how many three-letter "words" can Bob make using just these letters?

Answer:

a = 5, b = -12

Step-by-step explanation:

By basic factoring, you get 9 - 12i + [tex]4i^2[/tex]. Since [tex]i^2[/tex] is simply -1, the expression evaluates to 9 - 12i - 4, which is 5 - 12i.

The value of the quantity after 1 year, to the nearest hundredth is 4000.00

The standard exponential equation is eexpressed as:

[tex]P(t)=P_0e^{kt}[/tex]

Given the following parameters

[tex]P_0=4000\\r =0.0005\\t = \frac{1}{50} =0.02 (yearly)[/tex]

Substitute into the formula to have:

[tex]P(t)=4000e^{0.0005(0.02)}\\P(1)=4000e^{0.00001}\\P(1)=4000[/tex]

Hence the value of the quantity after 1 year, to the nearest hundredth is 4000.00

Learn more on exponential equations here: https://brainly.com/question/12940982

Answer:

  51 milligrams

Step-by-step explanation:

Exponential growth or decay can be modeled by the equation ...

  y = a·b^(x/c)

where 'a' is the initial value, 'b' is the "growth factor", and 'c' is the time period over which that growth factor applies. The time period units for 'c' and x need to be the same.

In this problem, we're told the initial value is a = 190 mg, and the value decays to 95 mg in 19 hours. This tells us the "growth factor" is ...

  b = 95/190 = 1/2

  c = 19 hours

Then, for x in hours the remaining amount can be modeled by ...

  y = 190·(1/2)^(x/19)

__

After 36 hours, we have x=36, so the remaining amount is ...

  y = 190·(1/2)^(36/19) ≈ 51.095 . . . . milligrams

About 51 mg will remain after 36 hours.

Answer:

A = -18.

Step-by-step explanation:

We are given that y = 3x +9.

From this, we gather 3x - y = -9.

We then multiply both sides by 2 to get 6x – 2y = -18. Therefore, A = -18.

Answer:

  (a)  6 months

Step-by-step explanation:

The formula for figuring the monthly payment on an amortized loan can be used for finding the length of time it takes to pay off the loan.

That formula is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the number of years.

__

Using the given information, we can solve for t:

  300 = 1568(0.113/12)/(1 -(1 +0.113/12)^(-12t))

  1 -(1 +0.113/12)^(-12t) = 1568(0.113)/(12(300))

  (1 +0.113/12)^(-12t) = 1 -(1568·0.113)/(12·300) ≈ 0.950782

Taking logs, we get ...

  -12t·log(1 +0.113/12) = log(0.950782)

  t = log(0.950782)/(-12·log(1 +0.113/12)) ≈ 0.448739 . . . . years

This fraction of a year is ...

  (12 months/year)(0.448739 years) = 5.38 months

It will take you 6 months to pay off the loan.

Answer:

2/45

Step-by-step explanation:

The probability that a banana is picked for the first one is:

1/10

because there are 10 fruits and one of them is a banana,

Then, the second piece has to be a pear.

For this we have already picked one fruit out of the bag, which leaves 9 fruits in the bag.

There are 4 pears so the probability of picking a pear second is

4/9

To find the probability of a banana and then a pear, you want to multiply these values together

So:

1/10 x 4/9 = 4/90 = 2/45

So the probability is 2/45

Answer:

x = 8

y = 6

Step-by-step explanation:

First and foremost, it's an equilateral triangle, therefore all sides and angles are equal.

Knowing that the sum of angle in a triangle is 180°, therefore each angle is 60°.

Then equating (7x+4)° to 60, we have that,

7x+4=60

7x=60-4

7x=56

x=56÷7

x=8.

Answer: D

Step-by-step explanation:

16+18+19+21+21=95

95/5 is 19
95+37=132

132/6=22

Answer:

12

Step-by-step explanation:

Hey there!

Answer: 25%

[tex] \rightarrow \: (\sf{ \frac{250}{1000} ) \times 100}[/tex]

[tex] \rightarrow \: ( \sf{0.25) \times 100}[/tex]

[tex] \rightarrow \: \sf{ = 25\%}[/tex]

Answer:

25%

Step-by-step explanation:

the quantities must have the same units

1 Kg = 1000 grams

express the quantities as a fraction and multiply by 100%

[tex]\frac{250}{1000}[/tex] × 100% = 0.25 × 100% = 25%

Answer:

37 Feet

Step-by-step explanation:

We can use Pythagoras Theorem to solve this:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]35^{2} +12^{2} =c^{2}[/tex]

[tex]1225+144=c^{2}[/tex]

[tex]1369=c^{2}[/tex]

[tex]\sqrt{1369} =c[/tex]

37 = c

Answer:

37 ft

Step-by-step explanation:

Use Pythagorean Theorem for right triangles to find the hypotenuse

35^2 + 12^2 = Ramp^2       ramp = 37 ft

Answer:

y = -13x+26

Step-by-step explanation:

13x+y=26

y= -13x+26

[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 8x = 33 [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 8x +16 = 33 + 16 [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x + 4) {}^{2} = 49[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 4 = \sqrt{49} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 4 = \pm7[/tex]

Hence, there are two solutions ~

[tex]\qquad \sf  \dashrightarrow \: x + 4 = 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 7 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 4 = - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 7 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 11[/tex]

I hope you understood ~

Answer:

