MATHEMATICS HIGH SCHOOL

RST is an equilateral triangle; TXIRS -T
A
R
х
S
If RT = 8, then
TX=

Answers

Answer 1

Answer:

Answer:

4√3

Step-by-step explanation:

I did a²+b²=c²

RX²+XT²=RT²

4²+XT²=8²

16+XT²=64

XT²=48

√XT=√48

4√3

Answer 2

Answer:

Answer:

TX=8, all sides of an equilateral triangle are congruent

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Yis directly proportional to the square of xy=96 when x = 4

Find a formula for y in terms of x

Answers

Answer:

$y=6x^2$

Step-by-step explanation:

y being directly proportional to the square of x means that the ratio between the two will always be equal to some constant (let's call it k). In equation form, we'd say:

$(y)/(x^2)=k$

We're told that y = 96 when x = 4, so we can plug those values in to find k:

$(96)/(4^2)=(96)/(16)=6=k$

Our more general equation is now

$(y)/(x^2)=6$

If we want to put y in terms of x, we need to get the y by itself on one side of the equation, which we can do here by multiplying both sides by x², giving us

$y=6x^2$

Final answer:

The question is about finding the equation given that y is directly proportional to the square of x. Based on the values in the question, the constant of proportionality 'k' is calculated as 6. Hence, the formula for y in terms of x is y = 6 * x^2.

Explanation:

When we say, y is directly proportional to the square of x, it simply means there is a constant constant of proportionality 'k', such that y = k * x2. Given in the problem, when x = 4, y = 96, we can substitute these values into the equation to solve for 'k'. This results in 96 = k * (42) which simplifies to 96 = 16k, and solving this gives us k = 6. Therefore, the formula for y in terms of x is y = 6 * x2.

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Chang 0.83 into a fraction

Answers

answer: 83/100

there you go!!!!

Hope it helps

Create a “fraction” with 0.83 in the numerator and 1.0 in the denominator:

0.83/1.0

Move the decimal point in 0.83 two places to the right to turn it into a whole number; move the decimal point in the denominator the same number of places. Do this one decimal place at a time:

0.83/1.0=8.3/10.0=83/100

At this point, you can drop the decimal points and trailing zeros in both the numerator and denominator.

To get from home to work, Felix can either take a bike path through the rectangular park or ride his bike along two sides of the park. How much farther would Felix travel by riding along two sides of the park than he would by taking the path through the park?

Answers

Answer:

c=5.9/6(G)

Step-by-step explanation:

first find the 2 distances.

a^2+b^2=c^2 c=2.4+.7

7^2+2.4^2=c^2 c=3.1

.49+5.85=c^2

c^2=6.34

c=√6.34

c=2.51.

next subtract the two distances to find the difference.

c=2.51-3.1

c=.59

so the distance would be .59 which can be rounded up to .60/G

explanation on how I knew the answer.

Im reviewing for the math 8th grade staar.

Find out the expected value and the standard deviation of the number of aces obtained in 60 rolls of a fair 6-face die. Ditto for 600 rolls. Use them to explain why the observed count of aces obtained is more likely to be within 2 from the expected value with 60 rolls than with 600 rolls.

Answers

Answer:

E(X) = 60*1/6 = 10

sd(X) = √8.666 = 2.886

E(Y) = 600*1/6 = 100

sd(Y) = √86.666 = 9.1287

Step-by-step explanation:

Lets call X the amount of aces obtained in 60 rolls, and Y the amount of aces obtained in 600 rolls.

Note that both X and Y are obtained from counting the amount of successful tries from repetitions of independent experiments that have 1/6 of probability of success. Thus, both X and Y are random variables with binomial distribution, with n = 60 and 600 respectively and probability 1/6.

Remember that if Z is a random variable, Z ≈ Bi(n,p), then

E(Z) = np, where E(Z) denotes the expected value of Z
V(Z) = np(1-p), where V(Z) denotes the variance of Z. Hence, the standard deviation is the square root of V(Z), √(np(1-p)).

As a result

E(X) = 60*1/6 = 10
V(X) = 10*(1-1/6) = 50/6 ≅ 8.666
sd(X) = √8.666 = 2.886
E(Y) = 600*1/6 = 100
V(Y) = 100*(1-1/6) = 500/6 ≅ 86.666

sd(Y) = √86.666 = 9.1287

The observed amount of aces is more likely to be closer from the expected value with 60 rolls because, since we have less rolls, it is more difficult to obtain spread results.

You can also notice that X and Y can be obtained by summing independent variables with distribution BI(1,p) (also called Bernoulli(p) ). When you sum independent variables with the same distribution you have this property:

E(r1+r2+...+rn) = n*E(r1)
V(r1+r2+...+rn) = n*V(r1)

sd(r1+r2+...+rn) = √n*sd(r1)

X can be obtained by summing 60 independent variables r1, ...., r60 with mean 1/6 and variance 1/6*(5/6) = 5/36. So we obtain that V(X) = 60*5/36, and sd(X) = √60 * √(5/36). While for the same argument sd(Y) = √600*√(5/36). The higher the number of rolls, the more spread the results are.

I hope this helped you!

The expected number of aces from 60 rolls of a fair die is 10 with a standard deviation of approximately 3.72. For 600 rolls, the expected number is 100 with a standard deviation of about 11.79. The observed count of aces is more likely to be closer to the expected value with fewer rolls due to the smaller standard deviation relative to the number of trials.

The expected value for the number of aces in a fair die roll is computed by multiplying the probability of rolling an ace $((1)/(6))$ by the number of rolls. For 60 rolls, the expected number is $60 * ((1)/(6)) = 10 aces$ . For 600 rolls, the expected number is $600 * ((1)/(6)) = 100 aces$

The standard deviation for the number of aces is calculated using the formula for the standard deviation of a binomial distribution, $\sqrt(n* p* (1-p))$ , where n is the number of trials, p the probability of success ( $((1)/(6))$ for an ace). For 60 rolls, it is $\sqrt(60* ((1)/(6))* ((5)/(6))) \approx 3.72$ . For 600 rolls, it's $\sqrt(60* ((1)/(6))* ((5)/(6))) \approx 11.79$ .

When you roll the die 60 times, the chances of the observed count of aces being within 2 from the expected value (10) is higher because the standard deviation is smaller relative to the number of trials than when you roll the die 600 times.

As the number of trials increases, the expected standard deviation grows larger, and the observed count is more likely to be within a wider range from the expected value (100).

Learn more about standard deviation here:

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A line passes through points (-4,-9) with a slope of 5/4 write an equation in slope intercept form