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Answer:

f(t) = 202,444(1.05)^t

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)^t

A = final amount

P = principle amount

r = interest rate

t = time

Step 1: Find rate r

212,566.20 = 202,444(1 + r)¹

1.05 = (1 + r)¹

1.05 = 1 + r

r = 0.05

Step 2: Define variables

P = 202,444

r = 0.05

Step 3: Plug in variables into formula

A = 202,444(1 + 0.05)^t

A = 202,444(1.05)^t

a)

X + Y = 5

2X - Y = 9      

X + 2X + Y - Y = 5 + 9

3X = 14

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:

X+ Y = 5

14/3 + Y = 5

Y = 5 - 14/3

.........................

b)

3X - Y = 10

X + Y = 18        

3X + X - Y + Y = 10 + 18

4X = 28

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:

X + Y = 18

7 + Y = 18

Y = 18 - 7

Answer:

Step-by-step explanation:

- 2(5y - 1) - y = - 4(y - 3)

Expand the terms in the bracket

That's

-10y + 2 - y = - 4y + 12

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

That's

- 10y - y + 4y = 12 - 2

- 7y = 10

Divide both sides by - 7

We have the final answer as

Hope this helps you

Answer:

$2.64

Step-by-step explanation:

Selling them at 5 cents each ($0.05), he could sell 1 dozen buttons for

12 * $0.05 = $0.60

As he bought them at $0.38 per dozen, the profit per dozen would be

$0.60 - $0.38 = $0.22

As 12 dozen is 1 gross, the profit per gross would be

12 * $0.22 = $2.64

3 x 12 = 36

.5 x 36 = 18.0

36 divided by .38 is about 94.7

18 - 94.7 = -76.7

ANSWER:

about -76.7

(I may have done this wrong

Answer:

0.0276

Step-by-step explanation:

The computation of the probability that the next driver is texting while driving is shown below:

= Fourth pull failure × fifth pull success

where,

Fourth pull failure is (1 - 0.52)^4

And, the fifth pull success is 0.52

Now placing these values to the above formula

So,

= (1 - 0.52)^4 × 0.52

= 0.0276

Hence, the probability is 0.0276

The number of weeks Bart has been depositing money is 9 weeks according to investment and time.

The number of weeks of money depositing will be given by the formula -

Number of weeks = total amount deposited each week/total number of weeks × 100

Keep the values in formula to find the number of weeks of money deposit

Number of weeks = 90/10

Perform division that will include cancelling zeroes

Number of weeks = 9

Hence, Bart deposited the money for 9 weeks.

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Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)

Answer:

[tex]\bold{sin(38^\circ)=cos(52^\circ)}[/tex]

Step-by-step explanation:

Given that [tex]\triangle KJL[/tex] is a right angled triangle.

[tex]\angle JKL = 52^\circ\\\angle KLJ = 38^\circ[/tex]

and

[tex]\angle KJL = 90^\circ[/tex]

Kindly refer to the attached image of [tex]\triangle KJL[/tex] in which all the given angles are shown.

To find:

sin(38°) = ?

a) cos(38°)

b) cos(52°)

c) tan(38°)

d) tan(52°)

Solution:

Let us use the trigonometric identities in the given [tex]\triangle KJL[/tex].

We have to find the value of sin(38°).

We know that sine trigonometric identity is given as:

[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]sin(\angle JLK) = \dfrac{JK}{KL}\\OR\\sin(38^\circ) = \dfrac{JK}{KL}[/tex]....... (1)

Now, let us find out the values of trigonometric functions given in options one by one:

[tex]cos\theta =\dfrac{Base}{Hypotenuse}[/tex]

[tex]cos(\angle JLK) = \dfrac{JL}{KL}\\OR\\cos(38^\circ) = \dfrac{JL}{KL}[/tex]....... (2)

By (1) and (2):

sin(38°) [tex]\neq[/tex] cos(38°).

[tex]cos(\angle JKL) = \dfrac{JK}{KL}\\OR\\cos(52^\circ) = \dfrac{JK}{KL}[/tex] ...... (3)

Comparing equations (1) and (3):

we get the both are same.

[tex]\therefore \bold{sin(38^\circ)=cos(52^\circ)}[/tex]

Answer:

B in EDG

Step-by-step explanation:

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Hi my lil bunny!

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Let's solve your equation step-by-step.

[tex]-8 + 4m = 2[/tex]

Step 1: Simplify both sides of the equation.

[tex]4m - 8 = 2[/tex]

Step 2: Add 8 to both sides.

[tex]4m - 8 + 8 = 2 + 8 \\4m = 10[/tex]

Step 3: Divide both sides by 4.

