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2 years ago

A school survey reported that

Mathematics

1 answer:

kozerog [31]2 years ago

6 0

The probability that the student has a part-time job, given that they have a cell phone is 5/8

<h3>What is probability</h3>

Probability is the likelihood or chance that an event will occur.

Given the following parameter:

Total student = 80%
Part-time jobs = 45%
Those with both a cell phone and a part-time job = 30%

Student will cellphone only = 80 - 30 = 50%

The probability that the student has a part-time job, given that they have a cell phone is 50/80 = 5/8

Learn more on probability here: brainly.com/question/25870256

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Solve the given integral equation for LaTeX: y(t)y ( t ). LaTeX: y(t)+9\displaystyle{\int_{0}^{t}e^{9(t-v)}y(v)\, dv}=\sin(3t)y

choli [55]

Looks like the equation is

$y(t)+9\displaystyle\int_0^te^{9(t-v)}y(v)\,\mathrm dv=\sin(3t)$

Differentiating both sides yields the linear ODE,

$y'(t)+9e^{9(t-t)}y(t)=3\cos(3t)$

$y'(t)+9y(t)=3\cos(3t)$

Multiply both sides by the integrating factor $e^{9t}$ :

$e^{9t}y'(t)+9e^{9t}y(t)=3e^{9t}\cos(3t)$

$\left(e^{9t}y(t)\right)'=3e^{9t}\cos(3t)$

Integrate both sides, then solve for $y(t)$ :

$e^{9t}y(t)=\dfrac1{10}e^{9t}(\sin(3t)+3\cos(3t))+C$

$y(t)=\dfrac{\sin(3t)+3\cos(3t)}{10}+Ce^{-9t}$

The given answer choices all seem to be missing C, so I suspect you left out an initial condition. But we can find one; let $t=0$ , then the integral vanishes and we're left with $y(0)=0$ . So

$0=\dfrac{0+3}{10}+C\implies C=-\dfrac3{10}$

So the particular solution is

$y(t)=\dfrac{\sin(3t)+3\cos(3t)-3e^{-9t}}{10}$

6 0

2 years ago

Use the Euclidean Algorithm to demonstrate that 621 and 82 are relatively prime to each other. Explain.

8090 [49]

Answer:

621 and 82 are relatively prime.

Step-by-step explanation:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one).

The greatest common divisor of two integers a and b is the largest integer that divides them both.

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

Given integers a, b find $d=gcd(a,b)$

The Euclidean algorithm provides a fast way to determine d without knowing the prime factors of a or b. Here is an outline of the steps:

Let $a=x$ , $b=y$
Given x, y, use the division algorithm to write $x=yq+r, \quad 0\leq r\leq |y|$ .
If r = 0, stop and output y; this is the gcd of a, b.
If $r \neq 0$ , replace (x, y) by (y, r). Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly until we get a result that lies between 0 (inclusive) and D (exclusive) and is the smallest non-negative number obtained by repeated subtraction.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

Applying the above steps,

$621-82=539\\539-82=457\\457-82=375\\375-82=293\\293-82=211\\211-82=129\\129-82=47\\\\621=82\cdot7+47$

$621 = 82\cdot 7 + 47\\ 82 = 47\cdot 1 + 35\\ 47 = 35\cdot1 + 12\\ 35 = 12\cdot2 + 11\\ 12 = 11\cdot1 + 1\\ 11 = 1\cdot11 + 0$

The gcd(621, 82) is 1. Therefore, 621 and 82 are relatively prime.

5 0

2 years ago

A prehistoric site was discovered. The site is a nearly perfect circle

Artemon [7]

Answer:

whats the question

Step-by-step explanation:

5 0

3 years ago

During the holiday sale at blooming department store all sweaters are discounted 30% on blockbuster Saturday the store discounts

RSB [31]

Answer: He would pay $62.37 for it on blockbuster Saturday.

Step-by-step explanation:

Since we have given that

Original price of sweater = $99

Discount on blockbuster Saturday = 30%

Additional discount on sweater = 10%

So, According to question,

$Net\ Price=Price\times \frac{100-Discount}{100}\\\\\text{As there are 2 successive discounts }\\\\So,\\\\Net\ Price=Price\times \frac{100-D_1}{100}\times\frac{100-D_2}{100}$

$99\times \frac{100-30}{100}\times \frac{100-10}{100}\\\\=99\times \frac{70}{100}\times \frac{90}{100}\\\\=\$62.37$

Hence, he would pay $62.37 for it on blockbuster Saturday.

3 0

2 years ago

What is a straight path that has a beginning but not an ending

ohaa [14]

The answer is a Ray.

7 0

3 years ago