9 times w = 9*w = 9w

9 times 8 = 9*8 = 72

Those products 9w and 72 form the answer 9w+72. Since 9w and 72 are not like terms, we cannot combine them.

Answer:

9w + 72

Step-by-step explanation:

Answer:

the green line

Step-by-step explanation:

its closest to the point

Hi there! The answer would be the green line and the dark blue line which is f(x)=2x+3 and h(x)=-2x+2.

Step By Step:

So you need to figure out the line for (2,-2).

This means that you would have to find a line that is between them which is the correct answer.

Well it can’t be orange since that it didn’t touch it and so can it not be red. So we have two answers left to choose from.

The last two pairs we have left would be the answer since they’re nothing touching the point for (2,-2).

This means that it would be D, dark blue and orange, or we can say f(x)=2x+3 and h(x)=-2x+2.

Answer:

the value of x is 7.

Step-by-step explanation:

2+19=21

21÷3=7

Check:

3×7=21

21-2=19

Therefore, 7 is the answer.

2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

For such more questions on trigonometric identity

https://brainly.com/question/7331447

#SPJ8

Answer:

60%

Step-by-step explanation:

There are a total of 45 people 24 boys and 21 girls=45

27 of them are in the club 27 out of 45=60%

The product of the slopes is -1, we can conclude that the two roads intersect at a right angle at the point (10/11, 18/11).

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

To build the new road such that it intersects the existing road at a right angle at the point (5,3), we can start by determining the slope of the existing road.

The slope of the existing road, given by the equation y=5x-2, is 5. This is because the equation is in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. Therefore, we know that the slope of any line perpendicular to this road will be -1/5, since the product of the slopes of perpendicular lines is -1.

To find the equation of the new road, we can use the point-slope form of a linear equation, which is y-y1=m(x-x1). We know that the new road passes through the point (5,3) and has a slope of -1/5. So, substituting these values into the equation gives:

y - 3 = (-1/5)(x - 5)

Simplifying this equation, we get:

y = (-1/5)x + 4

Therefore, the equation of the new road is y = (-1/5)x + 4, and the equation of the existing road is y = 5x - 2. These two equations represent the locations of the new road and the existing road, respectively.

To verify that the new road intersects the existing road at a right angle, we can find the point of intersection of the two roads and then check that the product of the slopes of the two lines is -1.

To find the point of intersection, we can set the two equations equal to each other:

(-1/5)x + 4 = 5x - 2

Solving for x, we get:

x = 10/11

Substituting this value of x back into either equation gives:

y = 18/11

So the point of intersection is (10/11, 18/11).

Now, to check that the two roads intersect at a right angle, we can find the slopes of the two lines and check that their product is -1:

Slope of existing road, m1 = 5

Slope of new road, m2 = -1/5

Product of slopes, m1m2 = 5(-1/5) = -1

Since the product of the slopes is -1, we can conclude that the two roads intersect at a right angle at the point (10/11, 18/11).

To learn more about slope from the given link:

https://brainly.com/question/2491620

#SPJ1

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

l5l - l-5l - (-5)

the absolute value of l5l and l-5l is 5

5 - 5 - (-5)

Subtracting a negative number is the same as adding that number

5 - 5 + 5

5

Answer = 5

x = -3y - 9 is the answer to the equation x+3y+9=0

Mathematics a number or values that, when used as a substitution for one or more variables inside an equation, makes the equation true. For instance,\(x^{2} = 4\) has two solutions, which are 2 & -2.

Because it is not a system, the single equation in a set of linear equations cannot be solved.

There are two or more multiple-variable equations in a linear equation system. The location that simultaneously fulfills all of the lines in the system, which each equation represents as a line, is the system's solution.

In the case of a single equation with a single variable, the answer can be obtained by solving for the variable. By removing 3y & 9 both from sides of the equation, x = x + 3y plus 9 = 0, we may find the value of x.

x = -3y - 9

To know more about equation visit:

brainly.com/question/29538993

#SPJ1

Answer:

A =54 units^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

A = 1/2 (12) (9)

A =54 units^2

Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

Answer:

i think For every hour Harriett bikes, the distance she travels increases by 12 miles

Answer:

n = -5 or -6

Step-by-step explanation:

\(n^2+ 11n + 30 = 0\)

Lets factorise the quadratic equation :-

→ Lets split the middle term of the equation.

\(=> n^2 + 5n + 6n + 30 = 0\)

→ Lets take 'n' common from the first 2 terms & '6' common from last 2 terms.

\(=> n(n + 5) + 6(n + 5) = 0\)

→ Lets take (n + 5) whole in common from the equation.

