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nata0808 [166]
3 years ago
10

Which statement is true about the product square root of 2(3square root of 2 + square root of 18)?

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
4 0
We are asked to determine the product of square root of 2 and 3 square root of 2 + square root of 14. In this case, we can use the calculator directly to find the answer to the given problem. The answer is A.12. we can also multiply 2 to the numbers under the radical and then simplify to get 12, nonetheless
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5. A deck should have a perimeter of 90 feet and a minimum area
Ket [755]

Answer:

The minimum value of the width is 15 ft and the maximum value of the width is 30 ft

Step-by-step explanation:

Let

x -----> the length of the deck

y ----> the width of the deck

we know that

The perimeter of the deck is equal to

P=2(x+y)

P=90\ ft

so

90=2(x+y)

45=(x+y)

x=45-y -----> equation A

The area is equal to

xy\geq 450 -----> inequality B  

(45-y)y\geq 450\\ \\-y^{2} +45y-450\geq 0

Solve the quadratic equation by graphing

The possible width of the deck are the values of y in the interval

[15,30]

All real numbers greater than or equal to 15 ft and less than or equal to 30 ft

see the attached figure

The minimum value of the width is 15 ft and the maximum value of the width is 30 ft

7 0
3 years ago
The digits 4 comma 5 comma 6 comma 7 comma and 8 are randomly arranged to form a​ three-digit number. ​ (Digits are not​ repeate
fenix001 [56]

Answer:

0.1 or 1/10

Step-by-step explanation:

The digits 4, 5, 6, 7 and 8 are randomly arranged to form a three digit number, where the digits are not repeated.

This is question of permutation.

Imagine this sum as; there are 3 boxes(blank spaces for digits) and 5 different fruits(digits) are to be put in these boxes, where a box can hold a maximum of only 1 fruit. The number of such permutations are: ⁵P₃

By formula (a! is factorial a):

ᵃPₙ = \frac{a!}{(a-n)!}

⁵P₃ = \frac{5!}{(5-3)!}

⁵P₃ = \frac{5!}{2!}

⁵P₃ = \frac{5*4*3*2*1}{2*1}

⁵P₃= 60

This is the total count of possible numbers that can be formed.

Now, for a number to be greater than 800 and even; first digit should necessarily be 8. Last digit can be 4 or 6. Using these conditions, there are 6 possibilities. 854, 864, 874, 846, 856, 876 are the numbers.

The probability that number is even and greater than 800 is:

P=\frac{ favorable outcomes}{equally likely possible outcomes}

P=\frac{6}{60}

P=\frac{1}{10}

3 0
3 years ago
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