B

Step-by-step explanation:

adding both sides will leave you at x/3=15

then diving by 3, the two 3s will cancel out and you will be left with x=15

The function N =1053(1.23)^m or 1053(1.23)^m = N is an illustration of an exponential function

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 0

So, we have:

N =1053(1.23)^0

N = 1053

Hence, there are 1053 deers on April 1, 2016

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 1

So, we have:

N =1053(1.23)^1

N =1295

Hence, there are 1295 deers on May 1, 2016

An exponential growth function is represented as:

y = a(1 + r)^x

Where r represents the growth rate

By comparison; the monthly growth rate (r) is calculated as:

1 + r = 1.23

Subtract 1 from both sides

r = 0.23

Express as percentage

r = 23%

Hence, the monthly growth rate is 23%

We have the monthly growth rate to be 23%

There are 12 months in a year.

So, the yearly growth rate is:

y = 23%^12

Evaluate

y = 0.00022%

Hence, the yearly growth rate is 0.00022%

We have the monthly growth rate to be 23%

There are 4 weeks in a months

So, the weekly growth rate is:

m = 23%^(1/4)

Evaluate

m = 69%

Hence, the weekly growth rate is 69%

Read more about exponential functions at:

https://brainly.com/question/11464095

Answer:

240 cm³

Step-by-step explanation:

Volume of prism= base area ×height

The base is a rectangle here, and its area has the formula of length ×breadth.

Given

length of base= 10 cm

breadth of base= 6 cm

height of prism= 4 cm

Base area

= 10(6)

= 60 cm²

Volume of prism

= 60(4)

= 240 cm³

Answer:

240 cm³

Step-by-step explanation:

Volume of a rectangular prism: l*w*h

V = l*w*h  <== substitute the numbers (above) for the variables

V = 10*6*4

V = 60*4

V = 240 cm³ (cubed)

Hope this helps!

Answer:

16 children

Step-by-step explanation:

divide 12 by .75 you get 16

hope that helps

Answer:

nonlinear

Step-by-step explanation:

Part B: nonlinear

The radius increases so the line is an arc going upwards not a linear line.

In other words, not a straight line.

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

it's 396

Step-by-step explanation:

I took the k-12 quiz math Surface Area quiz

antecedent : 16

ratio: 2 : 3

=========

antecedent : 2

consequent : 3

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

[tex]\rightarrow \sf \dfrac{2}{3}=\dfrac{x}{24}[/tex]           [ x is antecedent ]

[tex]\rightarrow \sf 2(24)=3(x)[/tex]

[tex]\rightarrow \sf 48=3(x)[/tex]

[tex]\rightarrow \sf x= 16[/tex]

Additional information:

In the ratio, a : b  Here the "antecedent is a" and "consequent is b"

Answer: 4 1/2 doezen cookies

Step-by-step explanation: just subtract. Hope this helps.

Answer:

5

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i had this question on my test

The random number simulator of Molly's throws is an illustration of probability.

The probability of making both free throws is 30%

From the complete question, we understand that:

The simulator is based on numbers 0 to 9

Given that she makes 70% of her free throws, then it means that 7 of the 10 numbers would represent a successful throw, while the other three would represent a missed throw

So, we have:

From the random numbers, she has two successful free throws in:

21 50 64 66 42 03 --- 6 numbers of 20

The probability of making two free throws is then calculated as:

P = 6/20

Evaluate

P = 30%

Hence, the probability of making both free throws is 30%

Read more about probability at:

https://brainly.com/question/251701

Answer:

6x+50=92

Step-by-step explanation:

The x is for how much the classes cost plus the amount they charged her for the gear.

Answer:

Step-by-step explanation:

6 Ampheres or 6A

Step-by-step explanation:

I = Current (unit is Amphere or A)

V = Voltage (unit is Volt or V)

R = Resistance ( unit is Ohm or Ω)

Formulas:

V=IR ; when getting the voltage

R=V/I; when getting the resistance

I=V/R; when getting the current

Solution of the Problem:

First, you have to get the resistance using the first given senario.

Distribute the given values (Voltage=15 Volts or 15V and Current= 5 Ampheres or 5A) to the formula on how to get the resistance.

R=V/I = 15 Volts/5 Ampheres

= 3 Ohms or 3Ω

Now, you have the value of the resistance which is 3 Ohms or 3Ω and the given value of voltage which is 18 Volts or 18V for the second senario.

I=V/R = 18 Volts/ 3 Ohms

= 6 Ampheres or 6A

So, the value of the current is 6 Ampheres or 6A

mark me brainliest and hope this helps!

Step-by-step explanation:

| x - 19 + 11 | = | x - 8 |

look at the picture.

The expression without the absolute value symbol is:

|x - 8| = x - 8, if x > 8

|x - 8| = 0, if x = 8

|x - 8| = 8 - x, if x < 8

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

|(x - 19) + 11|

This can be written as,

= |x - 19 + 11|
= |x - 8|

Now,

|x - 8| = x - 8, if x > 8

|x - 8| = 0, if x = 8

|x - 8| = 8 - x, if x < 8

Thus,

The expression without the absolute value symbol is:

|x - 8| = x - 8, if x > 8

|x - 8| = 0, if x = 8

|x - 8| = 8 - x, if x < 8

Learn more about expressions here:

https://brainly.com/question/3118662

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