Ask question

Ask question

All categories

3 years ago

14

Select the correct augmented matrices. Liam wants to buy a car and pay for it in three installments. The total cost of the car i

s $29,000. Two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. Liam must pay 15% interest on the second and the third installments: the interest will amount to $2,100. If x, y, and z represent the first, second, and third installments, respectively, identify the augmented matrices that model Liam's situation.

1 answer:

Alexxandr [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Given:

The total cost of the car is 29,000 dollars. Which is paid in three installments . x , y and z are the installments.

To Find:

The value of x, y and z.

Solving:

It is said that 2 times the 1 installment is $1,000 ore than the sum of the 3 rd installment and 3 times the second installment.

= 2x = 1000 + z + 3y

Transposing:

= z = 2x - 3y - 1000

x + y + z = 29000 + 2100

= x + y + z = 31100

= x + y + 2x - 3y - 1000 = 31100

= 3x - 2y = 32100

First installment at start paid = x (We have assumed)

Remaining Installment which is left to pay = 29,000 - x

(29,000 - x) * 15 /100 = Interest for First

= (29000 - x) * 3/20

=> 4350 - 0.15x

Installment Paid Second = y

(29000 - x) + 4350 - 0.15x - y ) * 15/100 = Interest Second

(29000 - x) + 4350 - 0.15x - y ) * 3/20

= 5002.5 - 0.1725x - 0.15y

Interest of 1st installment + Interest of 2nd installment = 2100

Using this principle solving:

= 4,350 - 0.15x + 5,002.5 - 0.1725x - 0.15y = 2,100

= 0.3225x + 0.15y = 7,252.5

= 6.45x + 3y = 1,45,050

= 12.9x + 6y = 2,90,100

= 4.3x + 2y = 96,700

= 4.3x + 2y = 96700

= 3x - 2y = 32,100

= 7.3x = 1,28,800

= x ≈ 17644 ( 17,643.8356)

3x - 2y = 32,100

= y ≈ 10416 (10,415.7534 )

x + y + z = 31100

= z ≈ 3040 ( 3,040.4110 )

You might be interested in

noname [10]

Answer:

A. Cylinder + cone

<u>Volume is the sum of volumes:</u>

V = Vcon + Vcyl = 1/3πr²h₁ + πr²h₂
V = 1/3π*9²*12 + π*9²*120 = 31554.2 cm³

<u>Surface area of cone:</u>

A = A=πr(r+√(h₁²+r²)) = π*9(9 + √(9²+12²)) = 678.6 cm²

<u>Surface area of cylinder minus bases:</u>

A = 2πrh₂ = 2π*9*120 = 6785.8 cm²

<u>Total surface area:</u>

678.6 + 6785.8 = 7464.4 cm²

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

B. Cube+ pyramid

<u>Volume:</u>

V = a³ + (1/3)a²h = a³ + (1/3)a²√(l²-(a/2)²)
V = 8³ + (1/3)8²√(10²-4²) = 707.5 cm³

<u>Surface area of pyramid:</u>

A = a² + 2al = 8² + 2*8*10 = 224 cm²

<u>Surface area of cube minus bases:</u>

A = 4a² = 4(8²) = 256 cm²

<u>Total surface area:</u>

A = 224 + 256 = 480 cm²

5 0

3 years ago

5. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. This can be written as N(8,4). Th

xz_007 [3.2K]

Answer:

The probability that X is between 1.48 and 15.56 is $P(1.48 \leq X \leq 15.56) = 0.919$

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.

This means that $\mu = 8, \sigma = 4$

The probability that X is between 1.48 and 15.56

This is the pvalue of Z when X = 15.56 subtracted by the pvalue of Z when X = 1.48. So

X = 15.56

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{15.56 - 8}{4}$

$Z = 1.89$

$Z = 1.89$ has a pvalue of 0.9706

X = 1.48

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.48 - 8}{4}$

$Z = -1.63$

$Z = -1.63$ has a pvalue of 0.0516

0.9706 - 0.0516 = 0.919

Write out the probability notation for this question.

$P(1.48 \leq X \leq 15.56) = 0.919$

The probability that X is between 1.48 and 15.56 is $P(1.48 \leq X \leq 15.56) = 0.919$

5 0

3 years ago

Can someone help me with this

Anastasy [175]

Answer:

Yes

sum of angle = 180°

First diagram

R+D+E=180°

110°+28°+E=180°

138°+E=180°

E=180°-138°

E=42°

Second diagram

T+V+A=180°

T+28°+42°=180°

T+70°=180°

T=180°-70°

T=110°

6 0

3 years ago

I WILL BRAINLIEST !!!

olya-2409 [2.1K]

Answer: 11/18

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

Explanation:

We need to add the fractions, but first we need to get each fraction to have the LCD (lowest common denominator) of 18

18 is the LCM of the denominators 6 and 9

The fraction 1/6 turns into 3/18 when multiplying top and bottom by 3

The fraction 4/9 turns into 8/18 after multiplying top and bottom by 2

Therefore,

(1/6) + (4/9) = (3/18) + (8/18) = (3+8)/18 = 11/18

So Mike has a total of 11/18 of a gallon of paint when combining the two given amounts 1/6 a gallon of blue paint and 4/9 of a gallon of green paint.

6 0

3 years ago

(P) to the sixth power times the 4th power

ValentinkaMS [17]

Answer:

$P^{24}$

Step-by-step explanation:

$P^{6*4}$

If this is what the question is asking, we would just multiply 6 and 4 to get P to the 24th power.

8 0

3 years ago