Enter the exponential function using t (for time) as the independent variable to model the situation. Then find the value of the function after the given amount of time. A new savings account is opened with $200 and gains 3.1% yearly for 8 years. The exponential function that models the situation is . After 8 years, the savings account has $ . , , , and .

Answer:

150.8 m³

48π m³

Step-by-step explanation:

V = πr²h/3

V = π · 4² · 9/3

150.8 m³

Answer:

OA. 81

Step-by-step explanation:

A composite number is a positive integer that can be formed by multiplying two smaller positive integers.

81 = 9 x 9

81 = 3 x 27

she can buy 10 cases

Step-by-step explanation:

200-159= 61

61÷5.99 = 10.1

Answer:

The 1st step in evaluating the expression is doing the equation in the paranthesis. PEMDAS states we do the paranthesis 1st.

Answer: 13/4

Step-by-step explanation: it was 3.25 and that as a fraction is 13/4

3/4 + ( 1/3 × 6 ) + 1/2 =

3/4 + 2/4 + ( 2 ) =

3 + 2/4 + 8/4 =

5/4 + 8/4 =

5 + 8/4 =

13/4

Answer:

The mass of Element X will reach 62 grams in 7.0 years.

Step-by-step explanation:

We can find the time of decay of Element X by using the exponential decay equation:

[tex] \frac{dm}{dt} = -\lambda t [/tex]

The solution of the above equation is:

[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex]     (1)

Where:  

t: is the time =?

λ: is the decay constant                                                                                        

[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams

[tex]m_{0}[/tex]: is the initial mass = 90 grams

First, we need to calculate λ

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]   (2)    

Where [tex]t_{1/2}[/tex] is the half-life = 13 years

By entering equation (2) into (1) and solving for "t" we have:

[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]    

[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]      

[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]  

Therefore, the mass of Element X will reach 62 grams in 7.0 years.

I hope it helps you!

Answer:

x=9

Step-by-step explanation:

Pretty self explanatory.

Answer:

15, 96, 2, 9, 12.

Answer: 8 feet below sea level is higher

Step-by-step explanation:

Answer:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

55 divided by 10 = 5.5 around 5

Add all your numbers

Divide by the many numbers there are, go by the exact value or estimate if needed.

Answer:

43.

Step-by-step explanation:

Follow PEMDAS (Parentheses, exponents, multiply, divide, add, subtract). First you do 8-4 which is 4, then you multiply 4 by 4 which is 16 since you multiply next, then you add 27 to 16 which then gets you to 43.

Answer:

300 watermelons

Step-by-step explanation:

3:2 ratio

3 is water melons and 2 is mangoes.

200 mangoes were purchased.

200/2=100

The unit rate is 100, so multiply 3 by 100, which is 300.

So Jack bought 300 watermelons, and 298 of which will be devoured by yours truly.

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hope it helps

Answer:

AA

Step-by-step explanation:

AA

Answer:

15+ 8d

After d day,she has read 15 +8d pages

Answer: A would be your answer.

Step-by-step explanation: Internal conflict is when you have a problem with yourself and this means your not intercating with others.

Answer:

88

Step-by-step explanation:

10a-9=14a-25

10a-14a=-25+9

-4a=-16

a=4

10(4)-9+14(4)-25+6(4)+2

40-9+56-25+24+2

88

Answer:

Right skewed

Step-by-step explanation:

The shape of a distribution could be classed based on the position of the peak and position of the tails formed by the distribution. A distribution is described as being Symmetric if the peak is situated at the middle of the distribution with the tails being evenly spread to the right and left of the peak.

When the peak of the distribution shifts either to the left of right, then we have a skewed distribution. A distribution is said to be right skewed if it has a longer tail to the right while it is left skewed if the loner tail is to the left of the distribution.

