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2 years ago

A group of pennies made in 2018 are weighed. The mean is approximately 2.5 grams

Mathematics

1 answer:

Hatshy [7]2 years ago

4 0

Answer:

* The mean (a measure of central tendency) weight value is the average of the weights of all pennies in the study.

* The standard deviation (a measure of variability or dispersion) describes the lowest and highest any individual penny weight can be. Subtracting 0.02g from the mean, you get the lowest penny weight in the group.

Step-by-step explanation:

Recall that a penny is a money unit. It is created/produced, just like any other commodity. As a matter of fact, almost all types of money or currency are manufactured; with different materials ranging from paper to solid metals.

A group of pennies made in a certain year are weighed. The variable of interest here is weight of a penny.

The mean weight of all selected pennies is approximately 2.5grams.

The standard deviation of this mean value is 0.02grams.

In this context,

* The mean (a measure of central tendency) weight value is the average of the weights of all pennies in the study.

Likewise, adding 0.02g to the mean, you get the highest penny weight in the group.

Hence, the weight of each penny in this study, falls within

[2.48grams - 2.52grams]

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Find x1 and x2.

stepladder [879]

Answer:

$x_1 = 7\\x_2 = 6$

Step-by-step explanation:

To find x₁ and x₂ :

$\left[\begin{array}{ccc}-4&1\\5&4\\\end{array}\right] \times \left[\begin{array}{ccc}x_1\\x_2\\\end{array}\right] + \left[\begin{array}{ccc}11\\-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\\\end{array}\right]$

Step 1

Multiply first 2 x 2 matrix with 2 x 1 vector, we get

$\left[\begin{array}{ccc}-4x_1&+ x_2\\5x_1&+ 4x_2\\\end{array}\right] + \left[\begin{array}{ccc}11\\-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\end{array}\right]$

Step 2

Add the 2 x 1 matrices on LHS, we get

$\left[\begin{array}{ccc}-4x_1&+x_2&+11\\5x_1&+4x_2&-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\end{array}\right]$

Step 3,

we get

$-4x_1 + x_2 + 11 = -11$

and

$5x_1 + 4x_2-19=40$

Step 4,

Simplify, we get

$-4x_1+x_2=-22----(1)\\ 5x_1+4x_2=59----(2)$

Step 5,

multiply eqn(1) by 4

we get

$16x_1+4x_2=-88$

Step 6,

eqn (2) - eqn(3)

we get

$21x_1 = 147\\x_1 =\frac{147}{21} \\x_1= 7$

substituting in eqn (1), we get

$(-4 \times 7) + x_2 = -22$

so, we get

$x_2 = 6$

Therefore

$x_1 = 7\\x_2 = 6$

5 0

2 years ago

Find the indicated length

OLga [1]

Answer:

ion know

Step-by-step explanation:

3 0

2 years ago

Which equation of the least squares regression line most closely matches the data set?

Rudiy27

Answer: y = 3.5 x+ 43.8

Step-by-step explanation:

Here x represents the number of years after 1990

Thus, we get the table that is used to find the equation will be,

x 0 2 4 6 8

y 45 51 57 61 75

Let the equation that shows the above data,

y = b + a x ---------(1)

$\text{Where, }a=\frac{\sum y \sum x^2-\sum x \sum xy}{n(\sum x^2)-(\sum x)^2}$

$\text{And, }b = \frac{\sum xy - \sum x\sum y}{n\sum x^2 - (\sum x)^2}$

By the above table,

$\sum x = 20$

$\sum xy = 1296$

$\sum x^2 = 120$

$\sum y = 289$

By substituting these values in the above value of a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equation (1)

we get, the equation that shows the given data is,

y = 3.5 x + 43.8

⇒ Option (3) is correct.

4 0

3 years ago

Read 2 more answers

Help with 19,20,21,23 please i don't understand geometry at all

Murrr4er [49]

19. What you know is that HK+KJ = HJ. If HJ = 25, the sum of the two equations will equal this length.

x-5+5x-12=25 First, combine your like terms. You will end up with 6x-17=25. Add the opposite of -17 to both sides. 6x = 42 Divide both sides by 6. x = 7. Substitute x=7 for your original expression of x-5, 7-5=2

20. (5x-6)/2 = x+6 Multiply each side by 2. 5x-6 = 2x +12 Add 6 to each side 5x = 2x + 18 then subtract 2x from both sides as well. 3x = 18 Finally divide each side by 3. x=6 To find the length of the remaining segment, substitute this value into (5x-6)/2. This results in each side equaling a distance of 12.

21. On the number line, the distance of FG is 16 units. If the distance of FP is 1/4 of FG, you would simply divide 16 by 4. The distance of FP is 4 and P lies at 8 on your number line.

23. The distance of SP is x+4 and ST=4x. Since P is the midpoint, you only have one half of the line as x+4, if you were to double it, you would find that 2x+8 = 4x. Balance and solve for x, subtract 2x from both sides. 8=2x Divide each side by 4, 8/4 = 4x/4 resulting in x=2. If ST equals 4x, substitute and solve, 4(2) = 8

8 0

2 years ago

Adult tickets for the school play are $12.00 and children's tickets are $8.00. If a theatre holds 300 seats and the sold out per

Vaselesa [24]

Let x = number of adult tickets, and y = number of children tickets. One equation must deal with the number of tickets, and the other equation must deal with the revenue from the tickets.

Then x + y = 300 is the number of tickets
12x + 8y = 3280 is the revenue from the tickets.

Using the substitution method:

x + y = 300   ⇒   y = 300 - x   ⇒   Equation (3)

12x + 8y = 3280   ⇒   12x + 8(300-x) = 3280   ⇒   x = 220

y = 300 - x   ⇒   y = 300-220 ⇒ 80

Therefore 220 adult tickets and 80 children's tickets were sold.

6 0

2 years ago