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AleksAgata [21]

2 years ago

15

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. How many cups of trail mix will she make if she uses 8 cup

s of raisins?

1 answer:

alexgriva [62]2 years ago

5 0

Answer:

48

Step-by-step explanation:

8 divided by 2 = 4

4 times 12 = 48

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A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred

Paha777 [63]

Answer:

Step-by-step explanation:

Treat this like compound interest: Use A = P(1 + r)^t.

Here, P is the initial population and A is 3 times that, or 3P. Since P = 20 people, 3P = 60 people,

and this population is reached after 100 years.

We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.

60 = 20(1 + r)^100

Simplifying, 3 = (1 + r)^100.

Taking the natural log of both sides,

ln 3 = 100 ln (1 + r), or

ln 3

ln (1 + r) = ---------------

100

= 1.0986 / 100 = 0.01986

We must solve this for r. Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:

1 + r = 3, so r must = 2.

Now find the pop of the village today. Use the same equation: A = P (1+r)^t.

A = 20(1 +2)^4 (hundreds),

or

A = 20(3)^4, or

A = 81

The population after 400 years is 81.

8 0

2 years ago

The sales data for January and February of a frozen yogurt shop are approximately normal. The mean daily sales for January was $

VashaNatasha [74]

Answer:

January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.

Step-by-step explanation:

z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

January:

The mean daily sales for January was $300 with a standard deviation of $20. On the 15th of January, the shop sold $310 of yogurt. This means, respectively, that $\mu = 300, \sigma = 20, X = 310$ . So

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

$Z = \frac{310 - 300}{20}$

$Z = 0.5$

February:

The mean daily sales for February was $320 with a standard deviation of $50. On the 15th of February, the shop sold $340 of yogurt. This means, respectively, that $\mu = 320, \sigma = 50, X = 340$ . So

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

$Z = \frac{340 - 320}{50}$

$Z = 0.4$

January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.

3 0

2 years ago

A square lawn has area 800ft^2. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the

mestny [16]

I'm pretty sure your radius is 14.14'

3 0

2 years ago

Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps

Firdavs [7]

ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the

x²y = -4 ... (I)

Condition 2: Real parts are the same

x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

x²y = -4 ... (I)
x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

y = -3 - x² ... (II)

Substituting into equation (I)

x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i

x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i

They result in conjugates

4 0

2 years ago

Read 2 more answers

A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the

stiv31 [10]

Speed of current ------ y km/h

<span>distance with the current = 4(x+y) </span>
<span>distance against the current = 5(x-y) </span>

<span>we know that 3.5(x+y) = 70 </span>
<span>x+y = 20 </span>

<span>but 4(x+y) = 4(20) = 80 </span>
<span>then 5(x-y) = 80 </span>
<span>x-y = 16 </span>

<span>x+y=20 </span>
<span>x-y=16 </span>
<span>add them </span>
<span>2x = 36 </span>
<span>x = 18 , then y = 2 </span>

5 0

2 years ago