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2 years ago

Triangle QRS is a right triangle.

Mathematics

1 answer:

olasank [31]2 years ago

5 0

Answer:

5.3

Step-by-step explanation:

a² + b² =² c² the Pythagorean theorem

RQ² + RS² = QS² Solve RS

6² + RS² = 8²

RS² = 64 -36

RS² = 28

RS = √28 28 is slightly > 25 and since √25 =5

RS = 5.3 actually 5.2915 to a few more significant digits

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What is the solution of 5y + 1=31

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Answer:

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kondor19780726 [428]

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Help....!! I need to solve this simultaneous equation y=x-2 and y=3x+5 With working out if possible please....

Blababa [14]

Step-by-step explanation:

Y= x - 2. Y = 3x + 5

Putting value of y

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2 years ago

Which of the following functions f : {0, 1, 2, 3} ! {0, 1, . . . , 7} are one-to-one?

allsm [11]

Answer:

1. No.

$f(0)=0\\1^2=1; \text{then } f(1)=1\\2^2=4\equiv 4 \text{ mod 8}; \text{then } f(2)=4\\3^2=9\equiv 1 \text{mod 8 }; \text{then } f(3)=1$

Since f(1)=f(3) and $1\neq 3$ then f isn't one-to-one.

2. No

$f(0)=0\\1^3=1\equiv 1\text{ mod 8}; \text{then } f(1)=1\\2^3=8\equiv 0\text{ mod 8}; \text{then } f(2)=0\\3^3=27\equiv 3 \text{ mod 8}; \text{then } f(3)=3$

Since f(0)=f(2) and $0\neq 2$ then f isn't one-to-one.

3. No

$0^3-8=-8\equiv 0\text{ mod 8}; \text{then } f(0)=0\\1^3-8=-7\equiv 1\text{ mod 8}; \text{then } f(1)=1\\2^3-8=0\equiv 0 \text{ mod 8}; \text{then } f(2)=0\\3^3-8=27-8=19\equiv 3 \text{ mod 8}; \text{then } f(3)=3\\$

Since f(0)=f(2) and $0\neq 2$ then f isn't one-to-one.

4. Yes

$0^3+2*0=0; \text{then } f(0)=0\\1^3+2*1=3\equiv 3\text{ mod 8}; \text{then } f(1)=3\\2^3+2*2=8+4=12\equiv 4 \text{ mod 8}; \text{then } f(2)=4\\3^3+2*3=27+6=33\equiv 1\text{ mod 8}; \text{then } f(3)=1$

Since $f(0)\neq f(1)\neq f(2) \neq f(3)$ , then f is one-to-one

5. Since f(1)=f(3) and $1\neq 3$ then, f isn't one-to-one

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3 years ago

A hotel manager believes that 14% of the hotel rooms are booked. If the manager is right, what is the probability that the propo

lara [203]

Answer:

0.4996

Step-by-step explanation:

We are given;

Population proportion; p = 14% = 0.14

Sample size; n = 804

Sample proportion; p^ = 13% = 0.13

Standard deviation; σ = √np(1 - p)

σ = √(804 × 0.14 × (1 - 0.14))

σ = 9.8388

Formula for z-score is;

z = (p^ - p)/σ

z = (0.13 - 0.14)/9.8388

z = -0.01/9.8388

z = -0.001

From online z-score and probability converter attached, we have;

P(Z < -0.001) = 0.4996

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2 years ago