[tex]\frac{4m}{4} = \frac{10}{4} \\m = \frac{5}{2}[/tex]

Answer : [tex]\boxed {m = \frac{5}{2} }[/tex]

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Have a great day/night!

❀*May*❀

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

Explanation:

The given exterior angle 97 is adjacent to the interior angle 180-97 = 83. This is the base angle of the isosceles triangle. The other base angle is directly above it. The base angles are always opposite the congruent sides.

The missing interior angle (adjacent to the blue angle x) is unknown, so we'll call it angle y. This angle adds to the other two base angles (83 each) to get a sum of 180. Adding any three interior angles of a triangle always gets you 180

y+83+83 = 180

y+166 = 180

y = 180-166

y = 14

Angle x and y are supplementary. They form a 180 degree angle

x+y = 180

x = 180-y

x = 180-14

x = 166

As you can see, the base angles combine to form the exterior angle we're after. This is because of the remote interior angle theorem.

Answer:

$7520.55

Step-by-step explanation:

Cost of truck = $8000

Residual value = $1000

Estimated useful life = 7 years

Depreciation = (cost of asset - salvage value) / useful life

Depreciation = (8000 - 1000) / 7

Depreciation = 7000 / 7

Depreciation = $1000

Truck was purchased on July 9, Therefore, Depreciation by the end of year one will be;

Number of days between July 9 and year end = 175 days

Daily Depreciation = $1000 / 365 = $2.739

Total Depreciation by year end = (daily Depreciation * 175 days) = $479.45.

Book value at the end of year 1 = (8000 - 479.45)

= $7520.55

Answer:

The answer is "$7,500".

Step-by-step explanation:

Formula:

In the month of July-December the depreciation:

[tex]\frac{\text{Cost-Residual}}{\text{Useful life}}\times \frac{6}{12} \\[/tex]

Cost-Residual= costs -residual value

Given:

Cost-Residual = $8, 000 - $ 1,00

                        = $7,000

Useful life= 7 years

Put the value in the above-given formula:

[tex]=\frac{7 000}{7}\times \frac{6}{12}\\\\= 1 000\times \frac{1}{2}\\\\= 5 00\\[/tex]

Therefore, the book value on point at the end of one year is:

= $8,000 -$ 500

= $7,500

Answer:

The next step is add x to each side

Step-by-step explanation:

-x + 6 = 5 - 3x

Subtract 5 from each side

-x + 6-5 = 5-5 - 3x

-x+1 = -3x

Add x to each side

-x+1 = -3x+x

1 = -2x

Answer:

Step-by-step explanation:

all you need to do is solve for x right? so in that case when you subtract 5 from both sides you get -x+1=-3x

then you will add x on each side

you should now have 1=-2x

divide each side by -2 and then you will have

-1/2=x

Answer:

1. One Solution

Step-by-step explanation:

y=2x+1

−3y=6x+6

Divide the second equation by -3

−3y/-3=6x/-3+6/-3

y = -2x-2

The slopes are different so we know that the lines are not parallel

The will intersect at a point

There will be one solution

Answer:

y = - 140

Step-by-step explanation:

The statement

y varies jointly as x & z is written as

to find y when x = 7 and z = -5 we must first find the relationship between the variables

when y = - 180

z = 15

x = - 3

- 180 = k(15)(-3)

-180 = - 45k

Divide both sides by - 45

k = 4

The formula for the variation is

when

x = 7

z = -5

y = 4(7)(-5)

y = 4(-35)

Hope this helps you

Answer:

113 degrees

Step-by-step explanation:

Measure of arc ADCB = 58+108+60 = 226 degrees

Measure of angle B = 226/2 = 113 degrees

Answer:50

Step-by-step explanation:

Answer:

[tex]\frac{1}{6^{2} }[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

Given a = 6, then

[tex]6^{-2}[/tex] = [tex]\frac{1}{6^{2} }[/tex]

The 3rd option is correct i.e. if a = 6, then by the property of exponentiation, we can conclude that a⁻² = 1/6².

Exponentiation is a mathematical operation that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b raised to the power of n." It is written as bⁿ and is pronounced as "b raised to the power of n."

When n is a positive integer, bⁿ = b × b × b ×...× b (n times)

and b⁻ⁿ = 1/bⁿ ...(1)

When n = 0, bⁿ = 1

Given that a = 6 and n = 2.

Using (1), we get

a⁻² = 6⁻² = 1/6²

Therefore, the 3rd option is correct i.e. if a = 6, then by the property of exponentiation, we can conclude that a⁻² = 1/6².

