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3 years ago

Find all solutions for a triangle with A = 40°, B = 60°, and c = 20.

Mathematics

1 answer:

Ket [755]3 years ago

3 0

Answer:C

Step-by-step explanation:

180-(60+40)=80°

C=80°

20/sin80. =a/sin40

a=(20sin40)÷sin80

=13.1

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Javier is biking at 15 miles per hour. There are 5280 feet in a mile. How many feet does he travel in one minute? plz help

AnnyKZ [126]

The answer is 1320 because 60 MPH = 1 mile per minute, so 15/60 (1/4) = 5280 divided by four

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3 years ago

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The first two terms of a sequence are 5 and 7. Each term after the second is found by taking the average (arithmetic mean) of al

ch4aika [34]

Answer:

Step-by-step explanation:

We can prove that every number after the second will be a six by induction.

Base case. Since $\frac{5 + 7}{2} = 6$ , so the third term is a six.

Inductive hypothesis. Fix the number of terms to be n and assume that

$\frac{1}{n} \sum\limits_{i=1}^{n}t_i = 6$

Inductive step. We will now show that $\frac{1}{n+1} \sum\limits_{i=1}^{n+1}t_i = 6$ .

Notice that

$\begin{array}{lll}\frac{1}{n+1} \sum\limits_{i=1}^{n+1}t_i & = \frac{n}{n(n+1)} \sum\limits_{i=1}^{n+1}t_i & \\& = \frac{t_{n+1}}{n+1} + \frac{n}{n(n+1)} \sum\limits_{i=1}^{n}t_i &\\& = \frac{t_{n+1}}{n+1} + \frac{6n}{n+1} & \text{(by the IH)}\\& = \frac{6}{n+1} + \frac{6n}{n+1} & \text{by de\\finition}\\& = \frac{6(n+1)}{n+1} & \\& = 6 & \end{array} \square$

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2 years ago

In January 2002, two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads—that’s 56%. Th

natita [175]

Answer with explanation:

The 90% confidence interval (51%, 61%) for proportion means that the proportion of getting heads lie in it.

Given : Total number of times coin is tossed = 250

Number of times they got head =140

The probability of getting a head = 0.56

The confidence interval for proportion is given by :-

$p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

Given significance level : $\alpha=1-0.90=0.1$

Critical value : $z_{\alpha/2}=z_{0.05}=\pm1.645$

Now, the 90% confidence interval for proportion will be :-

$0.56\pm (1.645)\sqrt{\dfrac{0.56(1-0.56)}{250}}\approx0.56\pm 0.0516\\\\=(0.56-0.0516,0.56+0.0516)=(0.5084,\ 0.6116)\approx(51\%,\ 61\%)$

Hence, the given confidence interval is correct.

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3 years ago

Convert the density of surface sea water to metric tons/cubic meter.

ryzh [129]

Answer: 1.029 tons/m³

Step-by-step explanation:

Density of sea water may varies for different temperature but at 25°C the density of sea water is taken as 1029 kg/m³.

Density of sea water is 1029 kg/m³

1 tons=1000 kg

1 kg=0.001 tons

Density of sea water=1029×0.001 tons/m³

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hence the density will be 1.029 tons/m³

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3 years ago

How many solutions exist for the given equation 1/2 (x+12)=4x-1

Daniel [21]

Answer:

x=2

Step-by-step explanation:

1/2 (x+12)=4x-1

Multiply each side by 2

2*1/2 (x+12)=2*(4x-1)

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x+12 = 8x - 2

Subtract x from each side

12 = 7x -2

Add 2 to each side

14 =7x

Divide by 7

14/7 = 7x/7

2 =x

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