What is the length of the segment

A small craft in lake Ontario sends out a distances signal. The coordinates of the boat in trouble are (57,64). One rescue boat

KatRina [158]

Answer:

The coast guard craft will get to the distressed boat the fastest.

Step-by-step explanation:

The coordinates of boat are (57,64).

The coordinates of rescue boat are (67,83).

The coordinates of coast guard craft are (65,46).

Both rescue crafts travel at the same rate. One of them will get to the distressed boat the faster, whose distance from the boat is least.

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The distance between boat and rescue boat is

$d_1=\sqrt{(67-57)^2+(83-64)^2}=21.4709105536\approx 21.47$

The distance between boat and coast guard craft is

$d_2=\sqrt{(65-57)^2+(46-64)^2}=19.6977156036\approx 19.70$

Since the distance between boat and coast guard craft is least, therefore coast guard craft will get to the distressed boat the fastest.

6 0

3 years ago

Assume in a certain city that housing costs have been increasing at 5.2% per year compounded annually for the past 8 years. A ho

liraira [26]

Answer:

$\$173,319.50$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=8\ years\\ A=\$260,000\\ r=5.2\%=5.2/100=0.052\\n=1$

substitute in the formula above

$260,000=P(1+\frac{0.052}{1})^{1*8}$

solve for P

$260,000=P(1.052)^{8}$

$P=260,000/(1.052)^{8}=\$173,319.50$

4 0

3 years ago

A local school donated canned goods to help the community. Cans were packed into boxes each weighing 16.4 pounds. The volunteers

Alex777 [14]

B if not comment so yeah ok

7 0

3 years ago

Read 2 more answers

How Do You Write .0676767 In Scientific Notation?

evablogger [386]

6.8 x 10^-2

The scientific notation of 70, 030, 000. To find the scientific notation of this value 
1. We first move the period which separates the whole number from the decimal number which is located after the numbers of the given value.
2. We move it in the very recent order number which is seventy million, seven and zero. 
3. It becomes 7.003
4. Thus we count how many moves we did from the tens to the ten million order place. 
5. 7.003 x 10^7

4 0

4 years ago

It is believed that a stock price for a particular company will grow at a rate of $5 per week with a standard deviation of $1. A

IgorLugansk [536]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = $5

For the alternative hypothesis,

µ < $5

number of samples taken = 10

Sample mean, x = (4 + 3 + 2 + 3 + 1 + 7 + 2 + 1 + 1 + 2)/10 = 2.6

To determine sample standard deviation, s

s = √(summation(x - mean)/n

n = 12

Summation(x - mean) = (4 - 2.6)^2 + (3 - 2.6)^2 + (2 - 2.6)^2 + (3 - 2.6)^2 + (1 - 2.6)^2 + (7 - 2.6)^2 + (2 - 2.6)^2 + (1 - 2.6)^2 + (1 - 2.6)^2 + (2 - 2.6)^2 = 30.4

s = √30.4/10 = 1.74

Since the number of samples is 10 and no population standard deviation is given, the distribution is a student's t.

Since n = 10,

Degrees of freedom, df = n - 1 = 10 - 1 = 9

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.6

µ = population mean = 5

s = samples standard deviation = 1.74

t = (2.6 - 5)/(1.74/√10) = - 4.36

We would determine the p value at alpha = 0.05. using the t test calculator. It becomes

p = 0.000912

7 0

3 years ago