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3 years ago

6

By decreasing each dimension by 1 unit, the area of a rectangle decreased from 40 square feet (on the left) to 28 square feet

(on the right). Find the percent decrease in area.

1 answer:

BabaBlast [244]3 years ago

7 0

Attached a pic of the solution (s).

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A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normall

Vlad1618 [11]

Answer: (2.54,6.86)

Step-by-step explanation:

Given : A random sample of 10 parking meters in a beach community showed the following incomes for a day.

We assume the incomes are normally distributed.

Mean income : $\mu=\dfrac{\sum^{10}_{i=1}x_i}{n}=\dfrac{47}{10}=4.7$

Standard deviation : $\sigma=\sqrt{\dfrac{\sum^{10}_{i=1}{(x_i-\mu)^2}}{n}}$

$=\sqrt{\dfrac{(1.1)^2+(0.2)^2+(1.9)^2+(1.6)^2+(2.1)^2+(0.5)^2+(2.05)^2+(0.45)^2+(3.3)^2+(1.7)^2}{10}}$

$=\dfrac{30.265}{10}=3.0265$

The confidence interval for the population mean (for sample size <30) is given by :-

$\mu\ \pm t_{n-1, \alpha/2}\times\dfrac{\sigma}{\sqrt{n}}$

Given significance level : $\alpha=1-0.95=0.05$

Critical value : $t_{n-1,\alpha/2}=t_{9,0.025}=2.262$

We assume that the population is normally distributed.

Now, the 95% confidence interval for the true mean will be :-

$4.7\ \pm\ 2.262\times\dfrac{3.0265}{\sqrt{10}} \\\\\approx4.7\pm2.16=(4.7-2.16\ ,\ 4.7+2.16)=(2.54,\ 6.86)$

Hence, 95% confidence interval for the true mean= (2.54,6.86)

7 0

3 years ago

A box contains four red, three blue, and six green lenses. two lenses are randomly selected from the box. find the probability o

andrew-mc [135]

The probability of getting two red lenses when two are selected will be 2/13.

<h3>What is probability?</h3>

The probability of favorable events to the total number of occurrences.

A box contains four red, three blue, and six green lenses.

Two lenses are randomly selected from the box.

Then the probability of getting two red lenses when two are selected if the first selection is not replaced before the second selection is made will be

The total number of the event will be

Total event = ¹³C₂

Total event = 78

Then the favorable event will be

Favorable event = ⁴C₁ x ³C₁

Favorable event = 4 x 3 = 12

Then we have

P = 12 / 78

P = 2/13

More about the probability link is given below.

brainly.com/question/795909

#SPJ1

6 0

1 year ago

Find the volume of the cone.<br> 13 cm<br> r= 9 cm<br> V = [?] cm3<br> Round to the nearest tenth.

Kaylis [27]

DONT GO TO THOSE LINKS

4 0

2 years ago

Select the polynomial that is a perfect square trinomial. 9x2 9x 1 36b2 − 24b 8 16x2 24x 9 4a2 − 10a 25.

alexgriva [62]

The polynomial that is a perfect square is 16x^2 + 24x +9. Option C shows the polynomial which is a perfect square.

<h3>What is square?</h3>

The square can be defined as a two-dimensional figure that has 4 equal sides.

Given are the equations of the areas of the polynomial.

Option C: $16 x^2 + 24x +9$

We can write the above equation as,

$(4x)^2 + 2 \times 4x \times 3 + (3)^2$

$(a+b)^2 = a^2 + 2ab+b^2$

Here a = 4x and b = 3, so

$16x^2 + 24x+9 = (4x+3)^2$

The simplification of the area of a polynomial is (4x+3)^2 which represents the area of a square.

Hence the polynomial that is a perfect square is 16x^2 + 24x +9. Option C shows the polynomial which is a perfect square.

To know more about the area of the square, follow the link given below.

brainly.com/question/1658516.

5 0

1 year ago

What is the midpoint of the segment (0,9) and (5,4)

Debora [2.8K]

This is easy the answer is 56

3 0

3 years ago