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3 years ago

A single die is rolled. How many ways can you roll a number that is prime, followed by a 6?

Mathematics

2 answers:

Grace [21]3 years ago

5 0

Answer:

3 ways

Step-by-step explanation:

Since 6 will remain constant throughout the testing, we just need to find all prime numbers 1-6.

1 - is not prime nor composite

2 - is prime

3 - is prime

4 - 2x2=4, so composite

5 - is prime

6 - 2x3=6, so composite

Therefore, 2, 3, and 5 are prime numbers, and there are 3 of them.

Anika [276]3 years ago

4 0

Answer:

3 ways

Step-by-step explanation:

2 , 3 and 5 are prime numbers.

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Find three consctive postive integers such that the prodect of the median integer and the largest integer is 72

Tcecarenko [31]

Answer: 7,8,9

Step-by-step explanation:

Let the numbers be a, a+1 and a+2. Therefore, based on the question, this will be:

= (a + 1)(a + 2) = 72

a² + 2a + a + 2 = 72

a² + 3a + 2 - 72 = a

a² + 3a - 70 = 0

a² + 10a - 7a - 70 = 0

a(a + 10) - 7(a + 10)

a - 7 = 0

a = 7

Since a = 7

a + 1 = 7+1 = 8

a + 2 = 7+2 = 9

The numbers are 7,8 and 9

8 0

2 years ago

Find the missing x- and y-values and Pythagorean triples can be generated using the identity given. Write the triple in parenthe

ddd [48]

The complete question is:

Find the missing x- and y-values and Pythagorean triples using the identity given:

(x² - y²)² + (2xy)² = (x² + y²)²

X Value: 4

Y Value: 3

Pythagorean Triples: ?

X Value: 5

Y Value: ?

Pythagorean Triples: (9,40,41)

X Value: ?

Y Value: 3

Pythagorean Triples: (27,36,45)

X Value: 7

Y Value: 5

Pythagorean Triples: ?

Step-by-step explanation:

Pythagorean triples are three numbers p, q, r, that satisfy Pythagoras' theorem.

That is, they are numbers such that

r² = p² + q².

Given the identity

(x² - y²)² + (2xy)² = (x² + y²)²

We can say tha

p = x² - y²

q = 2xy

r = x² + y²

Now, let us use this to solve the given problems.

X Value: 4

Y Value: 3

p = 4² - 3² = 7

q = 2×3×4 = 24

r = 3² + 4² = 25

Pythagorean Triples: (7,24,25)

X Value: 5

Y Value: ? = (4)

q = 2xy = 40

2×5×y = 40

y = 40/10 = 4

Pythagorean Triples: (9,40,41)

X Value: ? = (6)

Y Value: 3

2xy = q = 36

2×3×x = 36

x = 36/6 = 6

Pythagorean Triples: (27,36,45)

X Value: 7

Y Value: 5

p = 7² - 5² = 24

q = 2×7×5 = 70

r = 7² + 5² = 74

Pythagorean Triples: ? = (24,70,74)

8 0

3 years ago

What is the volume of corn held in this cone-shaped grain silo? Use 3.14 for π and round to the nearest cubic foot. Enter your a

babymother [125]

Answer:

V = 301 ft^3

Step-by-step explanation:

The volume of a cone is given by

V =1/3 pi r^2 h

We know pi = 3.14 r =6 and

We need to determine h

We can find h from the Pythagorean theorem where 6 is a leg and 10 is the hypotenuse

h^2 +6^2 = 10^2

h^2 +36 = 100

h^2 = 64

Taking the square root of each side

h = 8

V =1/3 pi r^2 h

V = 1/3 (3.14) (6)^2 * 8

V = 301.44 ft^3

Rounding to the nearest cubic foot

V = 301 ft^3

7 0

3 years ago

Read 2 more answers

Need help asap The answer is 100 or 126

Serga [27]

Answer:

The surface area of the cone is 126π cm².

Step-by-step explanation:

The surface area of a cone can be found using this formula:

$\text{SA} = \pi r ^2+\pi r l$
where r = radius and l = slant height

In this problem, we are told that the cone has a radius of 9 cm and a slant height of 5 cm.

Substitute these values into the formula for the surface area of a cone.

$\text{SA}= \pi (9)^2+ \pi(9)(5)\\$
$\text{SA}= \pi (81)+ \pi(45)$
$\text{SA}= 126 \pi$

The surface area of the right cone is 126 π cm².

6 0

2 years ago

Reality Check 4: Bringing the NBA into Math 0980

rusak2 [61]

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3 years ago

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