MATHEMATICS HIGH SCHOOL

True or False:8. V 40 has an infinite non-repeating decimal expansion.
9. The number 0.56 is a rational number
10. 200 and 500 are integers.
11. All numbers with infinite decimal expansions are irrational.
12.
the numbers -8, -3, 5, 17 are all whole numbers.

Answers

Answer 1
Answer:

Answer:

Below.

Step-by-step explanation:

8.  True ( all numbers of the form √n where n is not a perfect square have this property)

9.  True  ( we can write it as 56/100 or 14/25).

10. True.

11.   False. ( 1/3 is rational and its decimal form is 0.333............. )

12.  False. ( negative numbers are not whole numbers).

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At the beginning of this month, the balance of Agatha's checking account was $782.39. So far this month, she has received a paycheck via direct deposit of $932.48, been charged a monthly service fee from her bank of $20.00, used a debit card linked to her account to make a purchase of $36.82, written a check for $155.03 that has already been deposited, and deposited a check written to her for $79.13. What is the current balance of Agatha's checking account?

Answers

Agatha started out the month with $782.39 cents. After she received her paycheck, she had a balance of $1,714.87. Agatha then had a service fee and few purchases which left the total at $1503.02. She then had an additional check written to her for $79.13. The current balance after her last deposited check was $1,582.15.

Answer: $1582.15

Step-by-step explanation:

The orthocenter of an obtuse triangle always lies __________.A.on a vertex of the triangle
B.on the inside of the triangle
C.on the outside of the triangle
D.on the triangle

Answers

the correct answer is D

A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the​ width, find the dimensions of the pool.

Answers

Answer:

x \approx 21.080\,ft, y = 29.080\,ft

Step-by-step explanation:

The total area of the pool and the walkway is:

(x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^(2)

(x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^(2)

x^(2) + 20\cdot x + 84\,ft^(2) = 950\,ft^(2)

x^(2) + 20\cdot x - 866\,ft^(2) = 0

The roots of the second-order polynomial is:

x_(1) \approx 21.080\,ft and x_(2) \approx -41.081\,ft

The only possible root is:

x \approx 21.080\,ft

The other dimension of the pool is:

y = x + 8\,ft

y = 21.080\,ft + 8\,ft

y = 29.080\,ft

Please solve equations by completing square

Answers

x^2-4x+1=0\n x^2-4x+4-3=0\n (x-2)^2=3\n |x-2|=\sqrt3\n x-2=\sqrt3 \vee x-2=-\sqrt3\n x=2+\sqrt3 \vee x=2-\sqrt3

x^2+6x-9=0\n x^2+6x+9-18=0\n (x+3)^2=18\n |x+3|=√(18)=3\sqrt2\n x+3=3\sqrt2 \vee x+3=-3\sqrt2\n x=-3+3\sqrt2 \vee x=-3-3\sqrt2\n

x^2+20x+3=0\n x^2+20x+100-97=0\n (x+10)^2=97\n |x+10|=√(97)\n x+10=√(97) \vee x+10=-√(97)\n x=-10+√(97) \vee x=-10-√(97)

x^2-2x-5=0\n x^2-2x+1-6=0\n (x-1)^2=6\n |x-1|=\sqrt6\n x-1=\sqrt6 \vee x-1=-\sqrt6\n x=1+\sqrt6 \vee x=1-\sqrt6

Factor completely:
v^4+6v^2+5

Answers

v⁴ + 6v² + 5
v⁴ + 5v² + v² + 5
v²(v²) + v²(5) + 1(v²) + 1(5)
v²(v² + 5) + 1(v² + 5)
(v² + 1)(v² + 5)

Using your calculator, find the proportion of observations from a standard normal distribution that satisfies the following statement. Sketch the normal curve and shade the area under the curve that is the answer to the question: Z < –1.5.

Answers

Final answer:

The proportion of observations from a standard normal distribution that satisfies the statement Z < -1.5 is approximately 0.0668. To depict this, one can sketch a normal curve with the mean at the center and shade the area to the left of -1.5 under the curve.

Explanation:

To find the proportion of observations from a standard normal distribution that satisfies the statement Z < -1.5, we need to find the area to the left of -1.5 on the standard normal distribution curve. This area represents the proportion of observations that have a z-score less than -1.5.

Using a calculator or a z-table, we can find that the area to the left of -1.5 is approximately 0.0668, which is the proportion of observations that satisfy the given statement. To sketch the normal curve and shade the area under the curve, we would draw a standard normal distribution curve with the mean at the center, and then shade the area to the left of -1.5 under the curve.

Learn more about Proportion of observations in a standard normal distribution here:

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