the principal p is borrowed at a simple interest rate r for a period of time t. find the loan's future value g P = 700, r = 8.25, t = 3 months

Answer:

x = 5

AC = 6

DC = 8

Step-by-step explanation:

∆ABC ~ ∆CDE

Therefore, [tex] \frac{AB}{ED} = \frac{AC}{DC} [/tex]

AB = 3

ED = 4

AC = x + 1

DC = x + 3

Plug in the values and solve for x:

[tex] \frac{3}{4} = \frac{x + 1}{x + 3} [/tex]

Cross multiply

[tex] 3(x + 3) = 4(x + 1) [/tex]

[tex] 3x + 9 = 4x + 4 [/tex]

[tex] 3x - 4x = -9 + 4 [/tex]

[tex] -x = -5 [/tex]

[tex] x = 5 [/tex]

Plug in the value of x and find AC and DC

AC = x + 1 = 5 + 1 = 6

DC = x + 3 = 5 + 3 = 8

[tex]\\ \rm\Rrightarrow cosB+5cosB-6[/tex]

[tex]\\ \rm\Rrightarrow (1+5)cosB-6[/tex]

[tex]\\ \rm\Rrightarrow 6cosB-6[/tex]

[tex]\\ \rm\Rrightarrow 6(cosB-1)[/tex]

Answer:

6(cosB - 1)

BRAINLIEST, PLEASE!

Step-by-step explanation:

cosB + 5cosB - 6

6cosB - 6

6(cosB - 1)

[tex]4x=-17[/tex] has the same solution as  [tex]5x+8=x-9[/tex]

Option (E) is correct

"An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =."

We have,

[tex]5x+8=x-9[/tex]

By solving the given equation

⇒[tex]5x-x=-9-8[/tex]

⇒[tex]4x=-17[/tex]

Clearly, Option (E) is correct

⇒[tex]x=\frac{-17}{4}[/tex]

Explanation for other options:

(A) [tex]4x=-1[/tex]

⇒[tex]x=\frac{-1}{4}[/tex]

(B) [tex]4x=17[/tex]

⇒[tex]x=\frac{17}{4}[/tex]

(C) [tex]6x=-17[/tex]

⇒[tex]x=\frac{-17}{6}[/tex]

(D) [tex]6x=17[/tex]

⇒[tex]x=\frac{17}{6}[/tex]

∴ [tex]4x=-17[/tex] has the same solution as [tex]5x+8=x-9[/tex]

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Answer:

b x=5

Step-by-step explanation:

20x+10=110

20x+10-10=110-10

20x/20=100/20

x=5

Answer:

x=5

Step-by-step explanation:

20x + 10 = 110

Subtract 10 from each side

20x +10-10 = 110-10

20x = 100

divide by 20

20x/20 =100/20

x= 5

Answer:

the answer is 0.31/ 5.1/8.57.1% /207067

Step-by-step explanation:

ascending order from the smallest to the largest

Answer:

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

  y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

  y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

__

B) The continuous decay rate is the natural log of the growth factor, so is ...

  ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

__

C) For y=.10 (1/10 of the original amount) we find x to be ...

  .1 = .5^(x/30)

  ln(.1) = (x/30)ln(.5) . . . . . take the natural log

  30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

__

D) As x goes to infinity, y goes to zero.

_____

The relationship between growth rate and growth factor is ...

  growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Three identical numbers whose product is 1000

10 * 10 * 10

Answer:

[tex]k = 2.6[/tex]

Step-by-step explanation:

Given

[tex]5k + 3.8 = 3k + 9[/tex]

Required

Solve

[tex]5k + 3.8 = 3k + 9[/tex]

Collect like terms

[tex]5k -3k+ 3.8 = 3k -3k + 9[/tex]

[tex]2k+ 3.8 = 9[/tex]

Subtract 3.8 from both sides

[tex]2k+ 3.8 - 3.8= 9 - 3.8[/tex]

[tex]2k= 9 - 3.8[/tex]

[tex]2k = 5.2[/tex]

Divide through by 2

[tex]k = 5.2/2[/tex]

[tex]k = 2.6[/tex]

Answer:

  $0.50

Step-by-step explanation:

Each trip transports 50 packs at 12 kg each, for a total of 600 kg. That trip nets $300 in income.

Lennox gets paid ($300)/(600 kg) = $0.50/kg, or 50¢ for 1 kg of apples

Answer:5 trucks

Step-by-step explanation: in kahn it’s 4500 divided by 900 because she makes 300 a trip which makes 900$ a truck

Answer:

stop spamming

Step-by-step explanation:

Answer:

Cole's House

Step-by-step explanation:

Cole house is closer because molly and Sophia can go there together because there both girls

Answer:

3.75

Step-by-step explanation:

[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]

The volume of the rectangular prism will be 3.75 cubic meters.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

A box is 1 m high, 2.5 m long, and 1.5 m wide.

Then the volume of the rectangular prism will be

V = L x W x H

V = 1 x 2.5 x 1.5

V = 3.75 cubic meters

Thus, the volume of the rectangular prism will be 3.75 cubic meters.

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Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

Answer:

C Stratified sampling

Step-by-step explanation:

Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.

One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.

Answer:

x2  1-

Step-by-step explanation:

Answer:

x ≥ 0

Step-by-step explanation:

Domain of a function is the x values of a function

The graph extends from 0 to positive infinity.

Since the point at x=0 is closed, the graph includes 0

Answer: $1.83

Step-by-step explanation:

1. Solve this problem: 1+2+4+6+8+10+12+14+16+18+20+22+24+26. There are 15 numbers for 15 days. You want to solve this because each day is doubled. For example: first day is 1 cent, second day is 2 cents, third day is 4 cents, and so on.