\(=> (n + 5)(n + 6) = 0\)

Here , we get 2 values of n :-

1) \(n + 5 = 0\)

\(=> n = -5\)

2) \(n + 6 = 0\)

\(=> n = -6\)

∴ Hence , n = -5 or -6

Answer: 5,508 m3

Step-by-step explanation:  V= 18 x 17 x 18 = 5,508 m3

Answer:5, 508

Step-by-step explanation:

V 18×18×17=5,508

Answer:

6781632 ft ^ 3

Step-by-step explanation:

The first thing is to know the formula for the volume of a pyramid:

V = 1/3 * Ab * h

That is, it is one third of the product between the area of the base and the height.

The base area would be:

Ab = l ^ 2

the side equals 156 ft, replacing:

Ab = 156 ^ 2

Ab = 24336 ft ^ 2

now, replacing in the volume formula:

V = 1/3 * 24336 * 836

V = 6781632

Which means that the volume of the pyramid is 6781632 ft ^ 3

Answer:

The perimeter of a rectangle is the sum of all of it’s sides. Since a rectangle has 2 lengths of the same size and two widths of the same size, the perimeter is length + length + width + width, or 2(length) + 2(width), or, to make it shorter, 2l + 2w.

Since the length of the rectangle (l) in this scenario is really 4w, we can replace those, and get 2(4w) + 2w, and since we know the total is 50, we can say 2(4w) + 2w = 50.

Using the distributive property, we get 8w + 2w = 50, and 10w = 50, or w = 5. Since the length is 4w, the length is 4*5 = 20.

To find the area, you multiply length and width to get 5 * 20 = 100 sq meters.

PLEASE MARK ME BRAINLIEST FOR MY OWN EFFORT

Answer:

-3/5

Step-by-step explanation:

see the details in the attachment.

According to the percentage, Stephen played this week is 24.2 minutes.

According to the statement

We have to find that the number of minutes has he played this week.

So, For this purpose, we know that the

A percentage is a number or ratio expressed as a fraction of 100.

From the given information:

Stephen has logged 220 minutes of game play today. His dashboard says that today's game time represents 11% of his game play for the week.

Then

Time of logged of game play = 220 minutes

Today's game time = 11% of his game play

Then

The minutes he played game in a week = 11% of 220 minutes

The minutes he played game in a week = 11/100*220

The minutes he played game in a week = 0.11*220

The minutes he played game in a week = 24.2 minutes.

So, According to the percentage, Stephen played this week is 24.2 minutes.

Learn more about percentage here

https://brainly.com/question/843074

#SPJ9

Answer:

Step-by-step explanation:

y = mx + b

The line y = 3 is a horizontal line with slope zero

y = 0x + 3

All parallel lines will also have a slope zero

a parallel line passing through (-2, 7) will have the equation

y = 0x + 7

y = 7

Answer:

The length of the arc ADB is (8/3)π ft and the area of the shaded region is 4.5 ft^2 - 4π ft^2.

Step-by-step explanation:

In the given circle with center O and radius 3 ft, let's consider the angle AOB, which is given as 160°. We need to find the length of the arc ADB and the area of the shaded region.

To find the length of the arc ADB, we can use the formula for the circumference of a circle and calculate the fraction of the total circumference represented by the angle AOB.

The circumference of a circle is given by 2πr, where r is the radius. In this case, the radius is 3 ft. Therefore, the total circumference is 2π(3) = 6π ft.

To find the length of the arc ADB, we calculate the fraction of the total circumference represented by the angle AOB. Since the angle AOB is 160° out of 360°, the length of the arc ADB is (160/360) * 6π ft = (4/9) * 6π ft = (8/3)π ft.

Next, to find the area of the shaded region, we need to subtract the area of the sector AOB from the area of triangle AOB. The area of the sector AOB is (160/360) * π * (3)^2 = (4/9) * 9π = 4π ft^2. The area of triangle AOB is (1/2) * 3 * 3 = 4.5 ft^2.

Therefore, the area of the shaded region is 4.5 ft^2 - 4π ft^2 = 4.5 ft^2 - 4π ft^2.

In summary, the length of the arc ADB is (8/3)π ft and the area of the shaded region is 4.5 ft^2 - 4π ft^2.

For more on these types of questions refer to this:
https://brainly.com/question/14989383
#SPJ8

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

Answer: 7x+y+8

Step-by-step explanation:

Combining like terms is just like what it sounds. You take the like terms, or terms that have the same variables and such, and add them together.

For this problem, we can see that 12x and -5x are like terms because they both consist of a numerical coefficient and the variable x.

We can see that -3y and 4y are like terms because they both have a numerical coefficient and y for variable.

Now, we can combine like terms.

12x-3y+8-5x+4y                     [combine like terms]

7x+y+8