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4 years ago

What is x and what's m<M?

Mathematics

1 answer:

sweet [91]4 years ago

5 0

Use the property that angles sum up to 360 degrees.

Also use property that <M = <R and <A = <P.

That gives the following equation:

m<R + m<A + m<M + m<P = 360

6x+5 + 9x+25 + 6x+5 + 9x+25 = 360

30x + 60 = 360

x = 10

Answer:

x = 10

m<M = 6x+5 = 65 degrees

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Solve the decay equation y' = -ky using the integrating factors method. Show work

Alex777 [14]

Answer:

$y=\frac{c}{e^{kx}}$

Step-by-step explanation:

$\frac{\mathrm{d} y}{\mathrm{d} x} =-ky$

$\frac{\mathrm{d} y}{\mathrm{d} x} +ky=0$

comparing with equation

$\frac{\mathrm{d} y}{\mathrm{d} x} + Py=Q(x)$

$I.F.= e^{\int P dx}$

$I.F.= e^{\int k dx}$

$I.F.= e^{kx}$

$y=\frac{1}{I.F.} ( \int {Q(x)} dx +c)$

$y=\frac{1}{e^{kx}} ( \int {0} dx +c)$

$y=\frac{c}{e^{kx}}$

7 0

4 years ago

A punch recipe that serves 24 people calls for 4 liters of lemon-lime soda, 2 pints of sherbet, and 6 cups of ice. How much of e

andrew-mc [135]

For twelve people you need: 2 litres of lemon-lime soda, 1 pint of sherbet and 3 cups of ice tea.
For 36 people you need: 6 litres of lemon-lime soda, 3 pints of sherbet and 9 cups of ice.

5 0

3 years ago

How do I solve this word problem?

german

Answer:

280 student tickets
520 adult tickets

Step-by-step explanation:

You may recognize that you are given two relationships between two unknowns. You can write equations for that.

You are asked for numbers of adult tickets and of student tickets. It often works well to let the values you're asked for be represented by variables. We can choose "a" for the number of adult tickets, and "s" for the number of student tickets. Then the problem statement tells us the relationships ...

a + s = 800 . . . . . . 800 tickets were sold

12.50a + 7.50s = 8600 . . . . . . . revenue from sales was 8600

(You are supposed to know that the revenue from selling "a" adult tickets is found by multiplying the ticket price by the number of tickets: 12.50a.)

___

You can solve these two equations any number of ways. One way is to do it by <em>elimination</em>. We can multiply the first equation by 12.50 and subtract the second equation:

12.50(a +s) -(12.50a +7.50s) = 12.50(800) -(8600)

5s = 1400 . . . . simplify. (The "a" variable has been eliminated.)

s = 280 . . . . . . divide by 5

Then the number of adult tickets can be found from the first equation:

a + 280 = 800

a = 520

280 student tickets and 520 adult tickets were sold.

8 0

4 years ago

A recent survey of students at John Tukey High School revealed that

RoseWind [281]

Answer:

0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are in favor, or they are not. Students are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

18% of the students are in favor of changing the dress code.

This means that $p = 0.18$

You randomly select 15 students

This means that $n = 15$

What is the probability that at least three of these students are in favor of the proposal to change the dress code?

This is

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.18)^{0}.(0.82)^{15} = 0.051$

$P(X = 1) = C_{15,1}.(0.18)^{1}.(0.82)^{14} = 0.1678$

$P(X = 2) = C_{15,2}.(0.18)^{2}.(0.82)^{13} = 0.2578$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.051 + 0.1678 + 0.2578 = 0.4766$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.4766 = 0.5234$

0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.

8 0

3 years ago

Please help I haven’t been to school in a while and I need help

kakasveta [241]

You're given an angle, the side adjacent to the angle, and are looking for the hypotenuse.

Use cosine = adjacent / hypotenuse.

cos(60) = 2√(3) / x

Rearrange the equation to solve for x (multiply both sides by x, then divide both sides by cos(60)).

x = (2√(3)) / (cos(60))

x equates to about 6.928

5 0

3 years ago

Read 2 more answers