The distribution Given above, the tail is longer to the right with the peak in the left. Hence we have a right skewed or positively skewed distribution

Answer:

32 cartons

Step-by-step explanation:

Total sets needed

48 + 43 + 46 + 50 = 187

Cartons needed

187 / 6 = 31 1/6

need 32 cartons

Answer:

32 cartons

Step-by-step explanation:

add up all of the students = 187

divide by 6 = 187/6 = 31.16

round = 32 cartons

Answer:

179.996

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

3/4×16=12

12+16(2)=44

Answer:

44 scoops

Step-by-step explanation:

create a proportion of amt of choc syrup to # scoops

1/16 ÷ 1 = 11/4 ÷ s

cross-multiply to get:

s = 16 x 11/4

s = 44 scoops

Answer:

x=110˚

Step-by-step explanation:

We need to first find the other degree inside the triangle

first add 45˚ and 65˚

which is 110˚

subtract 110˚ with 180˚

which is 70˚

So we find x since a straight line is 180˚

subtract 70 and 180

which is 110˚

Hoped I helped!

Answer:

110 degrees

Step-by-step explanation:

A triangle is 180 degrees. So if the missing angle is 70, and 70+x=180 then x=110

Answer:

4.5 cm

Step-by-step explanation:

KL = LM as triangle is isosceles

LM = KM as LF = FM = KN = NM, so the triangle is equilateral

EF ║ NM as LE⊥EF and LN⊥NM

EF is half the midsegment as ∠KLN ≅ ∠MLN, and LN is angle bisector of ∠KLM

Midsegment is half the side length, and all sides are 18 cm.

EF = 1/2(1/2*18) = 4.5 cm

Answer:

95 square units

Step-by-step explanation:

Area of a triangle formula:

A = 0.5bh

Given:

b = 19

h = 10

Work:

A = 0.5bh

A = 0.5(19)(10)

A = 9.5(10)

A = 95

Answer:

Option B, 8 / 6

Step-by-step explanation:

Tangent = Opposite / Adjacent

Tangent of ∠A = Opposite / Adjacent

Tan(A) = 8 / 6 which is the same as Option B

Hope this helps!

Answer: f(x)=x^(2)+14x+40

Answer:

the answer is in the picture above

Step-by-step explanation:

and so is the solution pls give branliest if you wish

Answer:

[tex](g + f)(2) = \sqrt 3 - 3[/tex]

[tex](\frac{f}{g})(-1) = 0[/tex]

[tex](g + f)(-1) = \sqrt{15}[/tex]

[tex](g * f)(2) = -3\sqrt 3[/tex]

Step-by-step explanation:

Given

[tex]f(x) =1 - x^2[/tex]

[tex]g(x) = \sqrt{11 - 4x[/tex]

See attachment

Solving (a): (g + f)(2)

This is calculated as:

[tex](g + f)(2) = g(2) + f(2)[/tex]

Calculate g(2) and f(2)

[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]

[tex]f(2) = 1 - 2^2 = -3[/tex]

So:

[tex](g + f)(2) = g(2) + f(2)[/tex]

[tex](g + f)(2) = \sqrt 3 - 3[/tex]

Solving (b): [tex](\frac{f}{g})(-1)[/tex]

This is calculated as:

[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]

Calculate f(-1) and g(-1)

[tex]f(-1) = 1 - (-1)^2 = 0[/tex]

So:

[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]

[tex](\frac{f}{g})(-1) = \frac{0}{g(-1)}[/tex]

[tex](\frac{f}{g})(-1) = 0[/tex]

Solving (c): (g - f)(-1)

This is calculated as:

[tex](g + f)(-1) = g(-1) - f(-1)[/tex]

Calculate g(-1) and f(-1)

[tex]g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}[/tex]

[tex]f(-1) = 1 - (-1)^2 = 0[/tex]

So:

[tex](g + f)(-1) = g(-1) - f(-1)[/tex]

[tex](g + f)(-1) = \sqrt{15} - 0[/tex]

[tex](g + f)(-1) = \sqrt{15}[/tex]

Solving (d): (g * f)(2)

This is calculated as:

[tex](g * f)(2) = g(2) * f(2)[/tex]

Calculate g(2) and f(2)

[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]

[tex]f(2) = 1 - 2^2 = -3[/tex]

So:

[tex](g * f)(2) = g(2) * f(2)[/tex]

[tex](g * f)(2) = \sqrt 3 * -3[/tex]

[tex](g * f)(2) = -3\sqrt 3[/tex]

Answer:

sub duplicate ratio of

hope it helps

Step-by-step explanation:

1*-2=-2, -2*-2=4, -2*4=-8, -8*-32=256