All categories

3 years ago

A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

8 0

D) 1 1/3

(1/3) x reciprocal of 1/4 so (4/1) = 4/3 which simplifies to 1 1/3

kenny6666 [7]3 years ago

6 0

$\bf \begin{array}{ccllll}
milk&water\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
\frac{1}{3}&\frac{1}{4}\\
1&x
\end{array}\implies \cfrac{\frac{1}{3}}{1}=\cfrac{\frac{1}{4}}{x}\implies \cfrac{\frac{1}{3}}{\frac{1}{1}}=\cfrac{\frac{1}{4}}{\frac{x}{1}}
\\\\\\
\cfrac{1}{3}\cdot \cfrac{1}{1}=\cfrac{1}{4}\cdot \cfrac{1}{x}\implies \cfrac{1}{3}=\cfrac{1}{4x}\implies 4x=3\implies x=\cfrac{3}{4}$

You might be interested in

Simplify the expression below. (2n/6n+4)(3n+2/3n-2)

andrezito [222]

Answer:

$\frac{n}{3n-2}$

Step-by-step explanation:

Given the expression:

$\frac{2n}{(6n+4)} \cdot \frac{3n+2}{3n-2}$

Using the distributive property: $a \cdot (b+c) =a\cdot b+a\cdot c$

$\frac{2n}{2(3n+2)} \cdot \frac{3n+2}{3n-2}$

Simplify:

$\frac{2n}{2} \cdot \frac{1}{3n-2}$

Simplify:

$\frac{n}{3n-2}$

Therefore, the simplified given expression is, $\frac{n}{3n-2}$

7 0

3 years ago

Read 2 more answers

150% of $22 (math test)

Rom4ik [11]

Answer:

6.8181818

Step-by-step explanation:

3 0

3 years ago

The equation f(x) = 3x2 − 24x + 8 represents a parabola. What is the vertex of the parabola?

s2008m [1.1K]

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-24}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-24}{2(3)}~~,~~8-\cfrac{(-24)^2}{4(3)} \right)\implies (4~~,~~8-48)\implies (4~~,~-40)$

5 0

3 years ago

Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie

ludmilkaskok [199]

Answer:

$\lambda \geq 6.63835$

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

$P(X\geq 2)=1-P(X$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=\frac{e^{-\lambda} \lambda^0}{0!}=e^{-\lambda}$

$P(X=1)=\frac{e^{-\lambda} \lambda^1}{1!}=\lambda e^{-\lambda}$

And replacing we have this:

$P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^{-\lambda} +\lambda e^{-\lambda}[]$

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)$

And we want this probability that at least of 99%, so we can set upt the following inequality:

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)\geq 0.99$

And now we can solve for $\lambda$

$0.01 \geq e^{-\lambda}(1+\lambda)$

Applying natural log on both sides we have:

$ln(0.01) \geq ln(e^{-\lambda}+ln(1+\lambda)$

$ln(0.01) \geq -\lambda+ln(1+\lambda)$

$\lambda-ln(1+\lambda)+ln(0.01) \geq 0$

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

$x_{n+1}=x_n -\frac{f(x_n)}{f'(x_n)}$