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3 years ago

Write each vector in component form

1 answer:

meriva3 years ago

5 0

Answer to problem 1 is (9,9)
Answer to problem 2 is (0,-4)

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

Explanation:

To find the component form, they basically want the translation rule. To find the translation rule, we subtract the coordinates tip - head

In general, if we have two vectors M and N such that
M = (a,b)
N = (c,d)
then
vector MN = (c-a, d-b)

Applying this to the vector CD gives us
vector CD = (7-(-2), 10-1) = (7+2, 10-1) = (9, 9)
Basically meaning that we shift point C nine units to the right and nine units up to get to point D

Similarly,
vector RS = (-4-(-4), -3-1) = (-4+4, -3-1) = (0,-4)
so we shift point R four units down to get to point S

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pashok25 [27]

Answer:

Let's call:

f = price of 1 cup of dried fruit

a = price of 1 cup of almonds

In order to build the linear system, you need to consider that the total price of a bag is given by the sum of the price of cups times the number of cups in each bag, therefore:

Solve for a in first equation:

a = (6 - 3f) / 4

Then substitute in the second equation:

41/2 f + 6 · (6 - 3f) / 4 = 9

41/2 f + 9 - 9/2 f = 9

16 f = 0

f = 0

Now, substitute this value in the formula found for a:

a = (6 - 3·0) / 4

= 3/2 = 1.5

Hence, the cups of dried fruit are free and 1 cup of almond costs 1.5$

Step-by-step explanation:

8 0

2 years ago

The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

8 0

2 years ago

An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?

sesenic [268]

Answer:

$\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p0}$

Step-by-step explanation:

$-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}$

6 0

2 years ago

Rosa earns $120 per week tutoring math. Each week, she puts $36 from her paycheck in her bank account to save for college. Rosa

natita [175]

Answer:

36/120 x 100

= 30%

..............

3 0

2 years ago

Can someone please help me <br>I need 7 and 8

exis [7]

Answer:

7.irrational

8.integer ,whole number ,rational number

Step-by-step explanation:

7. that dash line on top of decimal shows that its keeps repeating

8. -18/6 = -3

4 0

3 years ago