Ask question

Ask question

All categories

svet-max [94.6K]

3 years ago

9

A recipe for cookies calls for 1 cup of butter, twice as much sugar as butter, and three times as much flour as sugar. How many

cups of flour will you need if you halve the recipe? (Hint: Halving an amount is the same as dividing the amount by 2)

1 answer:

slavikrds [6]3 years ago

3 0

You would need 3 cups of flour because 1*2 is 2 and 2*3 is 6 and 6 divided by 2 is 3

You might be interested in

UNA POBLACION DE CIERTA CIUDAD EN EL AÑO 2000 ERA DE 250,000 HABITANTES CON UNA TASA DE CRECIMIENTO RELATIVO DEL 2% , DETERMINA

Fofino [41]

Answer:

La población que se espera para el 2012, es 317,060

Step-by-step explanation:

Si la población tiene un crecimiento relativo del 2%, entonces cada año, la población es un 2% más grande que el año anterior.

Definamos P(t) = población después de t años

Entonces, si al año t = 0 (que corresponde con el año 2000) la población es A

P(0) = A

Un año después, en t = 1, la población incrementa en un 2%

P(1) = A + (2%/100%)*A = A + (0.02)*A = A*(1.02)

Otro año después, en t = 2, la población incrementa un 2% de vuelta.

P(2) = A*(1.02) + (2%/100%)*A(1.02) = A*(1.02) + 0.02*A*(1.02)

= A*(1.02)*(1.02) = A*(1.02)^2

Ya podemos notar un patrón, la población en el año t va a ser:

P(t) = A*(1.02)^t

Sabemos que en t = 0 (el año 2000) la población es 250,000

Entonces A = 250,000

P(t) = 250,000*(1.02)^t

Ahora queremos calcular la población en el año 2012

entonces si t = 0 es el 2000

2012 esta representado con t = 12

Reemplazando eso en la ecuación, obtenemos:

P(12) = 250,000*(1.02)^12 = 317,060.4

Como esto es una población tenemos que redondearlo al próximo número entero, como el primer digito después del punto es 4, redondeamos para abajo.

Entonces la población que se espera para el 2012 es: 317,060

5 0

2 years ago

Jacub is trying to find the volume of a traffic cone that has the height of 2.4 ft and a diameter of 1.25 ft. He calculated that

Lubov Fominskaja [6]

Answer:

he did half the diameter

Step-by-step explanation:

3 0

3 years ago

Help Please!!!!!!!!!!!

Semmy [17]

You do copies divided by minutes

360/30=12

the printer produces 12 pages per minute

8 0

3 years ago

The reciprocal of my number is one fewer than the sum of the reciprocals of the two largest single digit prime numbers. What is

antoniya [11.8K]

The answer would be 2

7 0

3 years ago

When we toss a coin, there are two possible outcomes: a head or a tail. Suppose that we toss a coin 100 times. Estimate the appr

marin [14]

Answer:

96.42% probability that the number of tails is between 40 and 60.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

100 tosses, so $n = 100$

Two outcomes, both equally as likely. So $p = \frac{1}{2} = 0.5$

So

$E(X) = np = 100*0.5 = 50$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5$

Estimate the approximate probability that the number of tails is between 40 and 60.

Using continuity correction.

$P(40 - 0.5 \leq X \leq 60 + 0.5) = P(39.5 \leq X \leq 60.5)$

This is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 39.5. So

X = 60.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60.5 - 50}{5}$

$Z = 2.1$

$Z = 2.1$ has a pvalue of 0.9821

X = 39.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.5 - 50}{5}$

$Z = -2.1$

$Z = -2.1$ has a pvalue of 0.0179

0.9821 - 0.0179 = 0.9642

96.42% probability that the number of tails is between 40 and 60.

8 0

3 years ago