how to find out the value of the lettered sides

How To Find Out The Value Of The Lettered Sides

Answers

Answer 1

Step-by-step explanation:

a

sin 46°= a/12.8

a = sin46° * 12.8 = 9.20

b

cos59°=b/16.8

b = cos59°*16.8 = 8.65

Answer 2

Answer:

a = 9.2b = 8.65

Step-by-step explanation:

First Question

To find a we use sine

sin ∅ = opposite / hypotenuse

a is the opposite

12.8 is the hypotenuse

sin 46 = a / 12.8

a = 12.8 sin 46

a = 9.2

Second question

To find b we use cosine

cos∅ = adjacent / hypotenuse

b is the adjacent

16.8 is the hypotenuse

cos 59 = b / 16.8

b = 16.8 cos 59

b = 8.65

Hope this helps you


Related Questions

Un comerciante de algodón de azúcar gana 40 cm por cada algodón vendido pero si no lo logra venderlo pierde 50 céntimos. un día en que fabricó 120 algodones obtuvo una ganancia de 39 soles ¿Cuántos algodones no logró vender ese día?

Answers

Answer:

He fails to sell that day 10 cottons.

Step-by-step explanation:

We are given that a cotton candy merchant earns 40 cents for each cotton sold, but if he cannot sell it he loses 50 cents.

One day when he made 120 cottons, he made a profit of 39 soles.

Let the number of cottons merchant is able to sold be 'x' and the number of cottons merchant is not able to sold be 'y'.

So, according to the question;

The first condition states that he made 120 cottons on one day, that is;

                                   x + y = 120

                                   x = 120 - y    ---------------------- [Equation 1]

The second condition states that merchant earns 40 cents for each cotton sold, but if he cannot sell it he loses 50 cents and due to which he made a profit of 30 soles, that is;

                               [tex]0.40x - 0.50y=39[/tex]

                               [tex]40x - 50y=3900[/tex]

                               [tex]40(120-y) - 50y=3900[/tex]  

                               [tex]4800-40y - 50y=3900[/tex]

                               [tex]90y=4800-3900[/tex]

                                [tex]90 y = 900[/tex]

                                  [tex]y=\frac{900}{90}=10[/tex]

This means that the merchant is not able to sell 10 cottons.

Bruno solved the following equation: 4x + one half(10x − 4) = 6 Step Work Justification 1 4x + 5x − 2 = 6 2 9x − 2 = 6 3 9x = 8 4 x = eight ninths Which of the following has all the correct justifications Bruno used to solve this equation? 1. Multiplication Property of Equality 2. Combine like terms 3. Subtraction Property of Equality 4. Division Property of Equality 1. Distributive Property 2. Combine like terms 3. Subtraction Property of Equality 4. Division Property of Equality 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality 1. Multiplication Property of Equality 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality

Answers

Answer:

Statement                                   Reason

1. [tex]4x+5x-2=6[/tex]                 1. Distributive Property

2. [tex]9x-2=6[/tex]                        2. Combine like terms

3. [tex]9x=8[/tex]                              3. Addition Property of Equality

4. [tex]x=\dfrac{8}{9}[/tex]                               4. Division Property of Equality

Step-by-step explanation:

The given equation is

[tex]4x+\dfrac{1}{2}(10x-4)=6[/tex]

Using distributive property, we get

[tex]4x+\dfrac{1}{2}(10x)+\dfrac{1}{2}(-4)=6[/tex]

[tex]4x+5x-2=6[/tex]

[tex]9x-2=6[/tex]         (Combine like terms)

Using Addition Property of Equality, add 2 on both sides.

[tex]9x=6+2[/tex]

[tex]9x=8[/tex]

Using Division Property of Equality, divide both sides by 9.

[tex]x=\dfrac{8}{9}[/tex]

it's 11 that grade, please help me I'm stuck ​

Answers

Answer:

Limit [tex]$\lim_{x \to 0} f(x)$[/tex] does not exist.

Step-by-step explanation:

To calculate left hand limit, we use a value slightly lesser than that of 0.

To calculate right hand limit, we use a value slightly greater than that of 0.

Let h be a very small value.

