One safe investment pays 10% per year, and a more risky investment pays 14% per year.
a. How much must be invested in each account if an investor of $102,000 would like a return of $11,320 per year?
b. Why might the investor use two accounts rather than put all the money in the 14% investment?
a. $
is invested in the 10% account.

Answer:

All positive real numbers i think

Answer:

B

Step-by-step explanation:

4^x can never be 0 or negative, the graph has a horizontal asymptote at y = 0

So the range only includes positive values

Answer:

B

Step-by-step explanation:

edg 2021

Answer: b

Step-by-step explanation:

Answer:

The answer would be greater since its being multiply the answer will always be greater than what you're multiplying.

Step-by-step explanation:

The product WILL be greater than the other two factors. When multiplying by a fraction the product is GREATER than the lesser factor.

Answer:

(2x+3)(x-7)

Step-by-step explanation:

2x^2+3x-14x-21

2x(x-7)+3(x-7)

The factors of the expression are (2x+3)(x-7).

Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

For the given situation,

The expression is \(2x^{2} -11x-21\)

The complete factorization of the expression is as,

⇒ \(2x^{2} -11x-21=0\)

⇒ \(2x^{2} -14x+3x-21=0\)

⇒ \(2x(x-7)+3(x-7)=0\)

⇒ \((2x+3)(x-7)=0\)

The value of x can be found as

⇒ \(2x+3 = 0\) or \(x-7 = 0\)

⇒ \(x=\frac{-3}{2}\) or \(x=7\)

Then -3/2 and 7 are the zeroes of the expression.

Hence we can conclude that the complete factorization of the expression are (2x+3)(x-7).

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer: 21

Step-by-step explanation:  im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah

Answer:

21

Step-by-step explanation:

I did the test

Hope this helps :)

Answer:

$42

Step-by-step explanation:

less than 8 is supposed to be 7 or less 6×7=$42

We need to compare some numbers to the measured temperatures and find out which is the one that is less than -1.9 and 2.4.

In order to do so, we can put those values on a number line. Remember that the numbers located to the right of zero are positive and the ones located to the left of zero are negative (the farther they are from zero, the more negative they are):

Notice that the numbers on the left are smaller than the ones on the right of them.

Therefore, as we see above, the only given number that is less than -1.9 is the number -2.6 (which is also less than 2.4).

Thus, the answer is -2.6º Celsius.

Step-by-step explanation:

work he in a department store

Answer:

The step that a mistake first occurs is in step 1.

Step-by-step explanation:

In step one, the constants in the parenthesis went from 24 + 3 + 10 to 8 + 10, which is essentially impossible, so step 1 was the step where a mistake first occurred.

Answer:

9

Step-by-step explanation:

length*width

3*3=9

Answer:

4 : 1

Step-by-step explanation:

(3 days : 18 hours) this is a ratio , where both the units must be same before simplifying.

1 day = 24 hours, 3 days = (3 × 24) hours

3 days = 72 hours

Now both the units are same, so we can easily simplify now.

72 hours : 18 hours

36 : 9 = 12 : 3

= 4 : 1 ( Answer)

Answer:

1/12 gallons

Step-by-step explanation:

We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.

Step 1:  Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2

(1/6) * (2/2) = 2/12

Step 2:  Now we can subtract 1/12 from 2/12:

2/12 - 1/12 = 1/12

Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.

Answer:

the probability of drawing a blue ball from bag A is 1/5 and the probability of drawing a red ball from bag B is 2/3.

The probability of drawing a blue ball from Bag A and a red ball from Bag B will be 2/15.

Probability denotes the likelihood of something happening. It is concerned with the occurrence of an unpredicted event.

Probability can only have a value between 0 and 1. Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of events is known as the favorable event ratio.

The probability of drawing a blue ball from Bag A is, 1/5

The probability of drawing a red ball from Bag B is, 2/3.

P(A)=1/5

P(B)=2/3

The probability of drawing a blue ball from Bag A and a red ball from Bag B will be;

P(A and B)=P(A). P(B)

P(A and B)=(1/5)×(2/3)

P(A and B)=(2/15)

Hence,the probability of drawing a blue ball from Bag A and a red ball from Bag B will be 2/15.

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Answer:

3

Step-by-step explanation:

The number line is showing x>3.

If the circle were closed it would be x≥3.

Answer:

3.

Step-by-step explanation:

Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

You cannot have 1 imaginary solution because the quadratic equation must have either two real solutions or two complex solutions

In mathematics, the discriminant (D = b2 - 4ac) aids in identifying the kind of solutions to quadratic equations of the form ax2 + bx + c = 0.

There are two unique real solutions if the discriminant is positive. There is only one viable option if the discriminant is zero. There are no practical solutions, however, if the discriminant is negative.

The quadratic equation in this instance has two complex solutions that are conjugates of one another. Because the quadratic equation must have either two real solutions or two complex solutions, there can never be just one hypothetical solution.

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Answer:

4/5

Step-by-step explanation:

Because 1/5 is winning chance.

and the rest percentage will be losing

Answer:

254 x 10^5

Step-by-step explanation:

Hope this helps :)

If anything is misunderstood plz comment and I will change to the answer which you give me thank you very much :)

Answer:

2.54 x 10^5

hope this answer helps u ._.

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Answer:

for the first question, the slope is -2/7 and the y-intercept is 2.

for the second question the slope is -1/3 and the y-intercept is 6

Step-by-step explanation:

Answer:

1/3 slope

y = mx + b

y =1/3 x + b

Step-by-step explanation:

y2-y1  -6 - -8 = 2

x2-x1    4 - -2= 6

6/2  simplified 1/3 (slope)mm

Answer:

3 × 2 × 1 + 3 + 8 + 6 + 7 - 9 - 9 ÷ 7 × 0 × 1

= 6 + 3 + 8 + 6 + 7 - 9 - 0

= 31 - 9

= 22

Therefore, the value of the expression is 22

Answer:

17

Step-by-step explanation:

if its wrong sorry im not as smart

The area of the parallelogram is 240 feet.

A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height. 

A quadrilateral's interior angles add up to 360 degrees.

The area of a parallelogram can thus be written as :

Area = Base × Height

In this diagram it is given that the Base = 20 feet and the height = 12 feet

Thus the area can be obtained by simply multiplying these two dimensions

So area = 20 × 12 = 240 feet .

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The additive inverse of [14/15*(-25/28)]+[2/3*6/7] is 1

You should be aware that the additive inverse of a number is the number that, when added to a, yields zero and the multiplicative inverse is the  reciprocal for a number

The given fractions are

[14/15*(-25/28)]+[2/3*6/7]

Let us solve it in parts

= 14/15*-15/28

=-392/420

The multiplicative inverse is

-392/420 *420/-392 =1

The second fraction is

[2/3*6/7]

The additive inverse is

12/21 -12/21 = 0

Therefore the additive inverse is 1+0 = 1

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