Christine, Dale, and Michael sent a total of 71 messages during the weekend. Dale sent 9 fewer messages than Christine. Michael sent 2 times as many messages as Christine. How many messages did they each send?

Answer:

B.

Step-by-step explanation:

All the possible outcomes are listed on choice B.

The event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have three coins.

As we know, in a coin there are two sides head and a tail.

If we flip three coins then the set of all the possible outcomes:

O = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

The set of outcomes has more tails than heads.

E = {ttt, tth, tht, htt}

We can find the probability, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Probability = 4/8 = 1/2

Thus, the event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

Learn more about the set here:

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Answer:

$11286.95 second year

$10335 first year

Step-by-step explanation:

9% of 9500 is 855, 9500 plus 855 = 10335. (first year)

9% of 10335 is 931.95, and 10335+931.95 is 11286.95. (second year)

The amount in the account at the end of 1 year  $10335 (first year)

The amount in the account at the end of 2 years $11286.95.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

$9500 is placed in an account that pays 9% interest compounded each year.

so, we get,

9% of 9500 is 855,

9500 plus 855 = 10335. (first year)

again,

9% of 10335 is 931.95,

and 10335+931.95 is 11286.95. (second year)

Hence, The amount in the account at the end of 1 year  $10335 (first year)

The amount in the account at the end of 2 years $11286.95.

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Answer:

Step-by-step explanation:

The formula we need for this is

4(4 + x) = 5(5 + 3) and

16 + 4x = 5(8) and

16 + 4x = 40 and

4x = 24 so

x = 6, choice C.

Answer:

-2, -1/2

Step-by-step explanation:

Step-by-step explanation:

The midpoint of a line segment between two points is given by

[tex]M = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

where ( x1 , y1) and ( x2 , y2) are the points

From the question

The midpoint of the line segment using points (-5,2) and (1, -3) is

[tex]M = ( \frac{ - 5 + 1}{2} , \frac{2 - 3}{2} )[/tex]

[tex]M = ( - \frac{ 4}{2} , - \frac{1}{2} )[/tex]

We have the final answer as

[tex]M = ( - 2, - \frac{1}{2} )[/tex]

Hope this helps you

Answer:

Step-by-step explanation:

In order to find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

x is the hypotenuse

the opposite is 19

So we have

sin 20 = 19/x

x = 19/sin 20

x = 55.55

We have the final answer as

Hope this helps you

Answer:

x = 55.6

Step-by-step explanation:

Answer: y: height, x: time.

Step-by-step explanation:

The data we have is:

The initial position of Greyson is 75ft above the river.

He needs 1.5 seconds to hit the water, and other 0.5s tho reach the bottom of the river.

Then we have a relationship of height vs time.

The y axis will represent the heigth of Greyson, and the x-axis will represent the time, such that at the time x = 0 seconds, we have y = 75ft

Answer:

  −13.8654599313 and 0.8654599313

Step-by-step explanation:

The two numbers of interest will be the solutions to ...

  xy = -12

  x +y = -13

Substituting for y, this becomes the quadratic ...

  x(-13 -x) = -12

  x^2 +13x = 12 . . . . . multiply by -1

  x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square

  (x +6.5)^2 = 54.25

  x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5

  x ≈ -13.865499313 or 0.8654599313

The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.

Answer:

20boys and 15girls

Step-by-step explanation:

Let no of boys be 4x

no of girls be 3x

4x+3x=35

7x=35

x=35/7

x=5

no of boys=4×5=20

no of girls=3×5=15

20+15=35 students

Answer:

Initial Value: 25, Rate of change -5.

First. Lets find the rate of change.

y2-y1/x2-x1 = m

We have A(1,20) B(3,10)

10-20/3-1=-5

m=-5(Rate of change)

Now let's find the initial value using slope-point form.

y-y₁=m(x-x₁)

y-20=-5(x-1)

=-5x+5+20

=-5x+25

The initial value is the value of y when the value of x is equal to 0. (Also the Y-Intercept)

Initial Value = -5(0)+25

=25

Answer:

[tex]\boxed{ 8 + x}[/tex]

Step-by-step explanation:

Hey there!

In most cases "the number" would be x.

So if the statement says 8 "more than a number",

It is saying 8 plus x or 8 + x.

Hope this helps :)

Answer:

x + 8 is the meaning.

Step-by-step explanation:

“more” means addition. Take the number as “x”, so it will be x + 8.

That's the answer.