Left hand limit will be calculate at 0-h

Right hand limit will be calculate at 0+h

First of all, let us have a look at the value of f(0-h) and f(0+h)

[tex]f(0-h)=f(-h) = \dfrac{-h}{|-h|}\\\Rightarrow \dfrac{-h}{h} = -1[/tex]

[tex]f(0-h)=-1 ....... (1)[/tex]

[tex]f(0+h)=f(h) = \dfrac{h}{|h|}\\\Rightarrow \dfrac{h}{h} = 1[/tex]

[tex]f(0+h)=1 ....... (2)[/tex]

Now, left hand limit:

[tex]$\lim_{x \to 0^{-} } f(x)$\\[/tex] = [tex]$\lim_{h \to 0} f(0-h)$[/tex]

[tex]\Rightarrow[/tex] [tex]$\lim_{h \to 0} f(-h)$[/tex]

Using equation (1):

[tex]$\lim_{x \to 0^{-} } f(x)$\\[/tex] = -1

Now, Right hand limit:

[tex]$\lim_{x \to 0^{+} } f(x)$\\[/tex] = [tex]$\lim_{h \to 0} f(0+h)$[/tex]

[tex]\Rightarrow[/tex] [tex]$\lim_{h \to 0} f(h)$[/tex]

Using equation (2):

[tex]$\lim_{x \to 0^{-} } f(x)$\\[/tex] = 1

Since Left Hand Limit [tex]\neq[/tex] Right Hand Limit

So, the answer is:

Limit [tex]$\lim_{x \to 0} f(x)$[/tex] does not exist.

By first calculating the angle of LMN, calculate the area of triangle MNL. You must show all your working.

Answers

Answer:

16.66cm²

Step-by-step Explanation:

Given:

∆LMN with m<N = 38°

Length of side NL = 7.2cm

Length of side ML = 4.8cm

Required:

Area of ∆MNL

Solution:

Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b

Where sin(A) = Sin(M) = ?

a = NL = 7.2cm

sin(B) = sin(N) = 38°

b = ML = 4.8cm

Thus,

Sin(M)/7.2 = sin(38)/4.8

Cross multiply

4.8*sin(M) = 7.2*sin(38)

4.8*sin(M) = 7.2*0.6157

4.8*sin(M) = 4.43304

Divide both sides by 4.8

sin(M) = 4.43304/4.8

sin(M) = 0.92355

M = sin-¹(0.92355) ≈ 67.45°

Step 2: Find m<L

angle M + angle N + angle L = 180 (sum of angles in a triangle)

67.45 + 38 + angle L = 180

105.45 + angle L = 180

Subtract 105.45 from both sides

Angle L = 180 - 105.45

Angle L = 74.55°

Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)

Where,

a = NL = 7.2 cm

b = ML = 4.8 cm

sin(C) = sin(L) = sin(74.55)

Thus,

Area of ∆MNL = ½*7.2*4.8*0.9639

= ½*33.31

= 16.655

Area of ∆MNL ≈ 16.66cm²

Solve the equation x^2 – 16x + 25 = 0 to the nearest tenth.

Answers

Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

Let Δ be our dicriminant a=1b= -16c= 25Δ= (-16)²-4*25*1=156≥0 so we have two solutions : x and y x= (16-[tex]\sqrt{156}[/tex])/2= 1.7555≈ 1.8y=(16+[tex]\sqrt{156}[/tex])/2=14.244≈ 14.3

Which expression can be simplified to find the slope of the line of best-fit in the scatterplot below? On a graph, a trend line goes through points (4, 35) and (16, 134). StartFraction 134 minus 35 Over 16 minus 4 EndFraction StartFraction 134 minus 16 Over 35 minus 4 EndFraction StartFraction 4 minus 16 Over 35 minus 134 EndFraction StartFraction 4 minus 16 Over 134 minus 35 EndFraction

Answers

Answer:

134-35/16-4 (A)

Step-by-step explanation:

I just know

Answer

A)  134-35/16-4

Step-by-step explanation:

Jim & Gavin share a lottery win of £4750 in the ratio 1 : 4. Jim then shares his part between himself, his wife & their son in the ratio 2 : 6 : 2. How much more does his wife get over their son?

Answers

Answer:

£380

Step-by-step explanation:

Consider the initial win of £4750

Sum the parts of the ratio, 1 + 4 = 5 parts

Divide the win by 5 to find the value of one part of the ratio.