2. Answer is 183 cents.

3. Convert 183 cents to dollars.

4. Your answer is $1.83.

Hope it helps!

Answer:

$1.83.

You start with one cent, and add two more cents after that day.

The equation is already solved for y

It's in y = mx+b form where

m = -3 = slope

b = 1 = y intercept

The graph is shown below. It's a straight line through the two points (0,1) and (1,-2).

Note that (0,1) is the y intercept. We use the slope = -3 = -3/1 to move 3 units down and 1 unit to the right to arrive at (1,-2).

Answer:

Option (2)

Step-by-step explanation:

In an arithmetic progression,

[tex]a_1,a_2,a_3.........a_{n-1},a_n[/tex]

First term of the progression,

a = [tex]a_1[/tex]

Common difference 'd' = [tex](a_2-a_1)[/tex]

Recursive formula for the sequence,

a = [tex]a_1[/tex]

[tex]a_n=a_{n-1}+d[/tex]

By applying these rules in the recursive formula,

[tex]a_1=\frac{4}{5}[/tex]

[tex]a_n=a_{n-1}+\frac{3}{2}[/tex]

Common difference 'd' = [tex]\frac{3}{2}[/tex]

Therefore, Option (2) will be the answer.

Answer:

Step-by-step explanation:

Given that:

[tex]x = 5 + In (t)[/tex]

[tex]y = t^2+2[/tex]

At point (5,3)

To find an equation of the tangent to the curve at the given point,

By without eliminating the parameter

[tex]\dfrac{dx}{dt}= \dfrac{1}{t}[/tex]

[tex]\dfrac{dy}{dt}= 2t[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ \dfrac{dy}{dt} }{\dfrac{dx}{dt} }[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ 2t }{\dfrac{1}{t} }[/tex]

[tex]\dfrac{dy}{dx}= 2t^2[/tex]

[tex]\dfrac{dy}{dx}_{ (5,3)}= 2t^2_{ (5,3)}[/tex]

t²  + 5 = 4

t² = 4 - 5

t² = - 1

Then;

[tex]\dfrac{dy}{dx}_{ (5,3)}= -2[/tex]

The equation of the tangent  is:

[tex]y -y_1 = m(x-x_1)[/tex]

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

By eliminating the parameter

x = 5 + In(t)

In(t)  = 5 - x

[tex]t =e^{x-5}[/tex]

[tex]y = (e^{x-5})^2+5[/tex][tex]y = (e^{2x-10})+5[/tex]

[tex]\dfrac{dy}{dx} = 2e^{2x-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2e^{10-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2[/tex]

The equation of the tangent  is:

[tex]y -y_1 = m(x-x_1)[/tex]

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

Answer:

This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term

   Let Pn represent the nth term in the sequence

   Then Pn = (1/3)^n-1

   From this P14 = (1/3)^13 = 1/1594323

5. The sum of the first n terms of a GP beginning a with ratio r is given by

   Sn = a* (r^n+1 - 1)/(r - 1)

   With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500

THIS IS THE COMPLETE QUESTION BELOW;

In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.

What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?

A. 0.10

B.0.50

C. 0.66

D. 0.06

Answer:

OPTION D is correct

d)0.06

the probability that a randomly selected team from Littletown goes to the city and state playoffs is [tex]0.06[/tex]

Step-by-step explanation:

The probability that a baseball team goes to city playoffs is 0.30.

P(baseball team goes to city playoffs)=0.30

The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.20.

P(team goes to state playoffs given that the team goes to the city playoffs)=0.20

From our knowledge of set, we know that

P(A | B)= P(A ∩ C)/P(C)

where A= city playoffs

B= state playoffs

P(State play off | city play off)=0.20

P(State play off ∩ city play off)/P(city play off,)=0.20

P(State play off ∩ city play off)/0.30 =0.20

P(State play off ∩ city play off)= 0.30 × 0.20

= 0.06

Hence,the probability that a randomly selected team from Littletown goes to the city and state playoffs is 0.06

Hence, the commutative property of addition is not used.

What is an expression?

A mathematical expression is in form of variables and constants separated by their arithmetic operation.

As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],

Distributive property which is [tex]a(b+c) = ab + ac[/tex],

Commutative property which is [tex]a + b = b + a[/tex].

Here given that,

[tex]2 (x+5)+7x=(2x+10)+7x[/tex]      

[tex](2x+10)+7x=(2x+10)+7x[/tex]         ( distributive property of multiplication)

[tex](2x+7x)+10=(2x+7x)+10[/tex]        ( it is associative property of addition)

[tex](8x)+10=(8x)+10[/tex]        ( it is a commutative property)

Hence, the commutative property of addition is not used.

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Answer:

7/12

Step-by-step explanation:

1/6 +1/12+2/6

=1×2/6×2 +1/12+2×2/6×2

=2/12+1/12+4/12

final answer is

= 7/12

1/6 + 1/12 + 2/6

= 2/12 + 1/12 + 4/12

= (2 + 1 + 4)/12

= 7/12

Answer:

c=-9

Step-by-step explanation:

Hello,

[tex](ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9[/tex]

We can identify the like terms so:

a = 4

b-3a = c

3b = 9 <=> b = 3

So c = 3 - 3*4 = 3-12 = -9

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

B. More

Step-by-step explanation:

This is according to the law of large numbers

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.

An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed

Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.

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Answer:

Step-by-step explanation:

Hello, this is false.

The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: 30 i think 10x3=30

Step-by-step explanation:

Answer:

Inokkohgy8uokokj76899