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2 years ago

6

A boat heads south at 120 mph while a steamer heads east at 50 mph. If they started from the same dock and at the same time, whe

n will the distance between them be 130 mi?

2 answers:

Snezhnost [94]2 years ago

8 0

Answer:

1 hour after they leave

Step-by-step explanation:

The distance each travels is proportional to its speed. The given speeds are at right angles to each other in a 5:12 ratio. The Pythagorean theorem tells you the hypotenuse of such a right triangle will have length ...

√(5²+12²)=√169 = 13

That is the speeds are in the ratio 5:12:13, where 13 represents the relative separation speed. Actual speeds are then 50 mph : 120 mph : 130 mph.

So the distance between the boat and steamer will be increasing at 130 mph. The distance will be 130 miles after 1 hour.

Aneli [31]2 years ago

4 0

Answer:

1 hour

Step-by-step explanation:

to solve, just use pythagerum therum!

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In the diagram below, AB and TC are tangent to 0. Which equation could be solved to find x, the measure of AC?

LekaFEV [45]

The equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

<h3>Circle theorem</h3>

The given diagram shows two intersecting lines tangential to a circle at points A and C.

Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.

Mathematically;

<B = 1/2(arcADC - arcAC)

58 = 1/2(238 -x)

Hence the equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

Learn more on circle theorem here: brainly.com/question/26594685

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1 year ago

-8x-10y=24;6x+-10x-10y

stiks02 [169]

Do you have a typo? ; < this maybe

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3 years ago

The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppos

xenn [34]

Answer:

(a) P(X > $57,000) = 0.0643

(b) P(X < $46,000) = 0.1423

(c) P(X > $40,000) = 0.0066

(d) P($45,000 < X < $54,000) = 0.6959

Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

<em>Let X = annual salaries in the metropolitan Boston area</em>

SO, X ~ Normal( $\mu=$50,542,\sigma^{2} = $4,246^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma }$ ~ N(0,1)

where, $\mu$ = average annual salary in the Boston area = $50,542

$\sigma$ = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

P(X > $57,000) = P( $\frac{X-\mu}{\sigma }$ > $\frac{57,000-50,542}{4,246 }$ ) = P(Z > 1.52) = 1 - P(Z $\leq$ 1.52)

= 1 - 0.93574 = <u>0.0643</u>

<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

P(X < $46,000) = P( $\frac{X-\mu}{\sigma }$ < $\frac{46,000-50,542}{4,246 }$ ) = P(Z < -1.07) = 1 - P(Z $\leq$ 1.07)

= 1 - 0.85769 = <u>0.1423</u>

<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

P(X > $40,000) = P( $\frac{X-\mu}{\sigma }$ > $\frac{40,000-50,542}{4,246 }$ ) = P(Z > -2.48) = P(Z < 2.48)

= 1 - 0.99343 = <u>0.0066</u>

<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.

(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)

P($45,000 < X < $54,000) = P(X < $54,000) - P(X $\leq$ $45,000)

P(X < $54,000) = P( $\frac{X-\mu}{\sigma }$ < $\frac{54,000-50,542}{4,246 }$ ) = P(Z < 0.81) = 0.79103

P(X $\leq$ $45,000) = P( $\frac{X-\mu}{\sigma }$ $\leq$ $\frac{45,000-50,542}{4,246 }$ ) = P(Z $\leq$ -1.31) = 1 - P(Z < 1.31)

= 1 - 0.90490 = 0.0951

<em>The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively</em>.

Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = <u>0.6959</u>

3 0

2 years ago

A color printer prints 7 pages in 3 minutes.

mojhsa [17]

Answer:

2 pages per minute

Step-by-step explanation:

when you divide 7 by 3, your answer would be 2.3333333333 and so on.

however, you can say

iT pRiNtS 2 aNd A tHiRd pAgEs PeR MiNuTe.

you should say it prints 2 whole pages a minute.

i hope this helps!

stay safe!

:)

4 0

2 years ago

An animal feed to be mixed from soybean meal and oats must contain at least 168 lb of protein, 27 lb of fat, and 14 lb of minera

atroni [7]

Answer:

The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

$Cost = 51.275$

Step-by-step explanation:

The given parameters can be summarized as:

$\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}$

Where: x = Soybeans and y = Oats.

So, the system of equations are:

$70x + 21y = 168$

$9x +7y = 27$

$7x + y = 14$

$Cost = 21x + 7y$

The best way to solve this, is using graph

Plot the following equations on a graph, and get the points of intersection:

$70x + 21y = 168$

$9x +7y = 27$

$7x + y = 14$

From the attached graph, we have:

$(x_1,y_1) = (1.636,2.545)$

$(x_2,y_2) = (1.775,1.575)$

$(x_3,y_3) = (2.023,1.256)$

Substitute each of the values of x's and y's in the cost function to get the minimum cost:

$Cost = 21x + 7y$

$(x_1,y_1) = (1.636,2.545)$

$Cost = 21 * 1.636 + 7 * 2.545$

$Cost = 52.171$

$(x_2,y_2) = (1.775,1.575)$

$Cost = 21 * 1.775 + 7 * 1.575$

$Cost = 48.3$

$(x_3,y_3) = (2.023,1.256)$

$Cost = 21 * 2.023 + 7 * 1.256$

$Cost = 51.275$

The values of x and y that gives the minimum cost is:

$(x_2,y_2) = (1.775,1.575)$

and the minimum cost is:

$Cost = 48.3$

Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

5 0

3 years ago