MATHEMATICS COLLEGE

Letter b on number 11 is all I need help with. Thank you

Answers

Answer 1

Answer:

distance = 500 feet

Since Δ VWX and Δ YZX are similar then the ratios of corresponding sides are equal, that is

$(VW)/(YZ)$ = $(VX)/(YX)$ = $(WX)/(ZX)$

completing the required values gives

$(100)/(l)$ = $(60)/(30)$ ( cross- multiply )

60l = 30 × 100 = 3000 ( divide both sides by 60 )

l = 500

distance across the swamp is 500 feet

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Which of the following statements about the image below is true?

Answers

Answer:

d. Line UR and Line VW are parallel

Step-by-step explanation:

If they were to continue going straight, they would not touch, making them parallel.

I hope this helps!

B. The difference between the cash price and the initial deposit in hire purchase is known as ?

Answers

The difference between the cash price and the initial deposit in hire purchase is known as $_$ \text{Principal} $_$ .

In hire purchase transactions, buyers can acquire goods by making an initial down payment and paying the remaining amount in installments. The difference between the total cost of the item and the initial deposit is a crucial concept known as the $_$ \text{Principal} $_$ in mathematical terms. Let's explore this in detail.

In the context of hire purchase, the total cost of the item is often referred to as the cash price. It represents the actual value of the item without considering any interest or finance charges. On the other hand, the initial deposit, also called the down payment, is the amount paid upfront by the buyer to secure the item.

Now, let's introduce some variables to help us understand this concept mathematically:

- Let CP be the cash price of the item.

- Let D be the initial deposit made by the buyer.

The difference between the cash price and the initial deposit is given by:

$\text{Principal} = CP - D$

The Principal is the amount that remains to be paid off in installments, and it serves as the basis for calculating the subsequent monthly or periodic payments in a hire purchase agreement.

The Principal is critical because it determines the total amount the buyer will end up paying for the item. It also affects the duration of the hire purchase agreement, as the buyer's installments are typically spread over a specific number of months or years.

To know more about Hire purchase here

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HirePurchaseagreement

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The population of a town increased from 3450 in 2005 to 5800 in 2011. Find the absolute and relative (percent) increase.

Answers

Answer:

The absolute difference is 1050

The relative percentage is 32.3076%

Step-by-step explanation:

During a game of cards, Megan divided the deck of cards into 4 equal groups. She then placed (3 ofher cards in the center of the table. If Megan now has
5 cards in her hand, how many cards were in the
entire deck?

Answers

There were originally 3 cards in the entire deck.

Let's denote the number of cards in the entire deck as $D$.

Megan divided the deck into 4 equal groups, so each group has $(D)/(4)$ cards.

She placed 3 cards in the center, and now she has 5 cards in her hand.

So, the equation representing this situation is:

$(D)/(4) - 3 + 5 = D$

Now, let's solve for $D$:

$(D)/(4) + 2 = D$

Multiply both sides by 4 to get rid of the fraction:

$D + 8 = 4D$

Subtract $D$ from both sides:

$8 = 3D$

Divide both sides by 3:

$D = (8)/(3)$

However, the number of cards in a deck must be a whole number, so we round up:

$D = 3$

Therefore, there were originally 3 cards in the entire deck.

Answer: 32

Step-by-step explanation: If she had 8 in her had and placed 3 cards down she would have 5 and if there were 8 cards in each group then, 8x4=32

An article in the ASCE Journal of Energy Engineering ("Overview of Reservoir Release Improvements at 20 TVA Dams," Vol. 125, April 1999, pp. 1-17) presents data on dissolved oxygen concentration from streams below 20 dams in the Tennessee Valley Authority system. The sample mean from the observations equals 3.234 and the sample standard deviation is s = 2.121. a) Calculate the 95% two-sided prediction interval on the dissolved oxygen concentration for the next stream that will be tested. (rounded to two decimal places)

Answers

Answer:

95% confidence interval: (2.241,4.227)

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 3.234

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, σ = 2.121

95% confidence interval:

$\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))$

Putting the values, we get,

$t_(critical)\text{ at degree of freedom 19 and}~\alpha_(0.05) = \pm 2.093$

$3.234 \pm 2.093((2.121)/(√(20)) ) = 3.234 \pm 0.993 = (2.241,4.227)$

(2.241, 4.227) is the required confidence interval.

A cryptarithm is a math puzzle in which the digits in a simple equation are replaced with letters. Each digit is represented by only one letter, and each letter represents a different digit. So, for example, we might represent 51+50 = 101 as AB + AC = BCB. In the cryptarithm SEND + MORE = MONEY, what digit does the letter Y represent?

Answers

Answer:

$\large \boxed{\sf \begin{aligned}9567&\n+1085&\n----&-\n10652&\n\end{aligned}}$

Step-by-step explanation:

Hello, let's do it step by step and see what we can find.

$\begin{aligned}\text{ SEND}&\n+\text{ MORE}&\n-----&-\n\text{ MONEY}&\n\end{aligned}$

We assume that M is different from 0, otherwise we could find several different solutions I would think.

It means that S + M is greater than 10, otherwise the number of digit of the result would have been 4 and not 5.

The only possible number for M is then 1. M = 1

$\begin{aligned}\text{ SEND}&\n+\text{ \boxed{1}ORE}&\n-----&-\n\text{ \boxed{1}ONEY}&\n\end{aligned}$

But then, S can only by 9, otherwise S + 1 < 10. S = 9

S + 1 = 10 + O if there is no carry over, so S = 9 + O

1 + S + 1 = 10 + O if there is a carry, so S = 8 + O

So O = 0 or O = 1. Wait !? M is already equal to 1 so O must be 0

E cannot be equal to N so 1 + E = N, meaning that there must be a carry over from column second from the right.

and E < 9 as we know that there is no carry over from column 3 from the right.

N + R = 10 + E => 1 + E + R = 10 + E => R = 9, impossible, as S=9

or 1 + N + R = 10 + E => 1 + 1 + E + R = 10 + E => R = 8

And there is a carry over from the column 1 from the right, so:

Y cannot be 0 or 1, as already used so D + E > 11

8 and 9 are already taken so we could have 7 + 5 = 12, 7 + 6 = 13 and that's it.

It means that E is 7 or D is 7.

If E is 7 then E+1=9=N, impossible, so D = 7

Then, E is 5 or 6

if E = 6 E + 1 = N = 7, impossible, so E = 5 and N = 6.

And 7 + 5 = 12 so Y = 2.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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