Smith and his friends are gaming online on a popular website. An hour later, 6 friends go offline. Five of them continue playing. How many of them were gaming online initially?

Answer:

the answer is 4) 10π/9 inches

Step-by-step explanation:

all answers have π on the nominator but i could not insert it for some reason

\(Question 7 options:\\1) \frac{40}{3}inches \\2) \frac{5}{3} inches\\3) \frac{100}{3} inches \\4) \frac{10}{9} inches\)

A circle is a curve sketched out by a point moving in a plane. The length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given that the radius of the circle is 2 inches, while the angle made by the arc at the centre of the circle is 100°. Therefore, the length of the arc can be written as,

Length of the arc = 2 × π × R × (θ/360°)

                              = 2 × π × 2 inches × (100°/360°)

                              = 10π / 9  inches

                              = 3.49 inches

Hence, the length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.

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Answer:

domain: (-∞, 5)∪(5, ∞)

domain in interval form: {x|x ≠ 5}

B is the correct answer

Answer:28

Step-by-step explanation:

Answer:

40 slices

Step-by-step explanation:

I rounded 38 to 40 and divided by 8

We first create a system of equations that can represent the problem given.

We let x represent the amount of chocolates, in pounds, and y be the amount of mixed nuts, also in pounds. Colin has a total of 10-lb bag of trail mix. We can write an equation representing this as:

Chocolate costs $3.00 per pound while mixed nuts cost $6.00 per pound. Colin's total budget is around $5.40 per pound. This can be represented in equation as:

Hence, we now have the system of equations written as:

Solve the system of equations using methods of elimination, as follows:

Therefore, Colin used 2 pounds of chocolates and 8 pounds of mixed nuts for this 10-lb trail mix.

Answer:

0.254

Step-by-step explanation:

Given that:

Percentage of those having health insurance = 71%

p = 71 / 100 = 0.71

Number of adults selected at random, n = 4

Probability that 4 selected have health insurance :

p^n = 0.71^4 = 0.25411681

= 0.254

The value of x is (-∞, -5) ∪ (1, ∞).

Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),

Solving for x,

Factors =

\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)

Therefore,

\(\left(x-1\right)^3\left(x+5\right) > 0\)

\(x < -5\quad \mathrm{or}\quad \:x > 1\)

Hence the value of x is (-∞, -5) ∪ (1, ∞).

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9514 1404 393

Answer:

  13

Step-by-step explanation:

The number is 1 more than the least common multiple of 3 and 4. That multiple is 12, so the number of stairs is 12+1 = 13.

Martha's school staircase has 13 steps, minimum.

_____

Additional comment

The real minimum is 1, not 13. We assume that we're interested in the non-trivial solution. (In a public building, staircases between floors often have 14 steps. 13 steps might attract the attention of those who are superstitious.)

Answer:

aob and boc are supplementary

angles 1 and 3 are adjacent .

Step-by-step explanation:

Answer:

Step-by-step explanation:

complimentary angles=90

∠R+∠T=90

3x+2x=90

5x=90

x=90/5

The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments

From the question, we have the following parameters that can be used in our computation:

The table of values

For the membership application, we have the following features

So, the function is

f(x) = 600 - 10x

For the membership available, we have the following features

So, the function is

g(x) = 20/3x

So, the functions are f(x) = 600 - 10x & g(x) = 20/3x

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Answer:

A(-3,4) B(1,-8)

y-y1/x-x1 =y2-y1/x2-x1

y-4/x--3 = -8-4/1--3

y-4/x+3 = -12/1+3

y-4/x+3 =-12/4

y-4/x+3 = -3

y-4 = -3(x+3)

y-4=-3x-9

y+3x +9-4=

y+3x+5=0

Answer:

y = -3x - 5

Step-by-step explanation:

-3, 4 and 1, -8

1 - -3 = 4

-8 - 4 = -12

\(\frac{-12}{4}\) = \(\frac{-3}{1}\) = -3

gradient/slope = -3

now substituting in the point -3, 4 to find the y intercept:

4= -3 x -3 + c

4 = 9 + c

-5 = c

y intercept = -5

equation is y = -3x - 5

Answer:

0.137

Step-by-step explanation:

The computation is shown below:

Educated = 0.27

And, unemployed to educated is 0.043

Now probability of educated and unemployed is

= 0.043 × 0.27

= 0.1161

So, the educated would be

= 0.01161 ÷ 0.085

= 0.137

Answer:

true

Step-by-step explanation:

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

Dena had 8 dollars left for gift C.

