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2 years ago

7

Juan is making a fruit salad. He has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. He wants

his fruit salad to contain five different fruits. How many ways can he make the fruit salad if it must contain watermelon?

1 answer:

nika2105 [10]2 years ago

3 0

The number of ways that he can make the fruit salad if it must contain watermelon is 35.

<h3>What is Permutation and combination?</h3>

Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.

The salad contains water melon, now we have to select 4 more fruits out of 7.

Using combination

$^{n{C}_r$ = n! / r! (n-r)!

$^{7}C_4$ = 7!/ 4! (7-4)!

= 7*6*5*4! / 4! * 3*2

= 35

Hence, number of ways that he can make the fruit salad if it must contain watermelon is 35.

Learn more about Permutation and combination here:

brainly.com/question/11732255

#SPJ1

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What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

1. $Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
$5\cdot 5=25=\overline{3};$
$5\cdot 6=30=\overline{8};$
$5\cdot 7=35=\overline{2};$
$5\cdot 8=40=\overline{7};$
$5\cdot 9=45=\overline{1};$
$5\cdot 10=50=\overline{6}.$

The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
$5\cdot 8=40=\overline{1};$
$5\cdot 9=45=\overline{6};$
$5\cdot 10=50=\overline{11};$
$5\cdot 11=55=\overline{3};$
$5\cdot 12=60=\overline{8}.$

The multiplicative inverse of 5 in $Z_{13}$ is 8.

8 0

4 years ago

Which angle measures create a triangle with three different side lengths. 40°, 40°, and 100° 65°, 65°, and 65° 45°, 45°, and 90°

Gala2k [10]

Answer:

29°, 58°, and 93°

Step-by-step explanation:

If the angles opposite are equal, the sides are equal. In order to have three different side lengths, you must have <em>three different angles</em>.

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3 years ago

Amy, Lee, Tom and Uma are candidates in the school election. The person

Reil [10]

Answer:

Tom/Lee

Step-by-step explanation:

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3 years ago

Solve by completing the square<br><br> x^2-6x-16=0

Greeley [361]

Answer:

x = 8 or

x = -2

Step-by-step explanation:

<h2><em>Completing The Square</em><em>:</em></h2>

x² - 6x - 16 = 0

Here,

a = 1

b = -6

c = -16

Now,

x² - 6x + [6/2(1)]² - [6/2(1)]² - 16 = 0

x² - 6x + (6/2)² - (6/2)² - 16 = 0

x² - 6x + (3)² - (3)² - 16 = 0

(x - 3)² - 9 - 16 = 0

(x - 3)² - 25 = 0

(x - 3)² = 25

x - 3 = +-√25

x - 3 = +- 5

x = 3 +- 5

x = 3 + 5 or x = 3 - 5

<em><u>x = 8 or x = -2</u></em>

Hope it's helpful

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3 years ago

Read 2 more answers

Suppose two radii of a circle determine a 45° angle, and the length of both radii is 64 yards. What is the arc length formed by

Ilia_Sergeevich [38]

The arc length formed by the 2 radio is 15.24 yards

Step-by-step explanation:

Angle between the 2 radio = 45°

Radius = 64 yards

Arc length = (45/360) (2π) (64)

= (1/8) (2π) (64

= 16π

= 16(3.14)

=15.24 yards

The arc length formed by the 2 radio is 15.24 yards

8 0

4 years ago