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2 years ago

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Mathematics

1 answer:

8090 [49]2 years ago

7 0

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b ) ( a − b ) where a = 7 and b = a + x . − ( 7 + a + x ) ( a + x − 7 )

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Keith is saving money for a car. He has saved the same amount each year for the past three years, and records how much he has at

noname [10]

Answer:

Keith's unit rate of change of dollars with respect to time is $1500.

Step-by-step explanation:

It is given that Keith is saving money for a car.

Year 1: 1500

year 2: 3000

year 3: 4500

Let y be the saved amount after x year.

The coordinate pairs according to the given table are (1,1500), (2,3000) and (3,4500).

The formula for rate of change is

Consider any two coordinate pairs.

Let as consider (1,1500) and (2,3000). So, Keith's unit rate of change of dollars with respect to time is

Therefore, Keith's unit rate of change of dollars with respect to time is $1500.

8 0

3 years ago

The area of a rectangle is 12.65 m^2. the length measures 5.5 m. what is the width of the rectangle?

Nat2105 [25]

Answer:

The width of the rectangle is 2.3 m

Step-by-step explanation:

Now, when we are asked to find the area of the rectangle, we will use the formula: $Area= length * width$ . We should be given with at least two values, and then we can use the above formula and can find the third variable.

Now, we are given that the area of a rectangle is 12.65 $m^2$ and the length measures 5.5 m

So the width is given as:

$Area= length * width\\\Rightarrow 12.56= 5.5 * width\\\Rightarrow width= \frac{12.56}{5.5}\\\Rightarrow width=2.3 ~m$

So this is the required with of the rectangle.

4 0

4 years ago

Read 2 more answers

4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ

galben [10]

Answer:

$\\ \mu = 118\;grams\;and\;\sigma=30\;grams$

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find $\\ \mu\;and\;\sigma$ .

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

$\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}$

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

$\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}$

$\\ 2.4 = \frac{190-\mu}{\sigma}$ (2)

<h3>Solving a system of equations for values of the mean and standard deviation</h3>

Having equations (1) and (2), we can form a system of two equations and two unknowns values:

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

$\\ 2.4 = \frac{190-\mu}{\sigma}$ (2)

Rearranging these two equations:

$\\ -0.6*\sigma = 100-\mu$ (1)

$\\ 2.4*\sigma = 190-\mu$ (2)

To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:

$\\ 0.6*\sigma = -100+\mu$ (1)

$\\ 2.4*\sigma = 190-\mu$ (2)

Summing both equations, we obtain the following equation:

$\\ 3.0*\sigma = 90$

Then

$\\ \sigma = \frac{90}{3.0} = 30$

To find the value of the mean, we need to substitute the value obtained for the standard deviation in equation (2):

$\\ 2.4*30 = 190-\mu$ (2)

$\\ 2.4*30 - 190 = -\mu$

$\\ -2.4*30 + 190 = \mu$

$\\ \mu = 118$

7 0

3 years ago

Your family goes to a Southern-style restaurant for dinner. There are 7 people in your family. Some order the chicken dinner for

butalik [34]

Answer:

a) 4 people ordered streak dinner

b) 3 people ordered chicken dinner

Step-by-step explanation:

Let the number of people that ordered steak dinner be x

and the number of people that ordered chicken dinner be y

From the question,

There are 7 people in your family

Hence, we can write that

x + y = 7 ...... (1)

Also from the question

Some order the chicken dinner for $13 and some order the steak dinner for $18 and the total bill was $111.

We can then write that

13y + 18x = 111 ...... (2)

From equation (1)

x + y = 7

Then,

x = 7 - y ...... (3)

Put this into equation (2)

13y + 18x = 111

13y + 18(7 - y) = 111

13y + 126 - 18y = 111

-5y = -15

5y = 15

y = 15 / 5

y = 3

Put the value of y into equation (3) to get x

x = 7 - y

Then

x = 7 - 3

x = 4

Hence, 4 people ordered streak dinner

and 3 people ordered chicken dinner

a) 4 people ordered streak dinner

b) 3 people ordered chicken dinner

3 0

3 years ago

A-b.a+b=<br> giúp mình nhé

lilavasa [31]

Step-by-step explanation:

Did you mean:

= (a - b)(a + b)

= a.a + b.a - b.a - b.b

= a² + ba - ba - b²

= a² - b²

3 0

3 years ago