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fgiga [73]
3 years ago
6

A certain recipe calls for 2 3/4 cups of sugar.if the recipe is to be doubled, how much sugar should be used

Mathematics
1 answer:
Morgarella [4.7K]3 years ago
3 0
2 and 3/4 + 2 and 3/4 is 5 and 1/2. 
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Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that
Mrrafil [7]

Answer:

The probability that a random selected student score is greater than 76 is \\ P(x>76) = 0.99865.

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two <em>parameters</em>, the <em>population mean</em> \\ \mu and the <em>population standard deviation</em> \\ \sigma.

To determine probabilities for the normal distribution, we can use <em>the standard normal distribution</em>, whose parameters' values are \\ \mu = 0 and \\ \sigma = 1. However, we need to "transform" the raw score, in this case <em>x</em> = 76, to a z-score. To achieve this we use the next formula:

\\ z = \frac{x - \mu}{\sigma} [1]

And for the latter, we have all the required information to obtain <em>z</em>. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

\\ \mu = 85

\\ \sigma = 3

\\ x = 76

From equation [1], we have:

\\ z = \frac{76 - 85}{3}

Then

\\ z = \frac{-9}{3}

\\ z = -3

Second: Interpretation of the previous result.

In this case, the value is <em>three</em> (3) <em>standard deviations</em> <em>below</em> the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of \\ z = -3, we can obtain this probability consulting <em>the cumulative standard normal distribution, </em>available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the <em>cumulative standard normal distribution</em> are for positive values of z. Fortunately, since the normal distributions are <em>symmetrical</em>, we can find the probability of a negative z having into account that (for this case):

\\ P(z>-3) = 1 - P(z>3) = P(z

Then

Consulting a <em>cumulative standard normal table</em>, we have that the cumulative probability for a value below than three (3) standard deviations is:

\\ P(z

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, \\ \mu = 85 and \\ \sigma = 3) is \\ P(x>76) = P(z>-3) = P(z.

As a conclusion, more than 99.865% of the values of this distribution are above (greater than) x = 76.

<em>We can see below a graph showing this probability.</em>

As a complement note, we can also say that:

\\ P(z3)

\\ P(z3)

Which is the case for the probability below z = -3 [P(z<-3)], a very low probability (and a very small area at the left of the distribution).

5 0
3 years ago
The square shown has a perimeter of 32 units. The square is rotated about line k. What shape is created by the rotation and what
harkovskaia [24]
The perimeter of the square is calculated through the equation,
                                        4x = P
where P is the perimeter and x is the measure of the sides.

When P is 32 units then,
                                         32 units = 4(x)
                                                 x = 8 inches

This 8 inches is the diameter of the cylinder formed by the rotation. 
The circumference of the base is calculated through,
                            C = 2πr = πD
Substituting the known values,
                              C = π(8 units) = <em>8π units
</em>
<em></em>When π is equal to 3.14, we solve for the numerical value of the cylinder as follows,
<em>                                      C = 8(3.14) = 25.12 units
</em>
<em></em>Thus, the figure formed is a cylinder with base circumference equal to 25 units. The answer is the third choice. <em>
</em>
6 0
3 years ago
Read 2 more answers
Please help with this question asap i will give brainliest
sergiy2304 [10]

Answer:

B is your answer,

With the factors of ( 2 )( 1 ), the lay out of the equation makes only sense with answer B.

6 0
3 years ago
Read 2 more answers
Find the value of x in the triangle.
Vinvika [58]

=  > 3x + 15 + 4x + 12 = 180 \\  =  > 7x + 27 = 180 \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  =  >  \: 7x = 180 - 27 = 153 \:  \:  \:  \:  \\ x =  \frac{153}{7} = 21  \\ x = 21

3 0
2 years ago
Use I = PRT to solve.
Mice21 [21]

Answer:

Time T = 15 year

Step-by-step explanation:

Given:

Interest I = $270,000

Principal P = $150,000

Rate R = 12% = 0.12

Find:

Time T

Computation:

I = PRT

270,000 = (150,000)(0.12)(T)

270,000 = (18,000)(T)

Time T = 15 year

4 0
3 years ago
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