£4750 ÷ 5 = £950 ← value of 1 part of the ratio

Thus Jim's share is £950

Sum the parts of the ratio shared in his family, 2 + 6 + 2 = 10 parts

Divide his share by 10 to find the value of one part

£950 ÷ 10 = £95 , thus

2 parts = 2 × £95 = £190 ← sons share

6 parts = 6 × £95 = £570 ← wife's share

£570 - £190 = £380

Wife gets £380 more than the son

n is an interger -15<3n《6
write the values of n

Answers

Answer:

So for the first few small values of n, we have proven by demonstration that f(n) = n / (n+1).

Our task is to prove that if it works for any positive integer value of n, then it works for n + 1. This way, it must by induction work for all subsequent values of n.

Formally said, we need to prove that if for some positive integer n we can show that f(n) = n / (n+1), then we can conclude that f(n+1) = (n + 1) / (n + 2).

We begin the real "proof" by expanding f(n + 1):

f(n + 1) = f(n) + 1 / ((n+1)((n+1)+1)) because that's based on the construction.

= n / (n+1) + 1 / ((n+1)(n+2)) because f(n) = n / (n+1); this is called "using what you know from earlier".

= n(n+2) / ((n+1)(n+2)) + 1 / ((n+1)(n+2)) because we can multiply the left fraction by (n+2)/(n+2).

= (n2 + 2n + 1) / ((n+1)(n+2)) because we have a common denominator and can combine the numerators.

= (n+1)2 / ( (n+1)(n+2)) because we can factor the numerator now; it is a perfect square.

= (n+1) / (n+2) because we can cancel the common (n+1) factor from the numerator and denominator.

Q.E.D. (which means "that which was to be proven", in other words: "voilà")

Step-by-step explanation:

A same side interior angle of two parallel lines is 20° less than the other same side interior angle. Find the measures of these two angles.

Answers

Answer:

The measures of the two angles are 80 and 100

Step-by-step explanation:

Let [tex]m_1[/tex] and [tex]m_2[/tex] represent the two angles such that

[tex]m_1 = m_2 - 20[/tex]

Required

Find [tex]m_1[/tex] and [tex]m_2[/tex]

The two angles of a same-side interior angle of parallel lines add up to 180;

This implies that

[tex]m_1 + m_2 = 180[/tex]

Substitute [tex]m_2 - 20[/tex] for [tex]m_1[/tex]

[tex]m_1 + m_2 = 180[/tex] becomes

[tex]m_2 - 20 + m_2 = 180[/tex]

Collect like terms

[tex]m_2 + m_2 = 180 + 20[/tex]

[tex]2m_2 = 180 + 20[/tex]

[tex]2m_2 = 200[/tex]

Divide both sides by 2

[tex]\frac{2m_2}{2} = \frac{200}{2}[/tex]

[tex]m_2 = \frac{200}{2}[/tex]

[tex]m_2 = 100[/tex]

Recall that [tex]m_1 = m_2 - 20[/tex]

[tex]m_1 = 100 - 20[/tex]

[tex]m_1 = 80[/tex]

Hence, the measures of the two angles are 80 and 100

convert 4 1/3 feet to inches​

Answers

Answer:

52 inches

Step-by-step explanation:

Answer:

we have, 1 feet =12 inches

13/3 foot =12×13/3 inches

=52 inches.

thereforethe , the answer is 52 inches.

Select the correct answer.
Identify the expression equivalent to 4(x + x + 7) - 2x + 8 - 4 by substituting x = 1 and x = 2.
PLZ HELP

Answers

Answer:

Option (C)

Step-by-step explanation:

Given expression is 4(x + x + 7) - 2x + 8 - 4

When x = 1,

Value of the expression will be,

= 4(1 + 1 + 7) - 2(1) + 8 - 4

= 4(9) - 2 + 8 - 4

= 36 - 2 + 8 - 4

= 38

For x = 2,

= 4(2 + 2 + 7) -2(2) + 8 - 4

= 44 - 4 + 8 - 4

= 44

Now we will check the same for the given options.

