-4 (9x-2) simplify expression using distributive property

A clothing store has just advertised at a bargain price, that a customer tries on a t-shirt is 0.40. a new range of t-shirts. Th

AlexFokin [52]

<h2>Answer:</h2>

The probability that the customer did not try on the t- shirt is:

0.2432

<h2>Step-by-step explanation:</h2>

It is given that the probability that a customer tries a t-shirt is: 0.40

After he will try

The probability that he will buy the t-shirt is: 0.70

The probability that he will not try t-shirt is: 1-0.40=0.60

If he will not try

then the probability of buying a t-shirt is: 0.15

This means that the total probability of Buying a t-shirt is:

0.40×0.70+0.60×0.15

= 0.37

It is given that the customer bought a t-shirt, we need to find the probability that he did not try the t-shirt:

The probability is given by:

$\dfrac{0.60\times 0.15}{0.37}\\\\\\=\dfrac{0.09}{0.37}\\\\\\=0.2432$

4 0

3 years ago

the area of a right triangle is 77 m^2. the hypotenuse has a length of √317 m. what is the length of the legs?

Alexxandr [17]

Answer:

11 m and 14 m

Step-by-step explanation:

Legs: x and y

---

1/2xy= 77 ⇒ xy= 154

√x²+y²= √317 ⇒ x²+y²=317

x²+y²+2xy= (x+y)²= 2*154+317= 625 ⇒ x+y= √625= 25

x= 25-y

xy=154 ⇒ y(25-y)= 154 ⇒ 25y- y²=154 ⇒ y²- 25y +154=0 ⇒ y=11 and y=14

x= 25-y= 14 and 11

4 0

4 years ago

3

DochEvi [55]

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve " $curve_{big}$ " and the three smaller curves " $curve_1$ " " $curve_2$ " " $curve_3$ " in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

<u>Parts of a circle</u>

Since values in the diagram are diameters, use the formula for the Perimeter of a circle $P=\pi d$ (where d is the diameter).

Let's call the diameters of each of our curves " $d_{big}$ " " $d_1$ " " $d_2$ " " $d_3$ ", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: $Length(curve_{big})=\frac{1}{2} \pi d_{big}$

Substituting back into the main equation above:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ $P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}$

Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

The diameter for the large Curve, is the sum of the three small diameters, so $d_{big}=12cm$ , and $d_{1}=d_{2}=d_{3}=4cm$

Substituting and simplifying (in terms of pi):

$P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm$

<u>Additional Understanding</u>

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve $d_{1} + d_{2} + d_{3} =d_{big}$ , one could make a different substitution into one of our formulas above:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

$P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))$

$P_{overall}=\frac{1}{2} \pi (2d_{big})$

$P_{overall}=\pi d_{big}$

Notice that $\pi d_{big}$ is just the full perimeter of a circle with the big diameter.

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.

7 0

2 years ago

Solve for x. Find the exact answer by simplifying the radical.<br> 3<br> 24

zvonat [6]

Download the app named connects works everytime i swear

6 0

3 years ago

A square television screen has a side length of 10 inches. What is the approximate length of the diagonal of the television scre

Sedbober [7]

14.142 inches is my answer. You would use the Pythagorean theorem for this by the way.

5 0

3 years ago