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

Explanation:

Focus on triangle BDH

Interior angles B and D are given to be 40 and 31 respectively. Interior angle H is unknown

For any triangle, the interior angles always add to 180

B+D+H = 180

40+31+H = 180

H+71 = 180

H = 180-71

H = 109

Interior angle H is 109 degrees for triangle BDH

The exterior angle is 180 minus this measure

exterior angle = 180 - (interior angle)

exterior angle = 180 - 109

exterior angle = 71

Note how this is the sum of interior angles B and D, so you could use the remote interior angle theorem here.

Hello, a car was purchased for $20,000.

This is the initial value.

The car depreciates by 22% of each year.

After 1 year, the value is the initial value 20,000 minus 22% of 20,000.

[tex]20000-20\%*20000=20000\cdot (1-20\%)=20000\cdot (1-0.20)=20000\cdot 0.8=16000[/tex]

After 2 years, the value is.

[tex]20000\cdot 0.8\cdot 0.8=20000\cdot0.8^2=12800[/tex]

Let's take n a positive integer, after n years, the value is.

[tex]\large \boxed{\sf \bf \ 20000\cdot0.8^n \ }[/tex]

a) After 12 years, the value is.

[tex]20000\cdot0.8^{12}=1374.389...[/tex]

This is rounded to $1,374

b) We need to find n such that

[tex]20000\cdot0.8^n=100\\\\ln(20000)+nln(0.8)=ln(100)\\\\n=\dfrac{ln(100)-ln(20000)}{ln(0.8)}=23.74...[/tex]

This is around 23.75 meaning 23 years and 75% of 1 year (meaning 9 months).

So to be worth less than $100, 23 years and 9 months are required.

Thank you

Answer:

Step-by-step explanation:

Imagine coordinate system

I quarter is where x>0 and y>0  {right top} and it is (0°,90°)

II quarter is where x<0 and y>0  {left top} and it is (90°,180°)

III quarter is where x<0 and y<0  {left bottom} and it is (180°,270°)

IV quarter is where x>0 and y<0  {right bottom} and it is (270°,360°)

Now, we have an angle wich vertex is point (0,0) and one of its sides is X-axis and the second lay at one of the quarters.

For the trig functons of an angle created by this second side always are true:

In first quarter all functions are >0

in second one only sine

in third one: tangent and cotangent

and in fourth one: cosine

{You can check this by selecting any point on the second side of angle and put it's coordinates to formulas of these functions:

[tex]\sin \phi=\dfrac y{\sqrt{x^2+y^2}}\,,\quad \cos \phi=\dfrac x{\sqrt{x^2+y^2}}\,,\quad \tan\phi=\dfrac yx\,,\quad \cot\phi=\dfrac xy[/tex]  }

So:

sinφ<0  ⇒ III or IV quarter

tanφ<0  ⇒ I or IV quarter

IV quarter  ⇒  φ ∈ (270°, 360°)

Answer:

Here's what I get  

Step-by-step explanation:

a. Net of a cube

Fig. 1 is the net of a cube  

b. Does the formula work?

Tony's formula works if you ignore dimensions.

There are six squares in the net of a cube.

If each side has a unit length s, the total area of the cube is 6s.

c. Will the formula work for any rectangular prism?

No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.

d. Area of a rectangular prism

A rectangular prism has six faces.

A top (T) and a bottom (b) — A = 2×l×w

A left (L) and a right (R)    —   A = 2×l×h

A front (F) and a back (B) —   A = 2×w×h

                                  Total area = 2lw + 2lh + 2wh

If l = 5 m, w = 6 m and h = 8 m,

[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]

Answer:

Loudness (L) = 6.48 dB

Step-by-step explanation:

Given:

Loudness (L) = k / d² , where k = constant

So,

70 = k / 14²

k = 13,720

New distance = 46 feet

Find:

Loudness (L) = ?

Computation:

Loudness (L) = 13,720 / 46²

Loudness (L) = 13,720 / 2,116

Loudness (L) = 6.48 dB

Answer:

The amount (revenue) she makes in the third month to break even is $97

Step-by-step explanation:

The given parameters are;

The cost of the app = Initial cost + fees for producing the app

The amount she loss in the first month = Cost of the app - revenue = $324

The amount she loss in the second month = Loss from first month - revenue in second month = $324 - revenue in second month = $97

The amount Whitney has to make in the third month to break even  is therefore;

The amount she makes in the third month to break even is given by the equation;

Revenue from third month - Loss from second month = 0

Which gives;

The amount she makes in the third month to break even is given by Revenue from third month - $97 = 0

∴ Revenue from third month = $97

The amount (revenue) she makes in the third month to break even = $97

Answer:

tan(π−2/5)

decimal form -0.42

Answer:

-0.42

Step-by-step explanation:

Answer:

4.61 m

Step-by-step explanation:

The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building

Using trig ratios

tan48° = H/d where H = height of taller building and d = their distance apart = 12 m

H = dtan48° = 12tan48° = 13.33 m

Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°

Using trig ratios

tan36° = h/d where h = height of shorter building

h =dtan36° = 12tan36° = 8.72 m

Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m

Answer:

The answer is 1/3

Answer:

1/3

Step-by-step explanation:

The factors of 5 are 1,5;

* The factors of 15 are 1,3,5,15.