Option (A). For x = 1,

6x + 11 = 6(1) + 11

           = 17

For x = 2,

6x + 11 = 6(2) + 11

          = 23

Option (B). For x = 1,

3(x + 7) = 3(1 + 7)

            = 24

For x = 2,

3(x + 7) = 2(2 + 7)

            = 18

Option (C), x = 1

2(3x + 16) = 2[3(1) + 16]

                = 38

For x = 2,

2(3x + 16) = 2[3(2) + 16]

                = 44

Option (D), For x = 1,

            = 19

For x = 2,

2(3x + 16) = 2[3(2) + 16]

                = 44

Since value of the expression for x = 1 and 2 matches with the value in option (C)

Therefore, Option (C) will be the answer.

52:PLEASE HELP Find the slope of the line that passes through the points (8,2) and (9,7)

Answers

Answer:

5/1

Step-by-step explanation:it goes up 5 and over 1

Answer:

5

Solution,

Let the points be A and B

A ( 8 , 2 ) -----> (X1 , y1 )

B ( 9 , 7 ) -------> (x2 , y2)

Now,

Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{7 - 2}{9 - 8} [/tex]

[tex] = \frac{ 5}{1} [/tex]

[tex] = 5[/tex]

Hope this helps..

Good luck on your assignment...

What is the equation for a straight line that would allow you to predict the value of Y from a given value of X. That is, calculate the value of "a" and the value of "b" and then substitute the 2 values into the generic equation (Y = a + bX) for a straight line. (Hint: calculate "b" first)

Answers

Answer:

[tex]m=-\frac{13}{20.8}=-0.625[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]

So the line would be given by:

[tex]y=-0.625 x +9[/tex]

Step-by-step explanation:

We have the following data:

X: 3,3,2,1,7

Y:6,7,8,9,5

We want to find an equationinf the following form:

[tex] y= bX +a[/tex]

[tex]a=m=\frac{S_{xy}}{S_{xx}}[/tex]

Where:

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]

So we can find the sums like this:

[tex]\sum_{i=1}^n x_i = 3+3+2+1+7=16[/tex]

[tex]\sum_{i=1}^n y_i =6+7+8+9+5=35[/tex]

[tex]\sum_{i=1}^n x^2_i =72[/tex]

[tex]\sum_{i=1}^n y^2_i =255[/tex]

[tex]\sum_{i=1}^n x_i y_i =99[/tex]

With these we can find the sums:

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=72-\frac{16^2}{5}=20.8[/tex]

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=99-\frac{16*35}{5}=-13[/tex]

And the slope would be:

[tex]m=-\frac{13}{20.8}=-0.625[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]

So the line would be given by:

[tex]y=-0.625 x +9[/tex]

A package of 8-count AA batteries cost $6.16. A package of 20-count AA batteries cost $15.60. Which statement about the unit prices is true?

Answers

Answer:

The unit prices will be within the range of $0.77 ≤x≤$0.78

Step-by-step explanation:

If a package 8-count AA batteries cost $6.16 and a package of same 20-count AA batteries cost $15.60, to calculate the unit price, the following steps must be carried out:

8 counts AA batteries = $6.16

A unit price (i.e 1 count) = x

Cross multiplying

8 × x = 6.16 × 1

x = 6.16/8

x = $0.77 for a unit price

Similarly, if 20-count AA batteries cost $15.60, then:

20 counta = $15.60

1 count = x

Cross multiplying

20 × x = $15.60 × 1

x = $15.60/20

x = $0.78 for a unit price

From above calculation, of can be seen that the unit price is almost similar but with a difference of $0.01 ($0.78-$0.77) which is insignificant. Based on this, we can conclude that a unit price of the battery is between the range

$0.77 ≤x≤$0.78

Answer:

The 8-count pack of AA batteries has a lower unit price of 0.77

per battery.

Step-by-step explanation:

Find the equation of the line that passes through (3,-4) and is parallel to 3x+y+2=0 Leave your answer in the form y=mx+c

Answers

Answer:

2x+y

Step-by-step explanation:

Simply remove the +2

Answer:

y = - 3x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + y + 2 = 0 ( subtract 3x + 2 from both sides )

y = - 3x - 2 ← in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus

y = - 3x + c ← is the partial equation

To find c substitute (3, - 4) into the partial equation

- 4 = - 9 + c ⇒ c = - 4 + 9 = 5

y = - 3x + 5 ← equation of line in form y = mx + c

1/5 of a chocolate chip cookie has 30 cal how many calories are in a whole cookie

Answers

Answer:

150 cal

Step-by-step explanation:

5x30=150

Answer:

150 calories.

