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3 years ago

An angle measures 10° less than the measure of its supplementary angle. What is the measure of each angle?

Mathematics

1 answer:

spin [16.1K]3 years ago

8 0

Answer:

The two angles are 85 and 95 degrees

Step-by-step explanation:

Supplementary angles add to 180

Let x be one angle

The supplement is 10 less, ( x-10)

They add to 180

x+ ( x-10) = 180

2x -10 = 180

Add 10 to each side

2x-10+10 =180-10

2x= 190

Divide by 2

2x/2 =190/2

x=95

The other angle is 95-10 = 85

The two angles are 85 and 95 degrees

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A bag contains n blue and m red marbles. You randomly pick a marble from the bag, write down its color, and then put the marble

Oksana_A [137]

Answer:

(mn+n²)/(m+n)

Step-by-step explanation:

probability of blue marble= n/(n+m)

probability of red marble= m/(n+m)

probability that process stops = Probability of both blue + probability of both red= n/(n+m) × n/(n+m) + m/(n+m)×m/(n+m)

= (n²+m²)/(n+m)²

P(1st marbel is blue)= P(blue and red) + P(blue and blue)

= mn/(n+m) + n²/(n+m)

= (mn+n²)/(m+n)

P(1st marble is blue | process stops)= ( (mn+n²)/(m+n)× (n²+m²)/(n+m)²)/ ((n²+m²)/(n+m)²)

= (mn+n²)/(m+n)

3 0

3 years ago

If Carbon Monoxide had a concentration in the air of 0.000518% how many particles out of 331,002,651 would be Carbon Monoxide?

Alex17521 [72]

Answer:

171,459 particles of CO

Step-by-step explanation:

331,002,651×0.000518 = 171459

5 0

3 years ago

Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choic

Semenov [28]

Answer:

Option B is not the most common correct choice.

Step-by-step explanation:

The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.

The probability that any of these five option is the correct answer is:

$p=\frac{1}{5}=0.20$

A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.

The results showed that 90 of the 400 questions having B as the answer.

To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:

H₀: All the options are equally probable, i.e. p = 0.20.

Hₐ: Option B is more likely the correct option, i.e. p > 0.20.

Compute the sample proportion as follows:

$\hat p=\frac{90}{400}=0.225$

The test statistic is:

$z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.225-0.20}{\sqrt{\frac{0.20(1-0.20)}{400}}}= 1.25$

The test statistic is 1.25.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

$p-value=P(Z>1.25)\\=1-P(Z$

*Use a z-table.

The p-value is 0.1057.

The p-value of the test is quite large. Thus, the null hypothesis was failed to rejected.

Hence, it can be concluded that option B is not the most common correct choice.

7 0

2 years ago

for a class of 24,78% of students got a B or better on the tex How many students is this? Round to a wholenumber

natita [175]

Step 1

Use the ratio of the number to the percentage to get the required answer.

$\frac{Total\text{ number of students}}{\text{The required number of students}}=\frac{Total\text{ percentage of the class}}{\text{Given percentage}}$

Where,

$\begin{gathered} \text{The total number of students = 24} \\ \text{The required number }of\text{ students= x} \\ \text{The total percentage of the class = 100} \\ \text{Given percentage = 78} \end{gathered}$

Step 2

Get the required answer

$\begin{gathered} \frac{24}{x}=\frac{100}{78} \\ 100x=24\times78 \\ 100x=1872 \\ \frac{100x}{100}=\frac{1872}{100} \\ x=\text{ 18.72} \\ \text{Hence} \\ x\approx19students\text{ rounded to a whole number } \end{gathered}$

The number of students that got B or a better grade on the test = 19 students rounded to a whole number.

4 0

10 months ago

Please help :)))) ( attachment )

Anastaziya [24]

Let,
f(x) = -2x+34
g(x) = (-x/3) - 10
h(x) = -|3x|
k(x) = (x-2)^2

This is a trial and error type of problem (aka "guess and check"). There are 24 combinations to try out for each problem, so it might take a while. It turns out that

g(h(k(f(15)))) = -6
f(k(g(h(8)))) = 2

So the order for part A should be: f, k, h, g
The order for part B should be: h, g, k f
note how I'm working from the right and moving left (working inside and moving out).

Here's proof of both claims

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

Proof of Claim 1:

f(x) = -2x+34
f(15) = -2(15)+34
f(15) = 4
-----------------
k(x) = (x-2)^2
k(f(15)) = (f(15)-2)^2
k(f(15)) = (4-2)^2
k(f(15)) = 4
-----------------
h(x) = -|3x|
h(k(f(15))) = -|3*k(f(15))|
h(k(f(15))) = -|3*4|
h(k(f(15))) = -12
-----------------
g(x) = (-x/3) - 10
g(h(k(f(15))) ) = (-h(k(f(15))) /3) - 10
g(h(k(f(15))) ) = (-(-12) /3) - 10
g(h(k(f(15))) ) = -6

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

Proof of Claim 2:

h(x) = -|3x|
h(8) = -|3*8|
h(8) = -24
---------------
g(x) = (-x/3) - 10
g(h(8)) = (-h(8)/3) - 10
g(h(8)) = (-(-24)/3) - 10
g(h(8)) = -2
---------------
k(x) = (x-2)^2
k(g(h(8))) = (g(h(8))-2)^2
k(g(h(8))) = (-2-2)^2
k(g(h(8))) = 16
---------------
f(x) = -2x+34
f(k(g(h(8))) ) = -2*(k(g(h(8))) )+34
f(k(g(h(8))) ) = -2*(16)+34
f(k(g(h(8))) ) = 2

5 0

3 years ago

An angle measures 10° less than the measure of its supplementary angle. What is the measure of each angle?​

An angle measures 10° less than the measure of its supplementary angle. What is the measure of each angle?