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2 years ago

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Brand A bird seed is 20% sunflower seeds by weight. Brand B is 60% sunflower seed b weight. How many pounds of each must be mixe

d to get 50 pounds of bird seed that is 50% sunflower seed?

1 answer:

iogann1982 [59]2 years ago

8 0

Answer:

12.5 lb of Brand A and 37.5 lb of Brand B

Step-by-step explanation:

Let a = weight of Brand A.

Let b = weight of Brand B.

To make 50 lb of bird seed, we get the equation:

a + b = 50

Now we deal with the amount of sunflower seed in each Brand and in the final mixture.

a amount of Brand A has 0.2a amount of sunflower seed.

b amount of Brand B has 0.6b amount of sunflower seed.

50 lb of the mixture has 0.5 × 50 lb = 25 lb of sunflower seed.

That gives us the second equation.

0.2a + 0.6b = 25

We have a system of equations:

a + b = 50

0.2a + 0.6b = 25

Solve the first equation for a and substitute in the second equation.

a = 50 - b

0.2(50 - b) + 0.6b = 25

10 - 0.2b + 0.6b = 25

0.4b + 10 = 25

0.4b = 15

b = 37.5

Now substitute 37.5 for b in the first original equation and solve for a.

a + 37.5 = 50

a = 12.5

12.5 lb of Brand A and 37.5 lb of Brand B

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gayaneshka [121]

Answer: $d_{AB}=11.31\ units$

Step-by-step explanation:

The formula for calculate the distance between two points is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this case, given the points A(4,-6) and B(-4,2), we can identify that, we just need to substitute values into the formula in order to calculate the distance between the given points.

Thierefore, this is (Rounded to the nearest hundred):

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4 years ago

Mrac [35]

Answer:

this answer requires that you do a little solving to find all the dimensions we need for the volume.

We know that H (height) = 2m

Diameter = 5 x height, so

Diameter = 5 x 2m = 10m

If you have the formula for finding the volume of a cylinder, it is basically the area of the circular base x cylinder height. You may know already that the area of a circle is (pi) x radius2

So this will be 2 (the height) x (pi) x r2

As we just figured out, the DIAMETER is 10, so the radius is half the diameter = 5.

This brings our volume to 2 x (pi) x 52

= 2 x (pi) x 25

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3 years ago

Math work help please

schepotkina [342]

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3 years ago

Read 2 more answers

A sine function had an amplitude of 3, period of 6pi, horizontal shift of 3pi/2, & vertical shift of -1.

Simora [160]

Answer: $\bold{y=\dfrac{1}{2}}$

<u>Step-by-step explanation:</u>

f(x) = A sin (Bx - C) + D

amplitude = |A|
period = $\dfrac{2\pi}{B}$
phase shift = $\dfrac{C}{B}$
vertical shift = D

<u>A</u>

amplitude of 3 is given so 3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

<u>B</u>

period of 6π is given so $6\pi=\dfrac{2\pi}{B}\quad \rightarrow \quad B=\dfrac{2\pi}{6\pi}\quad \rightarrow \quad B=\dfrac{1}{3}$

<u>C</u>

$\text{phase shift is given as}\ \dfrac{3\pi}{2}\ \text{so}\ \dfrac{3\pi}{2}=\dfrac{C}{\frac{1}{3}}\quad \rightarrow\quad \dfrac{(\frac{1}{3})3\pi}{2}=C\quad \rightarrow\quad \dfrac{\pi}{2}=C$

<u>D</u>

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

$f(x) = 3\ sin \bigg(\dfrac{1}{3}x - \dfrac{\pi}{2}\bigg) - 1$

Next, solve when x = 2π

$f(2\pi) = 3\ sin \bigg(\dfrac{1}{3}(2\pi) - \dfrac{\pi}{2}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{2\pi}{3} - \dfrac{\pi}{2}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{4\pi}{6} - \dfrac{3\pi}{6}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{\pi}{6}\bigg) - 1$

$= 3\ \bigg(\dfrac{1}{2}\bigg) - 1$

$=\dfrac{3}{2}-\dfrac{2}{2}$

$=\dfrac{1}{2}$

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3 years ago

A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3 hour

vitfil [10]

Testing the hypothesis using the z-distribution, it is found that since the p-value of the test is of 0.0262 < 0.05, it <u>can be concluded that the new booklet is effective</u>.

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$H_0: \mu = 3$

At the alternative hypothesis, we <u>test if there has been improvement</u>, that is, the time is of less than 3 hours. Thus:

$H_1: \mu < 3$

We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.
$\mu$ is the value tested at the null hypothesis.
$\sigma$ is the standard deviation of the population.
n is the sample size.

In this problem, the values of the parameters are: $\mu = 3, \sigma = 0.2, \overline{x} = 2.9, n = 15$ .

Then, the value of the test statistic is:

$z = \frac{2.9 - 3}{\frac{0.2}{\sqrt{15}}}$

$z = -1.94$

The p-value of the test is the probability of finding a sample mean of 2.9 hours or less, which is the <u>p-value of z = -1.94.</u>

Looking at the z-table, z = -1.94 has a p-value of 0.0262.

Since the p-value of the test is of 0.0262 < 0.05, it <u>can be concluded that the new booklet is effective</u>.

A similar problem is given at brainly.com/question/25413422

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3 years ago