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Whitepunk [10]
2 years ago
7

You just obtained a credit card. You immediately purchase a digital camera for $160. Your credit limit is $4000. Let’s assume th

at you make no payments and purchase nothing more and there are no other fees. The monthly interest rate is 1.42%. What is the growth factor of your credit card balance?
Mathematics
1 answer:
attashe74 [19]2 years ago
8 0
Every month your balance includes the original amount (100%) and the added the monthly interest  (1.42%)  so each  month  the balance will be 101.42%  of pior month's balance move  the decimal point two points two places to the left to make that into a decimal 

So the answer is 101.42
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Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 10x2+4xâ1, 3xâ4x2+3, and
lord [1]

I suppose

H=\mathrm{span}\{10x^2+4x-1,3x-4x^2+3,5x^2+x-1\}

The vectors that span H form a basis for P_2 if they are (1) linearly independent and (2) any vector in P_2 can be expressed as a linear combination of those vectors (i.e. they span P_2).

  • Independence:

Compute the Wronskian determinant:

\begin{vmatrix}10x^2+4x-1&3x-4x^2+3&5x^2+x-1\\20x+4&3-8x&10x+1\\20&-8&10\end{vmatrix}=-6\neq0

The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of H is 3.

  • Span:

Write an arbitrary vector in P_2 as ax^2+bx+c. Then the given vectors span P_2 if there is always a choice of scalars k_1,k_2,k_3 such that

k_1(10x^2+4x-1)+k_2(3x-4x^2+3)+k_3(5x^2+x-1)=ax^2+bx+c

which is equivalent to the system

\begin{bmatrix}10&-4&5\\4&3&1\\-1&3&-1\end{bmatrix}\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}a\\b\\c\end{bmatrix}

The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives

\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}-\dfrac{6a-11b+19c}3\\\dfrac{3a-5b+2c}3\\\dfrac{15a-26b+46c}3\end{bmatrix}

so the vectors do span P_2.

The vectors comprising H form a basis for it because they are linearly independent.

4 0
2 years ago
A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of the suspects. After fur
liberstina [14]

Answer:

a) MA conditional with C can be interpreted as A which is known and C which is unknown match

b) 10/11

c) 2/11

Step-by-step explanation:

A={A is the guilty party}

M_A = {A blood type matches that of the guilty party}

C = {B is the guilty party}

M_C = {B blood type matches that of the guilty party}

a) The chance is 10% because MA conditional with C can be interpreted as A which is known and C which is unknown match

b) the probability that A is the guilty party is given by P(A/M_A). Using bayes theorem:

P(A/M_A)=\frac{P(M_A/A)P(A)}{P(M_A/A)P(A)+P(M_C/C)P(C)} =\frac{1*1/2}{(1*1/2)+(1/10*1/2)} =\frac{10}{11}

c) the probability that B’s blood type matches that of the guilty party is given as P(M_C/M_A). Using LOTS Therefore:

P(M_C/M_A)=P(M_C/M_A,A)P(A/M_A)+P(M_C/M_A,A)P(C/M_A)=\frac{1}{10}*\frac{10}{11}  +1*\frac{1}{11}  =\frac{2}{11}

6 0
2 years ago
A price was increasing at a rate of 15% per month what is the annual growth rate enter your answer rounded to the nearest tenth
Leokris [45]
Hello there! I can help you! The formula for finding the annual growth rate is (1 + r)^t. In other words, you add the rate in decimal form from 1 and raise it to the t power, depending on how many times it is compounded. 15% is 0.15 in decimal form. 1 + 0.15 is 1.15. We have that number. Now, we are looking for the annual growth rate. It increases monthly, annual has to do with 1 year, and there are 12 months in 1 year. Now, let's raise 1.15 to the 12th power. 1.15^12 is 5.350250105. Don't delete it. We can subtract 1 from that number to get 4.350250105. Now, let's multiply it by 100 to get the answer in percent form. When you do, you get 435.0250105 or 435 when rounded to the nearest tenth, because there is a 0 in the tenths place. We can subtract There. The annual growth rate is about 435%.
7 0
1 year ago
Read 2 more answers
Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.
steposvetlana [31]
4(2 - x) > -2x - 3(4x + 1)
8 - 4x > -2x - 12x - 3
-4x + 2x + 12x > -3 - 8
10x > -11
x > -11/10
x > -1.1

Therefore, x = 0 and x = 10 zre solutions to the inequality.
4 0
2 years ago
Read 2 more answers
Complete the similarity statement for the two triangles shown. Enter your answer in the box. △XBR∼△ Two similar triangles B R X
Andreyy89

Answer:  

Here, BRX and NJY are two triangles in which,

BR = 30 cm, RX = 40 cm, BX = 60 cm, NJ = 15 cm, JY = 20 cm and NY = 30 cm,

Also, m∠B = m∠N, m∠R = m∠J and m∠X = m∠Y,

By the property of congruence,

\angle B \cong \angle N, \angle R \cong \angle J and \angle X \cong \angle Y

Thus, By AAA similarity postulate,

\triangle BRX\sim \triangle NJY

Hence, proved.

5 0
2 years ago
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