Step-by-step explanation:

Assuming there is the same amount of chocolate as well as cookie dough throughout the whole cookie.

You know that 1/5 of a chocolate chip cookie has 30 calories.

Find one cookie, by multiply 5 to both numbers. Set the equation:

1/5x = 30

Isolate the variable. Multiply 5 to both sides:

(1/5x) * 5 = (30) * 5

x = 30 * 5

x = 150

150 calories is your answer.

HELP PLEASEEE ASAAAAPPPPPPPPPPPP I WILL GIVE BRAINLY TO THE FIRST ONE!!!!!!!!

Answers

Answer:

the total amount is £ 756.

hope it helps..

2x-2/5=8 Please explain answer

Answers

Answer:

x=21

Step-by-step explanation:

1. 2x-2/5*5=8*5 Multiply the 5 on both sides to cancel out the denominator.

2. 2x-2+2=40+2 Add 2 on both sides to isolate the term with the variable.

3. 2x/2=42/2 Divide both sides by 2 in order to isolate the variable itself. Yay, you got the answer, 21!

Heyy I hope you have a great day, this took forever to type so it would be very appreciated if you marked this answer as brainliest... UwU

WILL MARK BRAINLIEST
PLEASE ANSWER

Answers

Answer:

no

Step-by-step explanation:

hey

Omg no way I don’t get it if u get the answer lmk

Bacteria in a petri dish doubles every 10 minutes.
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
(Show step by step)

Answers

Answer:

Step-by-step explanation:

Givens

Petri Dish A sees a double ever 10 minutes

Petri Dish B sees a double ever 6 minutes

Consequences

A doubles 60 / 10 = 6 times.

B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A

(42) A school only provides bus service
to students who live a distance greater
than 2 miles away from the school. On a
coordinate plane, the school is located at
the origin, and Michael lives at the closest
point to the school on Maple Street,
which can be represented by the line
y = 2x – 4. If each unit on the coordinate
plane represents 1 mile, does Michael
live far enough from the school for bus
service?

Answers

Answer:

~1.8 mile

Step-by-step explanation:

Michael lives at the closest  point to the school (the origin) on Maple Street,  which can be represented by the line  y = 2x – 4.

This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.

Denote equation of y2 is y = ax + b,

with a is equal to negative reciprocal of 2 => a = -1/2

y2 pass the origin (0, 0) => b = 0

=> Equation of y2:

y = (-1/2)x

To find location of Michael's house, we get y1 = y2 or:

     2x - 4 = (-1/2)x

<=> 4x - 8 = -x

<=> 5x = 8

<=> x = 8/5

=> y = (-1/2)x = (-1/2)(8/5) = -4/5

=> Location of Michael' house: (x, y) = (8/5, -4/5)

Distance from Michael's house to school is:

D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) =  ~1.8 (mile)

Create a birthday Polynomial with 07.01.2006

Answers

Answer:

Step-by-step explanation:

the birthday date is : 07/01/2006 so the numbers are :  07012006 let's switch them : 60021070 we have 8 numbers so our highest degree is 7 6*(x∧7)+0*(x∧6)+0*(x∧5)+2*(x∧4)+1*(x³)+0*(x²)+7*x+0*(x∧0) 6*(x∧7)+2*(x∧4)+x³+7x  

Here is another example :

1,305 divided by 31,828 x100

Answers

Answer:

[tex]4 \frac{1}{10}[/tex]

Step-by-step explanation:

=> [tex]\frac{1305}{31828} * 100[/tex]

=> 0.041 * 100

=> 4.1

=> [tex]4 \frac{1}{10}[/tex]

a right square pyramid has a slant height of 20 feet, and the length of a side of the base is 32 feet. what is the height, h, of the pyramid?

Answers

Answer:

The pyramid's height h = 12 ft

Step-by-step explanation:

Notice that the slant height of the pyramid forms a right angle triangle with the segment that joins the bottom end of the slant height with the center of the pyramid's base, and with the pyramid height (h).

