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2 years ago

[50 points]

Mathematics

1 answer:

Marina86 [1]2 years ago

4 0

Answer:

$\sf \dfrac{1}{10}$

Step-by-step explanation:

From the table:

Total number of Sophomores = 10
Total number of students = 37
Total number of Boys who are Sophomores = 1

$\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}$

$\sf \implies P(Sophomore)=\dfrac{10}{37}$

$\sf \implies P(Boy \cap Sophomore)=\dfrac{1}{37}$

$\begin{aligned}\sf P(Boy | Sophomore) & = \sf\dfrac{P(Boy \cap Sophomore)}{P(Sophomore)}\\\\ & = \sf \dfrac{1}{37} \div \dfrac{10}{37}\\\\ & = \sf\dfrac{1}{37} \times\dfrac{37}{10}\\\\ & = \sf\dfrac{1}{10}\end{aligned}$

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Find the most general antiderivative of the function. (Check yo f(x) = 3^x + 7 sinh(x) F(x) = Need Help? Watch It Talk to a Tuto

egoroff_w [7]

Answer:

F(x)= $\frac{3^x}{ln(3)}$ +7cosh(x)+C

Step-by-step explanation:

The function is f(x)=3ˣ+7sinh(x), so we can define it as f(x)=g(x)+h(x) where g(x)=3ˣ and h(x)=7sinh(x).

Now we have to find the most general antiderivative of the function this means that we have to calculate $\int\ {f(x)} \, dx$ wich is the same as $\int\ {(g+h)(x)} \, dx$

The sum rule in integration states that the integral of a sum of two functions is equal to the sum of their integrals. Then,

$\int\ {(g+h)(x)} \, dx$ = $\int\ {g(x)} \, dx + \int\ {h(x)} \, dx$

1- $\int\ {g(x)} \, dx =$ $\int\ {3^x} \, dx = \frac{3^x}{ln(3)}+C$ this is because of the rule for integration of exponencial functions, this rule is:

$\int\ {a^x} \, dx =\frac{a^x}{ln(x)}$ , in this case a=3

2- $\int\ {h(x)} \, dx =$ $\int\ {7sinh(x)} \, dx =7\int\ {sinh(x)} \, dx =7cosh(x)+C$ , number seven is a constant (it doesn´t depend of "x") so it "gets out" of the integral.

The result then is:

F(x)= $\int\ {(h+g)(x)} \, dx=\int\ {h(x)} \, dx +\int\ {g(x)} \, dx$

$\int\ {3^x} \, dx +\int\ {7sinh(x)} \, dx = \frac{3^x}{ln(3)} +7cosh(x) + C$

The letter C is added because the integrations is undefined.

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3 years ago

Solve the inequality below for x. -3.2(2x-1) less than or equal to 17.6

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X ≥ 2.25

You get this using the order of operations and by remembering to change the direction of the greater than or equal to sign when dividing by a negative.

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3 years ago

Read 2 more answers

Help with this math question please

Marat540 [252]

Re-arranging the inequality to find the test points:

$x- \frac{70}{x}\ \textless \ -3 \\ \\ 
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This means, we need to test the inequality for x = -10, x = 0 and x = 7

Since question assumes that x > 0, so we ignore the values less than 0.
So the test points are x = 0 and x = 7

At x = 0 the expression is undefined.
Between x = 0 and x = 7 the value of expression $\frac{(x-7)(x+10)}{x}$ is negative. At x = 7 the value of expression is 0. Above x = 7 the value of expression is positive.

So, the solution to the given inequality will be 0 < x < 7.
In Interval notation, the solution can be written as (0,7)

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Kamila [148]

Answer:

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