Ahhhhh what is 11/12-(-10)-5/6

Henri has $24000 invested in stocks and bonds. The amount in stocks is $6000 more than three times the amount in bonds. Call the

andrey2020 [161]

Answer:

Henri invested $ 4,500 in bonds and $ 19,500 in stocks.

Step-by-step explanation:

Given that Henri has $ 24000 invested in stocks and bonds, and the amount in stocks is $ 6000 more than three times the amount in bonds, to determine the amount that Henri invested in stocks (S) and the amount he invested in bonds (B), the following calculations must be performed:

6000 + 3B + B = 24000

3B + B = 24000 - 6000

4B = 18000

B = 18000/4

B = 4500

S = 6000 + 3x4500

S = 6000 + 13500

S = 19500

Thus, Henri invested $ 4,500 in bonds and $ 19,500 in stocks.

7 0

2 years ago

An object is heated to 100°. It is left to cool in a room that

stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one. It involves natural logs and being able to solve equations that require natural logs. The formula is as follows:

$T(t)=T_{1}+(T_{0}-T_{1})e^{kt}$ where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value. That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

$80=30+(100-30)e^{5k}$ which simplifies to

$50=70e^{5k}$ Divide both sides by 70 to get

$\frac{50}{70}=e^{5k}$ and take the natural log of both sides:

$ln(\frac{5}{7})=ln(e^{5k})$

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared). That gives us:

$-.3364722366=5k$

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

$T(20)=30+(100-30)e^{-.0672944473(20)}$ which simplifies to

$T(20)=30+70e^{-1.345888946}$

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

$35=30+100-30)e^{-.0672944473t}$ which simplifies to

$5=70e^{-.0672944473t}$

Now divide both sides by 70 and take the natural log of both sides:

$ln(\frac{5}{70})=ln(e^{-.0672944473t})$ which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

3 0

2 years ago

12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

never [62]

Answer:

Part a) Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Domain of f+g = {-1, 0, 1, 2, 3}

Part d) Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

Part a) Determining the domain of f

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Determining the domain of g

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Determining the domain of f+g

When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.

As,

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

Domain of g : {-1, 0, 1, 2, 3, 4}

As when there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains

So, the domain of f+g = {-1, 0, 1, 2, 3}

Part d) List the ordered pairs of f-g

As

f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1) = 14 - 4 = 10

(f - g)(x) = f(0) - g(0) = 7 - 5 = 2

(f - g)(x) = f(1) - g(1) = 4 - 6 = -2

(f - g)(x) = f(2) - g(2) = 5 - 1 = 4

(f - g)(x) = f(3) - g(3) = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords: domain, function, f+g, f-g

Learn more about domain, and ordered pairs from brainly.com/question/11422136

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7 0

2 years ago

Two fractions equivalent to 28/32

DanielleElmas [232]

14/16 & 7/8 Would be two Equivalent

6 0

2 years ago

Read 2 more answers

94b + 48 < b + 54 < 94b + 82

Softa [21]

DATES: The rule amendments will become effective October 29, 1999. Section IV of this release contains information on compliance dates.

3 0

2 years ago