The segment joining the slant height with the center of the pyramid's base is one half of the side of the base in length, so that it; 16 feet.

then we have a right angle triangle with hypotenuse given by the pyramid's slant height (20 ft), a leg given by 16 ft, and we need to find the length of the second leg (pyramid's height (h).so we use the Pythagorean theorem:

[tex]hyp^2=leg_1^2+leg_2^2\\(20\,ft)^2= (16\,ft)^2+h^2\\h^2=400\,ft^2-256\,ft^2\\h^2=144\,ft^2\\h=12 \,ft[/tex]

Answer:

C.12ft

Step-by-step explanation:

for people on edmentum

What is this expression in simplified form? 3√3 * 6√6

Answers

Answer:

The answer is 54√2

Step-by-step explanation:

( 3 √ 3)(6√6) = ( 3 × 6) (√ 6 × 3)

= 18√18 = 18( √ 9 × 2)

= 18 ( √9 × √2)

= 18( 3√2)

= ( 18 × 3)√2

= 54√2

Hope this helps you

3√3 x 6√6

multiply whats outside the radical and put it outside:

6 x 3 = 18 ------> 18√x

and multiply what's inside and place it inside:  

3 x 6 = 18  --------> x√18

so now, you have 18√18, which can be simplified to:

18√(9 x 2)

18√9√2 = 18*3√2 =   54√2                                    

                                                                                               

identify an equation in slope intercept form for the line parellel to y=-3x+7 that passes through (2,-4)

Answers

Answer:

y= -3x+2

Step-by-step explanation:

Parallel lines have the same slope. We can form an incomplete equation:

y= -3x+b

(make sure to see why the slope is -3)

We can plug in the coordinates of (2, -4):

-4= -3(2)+b

-4= -6+b

2=b

b is 2! We can form an equation: y= -3x+2

Written Response! Please help!
Evelyn believes that if she flips a coin 480 times, it will land tails up exactly 240 times. What would you tell Evelyn about her prediction?

Answers

Based on Evelyn's response, it can be said that she predicts that there is a 50% chance of the coin landing on tails and a 50% chance of the coin landing on heads.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the coin lands on tails is half of the number of times the coin is tossed. This means she belives that there is an equal chance that the coin would land on either heads or tails.

To learn more about probability, please check: https://brainly.com/question/13234031

Simplify the following expression. 3 – 2(–6x + 3)

Answers

Answer:

-3 + 12x

Step-by-step explanation:

3 - 2(-6x + 3)

3 + 12x - 6

-3 + 12 x

Hope this helped! :)

Suppose it takes
12
hours for a certain strain of bacteria to reproduce by dividing in half. If
45
bacteria are present to begin with, the total number present after
x
days is

f
(
x
)
=
45

4
x
.

Find the total number present after
1
,
2
, and
3
days.

Answers

Answer:

Step-by-step explanation:

The formula is

[tex]y=45(4)^x[/tex]

which models the exponential function

[tex]y=a(b)^x[/tex] where a is the initial amount of whatever it is you have (in our case it's bacteria), b is the growth rate (ours is 4 which means that every day the number from the day before increases by a factor of 4), and x is the number of days. We plug into the formula the values we have, starting with x = 1:

[tex]y=45(4)^1[/tex]

Always raise what's inside the parenthesis first, then multiply in the 45. 4 to the first is 4, and 4 multiplied by 45 is 180. After the first day, there are 180 bacteria present in the culture.

Next, x = 2:

[tex]y=45(4)^2[/tex] which simplifies to

y = 45(16) so

y = 720.

Next, x = 3:

[tex]y=45(4)^3[/tex] which simplifies to

y = 45(64) so

y = 2880

The power in watts,P, that is generated by a certain electric circuit depends on the current in amperes ,i, and can be modeled by the equation P=20(i-3)^2+180, Where i>3. Which of the following gives the value of i in terms of P?


i=3+2squareroot5(P-180)

i=3+1/2sq p-180/5

Answers

Answer:

i = {√(P-180)/20}+ 3

Step-by-step explanation:

Here, we simply need to make i the subject of the formula

that would be;

P -180 = 20(i-3)^2

Divide through by 20

(P-180)/20 = (i-3)^2

Find the square root of both sides

sqr (P-180)/20 = i-3

i = {√(P-180)/20}+ 3

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