Answer:

Step-by-step explanation:
Rolled the dice 6 times each with different values.
The total values after the 6 rollings is 31 you just add the sticks after each roll that's how you get the 31.
But the question is asking how many times are we likely to get 5.
You look for the numbers that are equal or greater than 5 / the total values found
The answer will be 5/331
Hope this helped.

Answer:

The answer is $0.07 cents per inch

Step-by-step explanation:

If you take 6 feet into inches (72)

and divide the total cost by the amount of inches (5.04 / 72)

You get the answer

the correct answer is option b) 0.11. To find the experimental probability of drawing a K or 6, we need to first determine how many K's and 6's are in a standard deck of cards.

A standard deck of cards contains 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards, including an ace, numbered cards 2-10, and face cards (jack, queen, king).

Out of the 52 cards in the deck, there are four K's and four 6's, for a total of eight cards that satisfy the condition of being a K or 6.

To calculate the experimental probability of drawing a K or 6 from the table, we need to add up the frequency of drawing a K and the frequency of drawing a 6, and then divide by the total number of draws (100).

From the table, we see that the frequency of drawing a K is 4, and the frequency of drawing a 6 is 7. Therefore, the total frequency of drawing a K or 6 is:

4 (K's) + 7 (6's) = 11

So the experimental probability of drawing a K or 6 is:

11/100 = 0.11

Therefore, the correct answer is option b) 0.11.

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Considering that each student has only one birthday, each input will be related to only one output, hence this relation is a function.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

Each student has only one birthday, hence each input will be related to only one output, hence this relation is a function.

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Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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No, his answer is not correct because each of the smaller divisions represents 1/6, not 3.

Mark's answer is not correct.

When dividing a number line into equal sections, the value of each section represents a fraction of the whole.

In this case, Mark divided the number line from 0 to 1 into 3 equal sections and then divided each of those sections into 2 equal parts.

Initially, the whole number line from 0 to 1 represents the number 1. When Mark divided it into 3 equal sections, each section represents 1/3 (one-third) of the whole.

So far, this is correct.

However, when Mark further divided each of the 1/3 sections into 2 equal parts, each part represents 1/2 (one-half) of the 1/3 section.

So, each of these smaller divisions represents 1/2 \(\times\) 1/3 = 1/6 (one-sixth) of the whole.

Therefore, the correct representation of each of the smaller divisions is 1/6, not 3.

Mark made an error by mistakenly assuming that each smaller division represents the number 3.

In summary, Mark's answer of 3 is incorrect because each of the smaller divisions represents 1/6, not 3.

The correct representation for dividing the number line as described is 1/6.

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Answer:

20 is a composite number.

Ways that can be arranged:

5 x 4

10 x 2

20 x 1

Answer:

Once upon a time, there was a flock of doves that flew in search of food led by their king. One day, they had flown a long distance and were very tired. The dove king encouraged them to fly a little further. The smallest dove picked up speed and found some rice scattered beneath a banyan tree. So all the doves landed and began to eat.

Suddenly a net fell over them and they were all trapped. They saw a hunter approaching carrying a huge club. The doves desperately fluttered their wings trying to get out, but to no avail. The king had an idea. He advised all the doves to fly up together carrying the net with them. He said that there was strength in unity.

Each dove picked up a portion of the net and together they flew off carrying the net with them. The hunter looked up in astonishment. He tried to follow them, but they were flying high over hills and valleys. They flew to a hill near a city of temples where there lived a mouse who could help them. He was a faithful friend of the dove king.

The original price of the shirt was $68

We know that the price after a discount of the 20% and an added $3.80 in taxes is $58.20

Then we can write:

$58.20 = P*(1 - 0.2) + $3.80

Where the factor (1- 0.2) corresponds to a discount of 20%.

Solving that for P we will get:

P = ($58.20 - $3.80)/0.8

P = $68

That is the original price of the shirt.

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The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

\( 6.7 -0.674 *1.1 =5.96\)

\( 6.7 +0.674 *1.1 =7.44\)

Step-by-step explanation:

Let X the random variable that represent the  head breadths of a population, and for this case we know the distribution for X is given by:

\(X \sim N(6.7,1.1)\)  

Where \(\mu=6.7\) and \(\sigma=1.1\)

We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.

We can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

The critical values that accumulates 0.25 of the area on each tail we got:

\( z_{crit}= \pm 0.674\)

And if we solve x from the z score we got:

\( x = \mu \pm z \sigma\)

And replacing we got:

\( 6.7 -0.674 *1.1 =5.96\)

\( 6.7 +0.674 *1.1 =7.44\)

Express 0.9 as:

Use distributive property:

In order to multuply fractions you can use the following formula:

so:

Finally, use this property:

so:

Answer: