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2 years ago

In triangle XYZ, XY = 13, YZ=20, and XZ=25. What is the measure of angle Z to the nearest degree?

1 answer:

4 0

We can use Law of Cosines to solve for the angle of Z. The solution is shown below:
cos C=(a²+b²-c²)/2ab
cos Z = (yz² + xz² - xy² )/2*yz*xz
cos Z = (20² + 25 - 13²)/2*20*25
cos Z = 856 / 1000
Z=31.13°

The answer is angle 31.13°.

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Lin has 13 coins in her pocket that equal 40 cents. All the coins are dimes, d, and pennies, p. Which combination of coins does

Luden [163]

To answer this question you should begin with the coin that has a higher value. If you start with the dime and then just add the correct number of pennies to total $0.40, you will see that you will need 3 dimes ($0.30) and 10 pennies ($0.10).

I used a guess and check strategy starting with 2 dimes.

7 0

2 years ago

Read 2 more answers

The equations 3 x minus 4 y = negative 2, 4 x minus y = 4, 3 x + 4 y = 2, and 4 x + y = negative 4 are shown on the graph below.

stich3 [128]

Answer:

(–1.4, 1.5)

Step-by-step explanation:

The blue line and the purple line are the lines corresponding to the equations of interest. Their point of intersection is in the 2nd quadrant, so is nearest to ...

(–1.4, 1.5)

It can be useful to understand that for equations in standard form:

ax +by = c

the x- and y-intercepts are ...

x-intercept: c/a . . . . value of x for y = 0
y-intercept: c/b . . . . value of y for x = 0

For the equations of interest, the first has intercepts of ...

x=2/3, y=1/2 . . . . graphed line makes a 1st-quadrant triangle with the axes (blue line)

And the second has intercepts of ...

x=-1, y=-4 . . . . graphed line makes a 3rd-quadrant triangle with the axes (purple line)

Since the purple line has a steeper slope, the point of intersection of the lines will be in the 2nd quadrant. There is only one 2nd-quadrant answer choice: (-1.4, 1.5).

5 0

2 years ago

Read 2 more answers

A few people who have a particular disease take part in a medical trial that tests the effect of a medicine on the disease. Half

Rom4ik [11]

Answer:

1.The probability that a person gets well is 70%,

2.the probability that the person was cured because of the medicine is 60%

Step-by-step explanation:

chance of curing by medicine=60%

chance of curing without medicine=10%

total chance of curing=60%+10%=70%

chance of person being cured by medicine=60%

3 0

2 years ago

Let the random variable x have a discrete uniform distribution on the integers 8 ≤ x ≤ 10. determine the mean, μ, and variance,

arsen [322]

The discrete uniform distribution is on the interval 8 ≤ x ≤ 10.
Therefore the probability density function (shown in the figure) is
P(x) = 1/3 = 1/3 for x = 8, 9, 10
= 0 otherwse

The mean is μ = 1/3.

The variance is
σ² = Σp(x) (x- μ)²

Because x - μ = 0 for x = 8,9,10, therefore
σ² = 0

Answer:
μ = 1/3
σ² = 0

8 0

2 years ago

Nyoko needs to be at school at 7:45 AM. It takes her 15 minutes to walk to school, 5/12 hour to eat breakfast, 0.7 hour to get d

defon

So, she wants to be at school at 7.40 (5 mins early)

she needs:

15 mins
5/12 hours (which is $\frac{5}{12} = \frac{25}{60}$ , so 25 mins

so far: 40 mins

then 0.7 and 0.15: we can add those, since they're in decimals: 0.85.

how many minutes is this?

$\frac{85}{100} *60= \frac{85}{10} *6=\frac{85}{5} *3=\frac{13}{1} *3=39$

so 39 mins.

together with the previous 40, it's 79 minutes, which is 1 hour and 19 minutes: so she needs to wake up 1 hour and 19 minutes before 7.40 , which is

6.21!

6 0

2 years ago