Which choice shows (50 + 20) + 30 correctly rewritten using the associative

3 Fred is making a fruit salad. The ratio

marusya05 [52]

Answer: 24 cups.

Step-by-step explanation:

Let be "x" the amount of cups of peaches that Fred will need to make 60 cups of fruit salad.

According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:

$2:3$

Which can also be written as a fraction:

$\frac{2}{3}$

Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.

Knowing the above, you can set up the following proportion:

$\frac{2}{5}=\frac{x}{60}$

Now you must solve for "x" in order to find its value. This is:

$(60)(\frac{2}{5})=x\\\\x=24$

5 0

3 years ago

Lou has a solid clay brick in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of

Rzqust [24]

The weight of solid clay brick is 66.465 ounces, if solid brick with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches and the clay weighs 1.055 ounces per cubic inch.

Step-by-step explanation:

The given is,

A solid clay brick in the shape of a rectangular prism.

A length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches.

The clay weighs 1.055 ounces per cubic

Step:1

Formula for volume of rectangular prism,

$Volume, V= whl$ ...................(1)

Where, w - Width of the rectangular prism

h - Height of rectangular prism

l - Length of rectangular prism

From the given,

w = 3.5 inches

h = 2.25 inches

l = 8 inches

Equation (1) becomes,

$= (3.5)(2.25)(8)$

$= (7.875)(8)$

$= 63$

Volume, V = 63 cubic inches

Step:2

Weight of brick = Volume of brick × Weight per cubic inch

$= (63) (1.055)$

= 66.465 ounces

Weight of brick = 66.465 ounces

Result:

The weight of solid clay brick is 66.465 ounces, if solid brick with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches and the clay weighs 1.055 ounces per cubic inch.

7 0

2 years ago

What is the mean of this data set? 17,34,19,27,30,23

Morgarella [4.7K]

Answer: The mean of the data set is 25.

Step-by-step explanation:

To calculate the mean of a data set, first add up all the values.

17 + 34 + 19 + 27 + 30 + 23 = 150

Then divide the sum by the amount of values in the data set. Our sum here is 150 and the amount of data values is 6.

150 ÷ 6 = 25

8 0

3 years ago

Read 2 more answers

If a+b+c=−10 and x + y + z =−10 what is -6c - 6b + 6z + 6x + 6y −6a

vovikov84 [41]

-6(a+b+c) +6(x+y+z)
= -6(-10) +6(-10)
= 60 -60 = 0

7 0

3 years ago

Please answer that question

german

The polar form of the complex numbers are z₁ = 6 · $e^{i\,\frac{11\pi}{6} }$ and z₂ = √2 · $e^{i\,\frac{3\pi}{4} }$ . The multiplication of the numbers is z₁ · z₂ = 6√2 · $e^{i\,\frac{31\pi}{12} }$ , the division of the numbers is z₁ / z₂ = 3√2 · $e^{i\,\frac{13\pi}{12} }$ and the reciprocal of a number is 1 / z₁ = (1 / 6) · $e^{-i\,\frac{11\pi}{6} }$ .

<h3>How to find complex numbers in polar forms and make operations with them </h3>

In this problem we find two complex numbers in rectangular form (z = a + i b), whose polar form has to be found. The complex form is described below:

z = r · $e^{i\,\theta}$

Where:

r - Norm
θ - Direction, in radians.

The magnitude is determined by Pythagorean theorem:

r = √(a² + b²)

And the direction by inverse trigonometric functions:

θ = tan⁻¹ (b / a)

Polar form offers a quicker manner to perform multiplication and division of complex numbers. Thus:

Multiplication

z₁ · z₂ = r₁ · r₂ · $e^{i\,(\theta_1 + \theta_2)}$

Division

z₁ / z₂ = (r₁ / r₂) · $e^{i\,\frac{\theta_{1}}{\theta_{2}} }$

First, determine the magnitudes of each complex number:

r₁ = √[(3√3)² + (- 3)²]

r₁ = 6

r₂ = √[(- 1)² + 1²]

r₂ = √2

Second, determine the directions of each complex number:

θ₁ = 11π / 6

θ₂ = 3π / 4

Third, write the complex numbers in polar form:

z₁ = 6 · $e^{i\,\frac{11\pi}{6} }$

z₂ = √2 · $e^{i\,\frac{3\pi}{4} }$

Fourth, find the multiplication of the complex numbers:

z₁ · z₂ = 6√2 · $e^{i\,\frac{31\pi}{12} }$

Fifth, find the division of the complex numbers:

z₁ / z₂ = 3√2 · $e^{i\,\frac{13\pi}{12} }$

Sixth, find the reciprocal of the complex number:

1 / z₁ = (1 / 6) · $e^{-i\,\frac{11\pi}{6} }$

To learn more on complex numbers: brainly.com/question/20566728

#SPJ1

6 0

10 months ago