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Answer:

Step-by-step explanation:

y = -2x - 5

perp. slope: 1/2

y + 2 = 1/2(x + 1)

y + 4/2 = 1/2x + 1/2

y = 1/2x - 3/2

Answer:

B. Congruent - SSS

Step-by-step explanation:

Since, corresponding sides of both the triangles are congruent. Hence, both the triangles are congruent by SSS Postulate.

ΔMNO ≅ ΔPQR due to Congruent-SSS

Two triangles are said to be congruent if their corresponding sides and angles are equal.

Given:

In ΔMNO and ΔPQR

Side ME=Side PQ

Side NO=Side QR

Side MO=Side PR

MNO ≅PQR

Since, corresponding sides of both the triangles are congruent.

So, both the triangles are congruent by SSS Postulate.

Hence , ΔMNO ≅ ΔPQR

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The equation is written as 3x + 7 = x - 15. And the solution of the equation will be negative 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Multiple times the amount of a number expanded by 7 is equivalent to a similar number diminished by 15.

Let the number be 'x'.

The three times the number plus 7. Then the expression is given as,

⇒ 3x + 7

The number 'x' is decreased by 15. Then the expression is given as,

⇒ x - 15

Both expressions are equal to each other. Then we have

3x + 7 = x - 15

3x - x = - 15 - 7

2x = - 22

x = - 11

The equation is written as 3x + 7 = x - 15. And the solution of the equation will be negative 11.

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Answer:

5, 5, 10, 15, 20

Step-by-step explanation:

Since the mean of the 5 numbers is 11, we know that the sum of the 5 numbers is 5 * 11 = 55. If we call the numbers x, x, 2x, 3x and 4x respectively based off of the ratio, we can write:

x + x + 2x + 3x + 4x = 55

11x = 55

x = 5 so 2x = 2 * 5 = 10, 3x = 3 * 5 = 15 and 4x = 4 * 5 = 20, therefore, the numbers are 5, 5, 10, 15, and 20.

Given that

To Find.

Solution .

→ Let's assume these numbers as

→ x , x , 2x , 3x and 4x

→ Mean of any observations is = Sum of observations/ Number of observations.

→ Sum of observations = x+x+2x+3x+4x

→ 11x

→ Number of observations = 5

→ Mean = 11

→ 11 = 11x/5

→ 11 (5) = 11x

→ 11(5)/11 = x

→ value of x = 5

Putting the value of x for finding all numbers .

→ 1st number = x → 5

→ 2nd number = x → 5

→ 3rd number = 2x → 10

→ 4th number = 3x → 15

→ 5th number = 4x → 20

Answer:

Option (D) : 13

Step-by-step explanation:

Mode is the observation which occurred the most number of time.

Therefore, mode = 13

Answer:

x= 8

Step-by-step explanation:

The equation of direct variation is

y = kx

When y = 50  when x = 40

50 = k* 40

Divide each side by 40

50/40 = k

5/4 = k

The equation is

y = 5/4x

Let y = 10

10 = 5/4x

Multiply each side by 4/5

4/5 * 10 = 5/4 x * 4/5

8 = x

Answer:

Step-by-step explanation:

A kite is symmetrical about its vertical axis, so

if it is a kite, P is the reflection of  (b,0), so its coordinates are

(-b,0) by reflection about the y-axis.

Answer:

a^5b^8/a^4b^10

= a^5-4 b^8-10

= a^1 b^-2

= a/b^2

I hope this helps

if u have question let me know in comments ^_^

Answer:

Hey there!

Point n is either -3+5 or -3-5.

Thus, the two possible values are 2 or -8.

Let me know if this helps :)

Answer:

x=27

Step-by-step explanation:

expanding the above expression we get

5x+5=4x+32

grouping numbers with coefficient of x at the left side and constant at the right side we get

5x-4x=32-5

x=27

Answer:

w + 2

Step-by-step explanation:

Niki's height = w in

Desmond height = w + 2

Answer:

w+2

Step-by-step explanation:

Since Desmonds is 2 inches taller than Niki, w+2 would make the most sense.

Answer: -12s + -2

Step-by-step explanation: You need to combine the like terms so -3sx4s = -12s and 2+-1 = -2 so it’s -12s + -2 or -12s - 2

Answer:

-12s²+11s-2

Step-by-step explanation:

(-3s+2)(4s-1)

First you have to FOIL (First, inner, outter, last)

First: -3s × 4s

Inner: -3s × -1

Outter: 2 × 4s

Last: 2 × -1

Now you should have -12s² + 3s + 8s -2

----------------------

Next you combine your like terms

Finally you have your answer, -12s²+11s-2 .

Answer:

11

Step-by-step explanation:

4=1

14=2

24=3

34=4

40=5

41=6

42=7

43=8

44=9

45=10

46=11

You will encounter 11 4s.