We can see that the GCD is 5 because it is the largest number by which 5 y 15 can be divided without leaving any residue.

To reduce this fraction, simply divide the numerator and denominator by 5 (the GCF).

So, 5 /15

= 5÷5 /15÷5

= 1 /3

Answer:

At x intercept, x = 0

2.8(0)+5.7y+5.8=0

y=-5.8/5.7

=-1.02

At y intercept, y=0

2.8x+5.7(0)+5.8=0

x=-5.8/2.8

=-2.07

Answer:

X ans y intercepts are

xintercept (s) : (-2.0,0) you can roud if necessary

y intercept(s) : (0,-1.01754385) you can round if nessecary

Step-by-step explanation:

to find the [tex]x[/tex] and [tex]y[/tex] intercepts simply plug in [tex]o[/tex] to replace [tex]x[/tex] then when you solve for [tex]x[/tex] plug in [tex]x[/tex]to solve for [tex]y[/tex]

Answer:

7 * 4 / 2 = 28/2 = 14

Step-by-step explanation:

You are timed. I will just give you the formula where its multiplying the Diagonals and dividing by 2.

x= -4 w= 1 z= -3 y= 5

This is the answer!

Answer:

82

Step-by-step explanation:

78 + 4 = 82

Answer:

82 students

Step-by-step explanation:

The chart has a total of 82 students in the 18 to 22 age category, as 78 + 4 = 82.

Answer:

The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.

Step-by-step explanation:

The perimeter ([tex]p[/tex]) of a rectangle, measured in centimeters, is represented by this formula:

[tex]p = 2\cdot (w+l)[/tex]

Where [tex]w[/tex] and [tex]l[/tex] are width and length, measured in centimeters.

If [tex]w = 6.8\cdot d-4.2[/tex] and [tex]l = 9.2\cdot d+8.7[/tex], the expression that represents the perimeter is:

[tex]p = 2\cdot (16\cdot d +4.5)[/tex]

[tex]p = 32\cdot d + 9[/tex]

The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.

Answer:

linear equation to express the price is:

y=0.72x+0.21

An eight quarts will cost :  $5.97

Step-by-step explanation:

linear equation represent y=mx+b

let x=quarts ( x=4, x=2)

y= price (3.09 and y=1.65 )

two points (4,3.09) and (2,1.65)

need to find the slope m:

y2-y1/x2-x1

(1.65-3.09)/(2-4) ⇒ m=0.72

y=0.72x+b  find b at point (2,1.65)

1.65=0.72(2) +b  ⇒ b=0.21

y=0.72x +0.21

check : point (4,3.09)

y=0.72(4) +0.21

y=3.09  ( correct)

An eight quarts will cost :

y=0.72(8)+0.21

y=5.97 dollars

Explanation:

Assuming you meant to say

P(A) = 11/20

P(B|A) = 13/20

then,

P(A∩B) = P(A)*P(B|A)

P(A∩B) = (11/20)*(13/20)

P(A∩B) = (11*13)/(20*20)

P(A∩B) = 143/400

Answer:

a

Step-by-step explanation:

Answer:

A.   L = 240 m

Step-by-step explanation:

use similar triangle

L / 60 = 80 / 20

L = (80 * 60) / 20

L = 240 m

YES! quite easily.

I hope you can see the two pairs of corresponding angles between the parallel lines. they'll be equal

and then there's a pair of vertically opposite angle at centre.

that means all pairs of corresponding angles are equal, thus, triangles are similar by AAA

Answer:

[tex]\Large \boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

The triangles can be proven by AA or Angle-Angle similarity.

[tex]\angle QUR \cong \angle TUS[/tex]

The vertical angles are congruent.

[tex]\angle R \cong \angle S[/tex]

The alternate interior angles are congruent.

Answer:

Hey there!

a+b

34+(-6)

34-6

28

Let me know if this helps :)

Answer:

a = 2b/3−1/3

Step-by-step explanation:

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