How many solutions does this system of equations have? Explain how you know.

Answer:

[tex](a)\ Pr = 0.25[/tex]

[tex](b)\ Pr = 0.50[/tex]

Step-by-step explanation:

Given

[tex]Flips = 4[/tex]

First, we calculate the sample size;

The coin has two possible outcomes (i.e. head or tail) and the number of flips is 4.

So, the sample size (N) is:

[tex]N = 2^4[/tex]

[tex]N = 16[/tex]

Solving (a): Probability the outcome of the first and last flip is head.

The possible outcomes for this event are:

[tex]n = \{(HHHH), (HHTH), (HTHH),(HTTH)\}[/tex]

[tex]n(n) = 4[/tex]

The probability is:

[tex]Pr = \frac{n(n)}{N}[/tex]

[tex]Pr = \frac{4}{16}[/tex]

[tex]Pr = 0.25[/tex]

Solving (a): Probability that the outcome of at least 2 consecutive flips is head.

The possible outcomes for this event are:

[tex]n = \{(HHHH), (HHHT),(HHTH), (HTHH),(THHH),(TTHH),(HHTT), (THHT)\}[/tex]

[tex]n(n) = 8[/tex]

The probability is:

[tex]Pr = \frac{n(n)}{N}[/tex]

[tex]Pr = \frac{8}{16}[/tex]

[tex]Pr = 0.50[/tex]

Answer:

First - Perpendicular Bisector

Second - Angle Bisector

Fourth - Altitude

Step-by-step explanation:

It is not the median because it does not touch the base in the middle.

Answer:

EF is 109

DAB is 54.5

Step-by-step explanation:

Applying the central angle theorem, the correct statement would be:

The central angle theorem states that:

Thus:

Measure of minor arc EF = m∠ECF = 109°

m∠DAB = 1/2(109°) [m∠ECF = m∠BAD = 109°]

m∠DAB = 54.5°

Therefore, applying the central angle theorem, the correct statement would be:

Learn more about central angle theorem on:

https://brainly.com/question/5436956

Answer:

$220.2

Step-by-step explanation:

Multiply 18.35 to 12

Answer:

C. 10

Step-by-step explanation:

AC = 4 units

BC = 5 units

use the triangle formula

1/2 × 4 × 5 = 10

1/6

approximately the same as

Answer:

✔1/6

✔ approximately the same as

Step-by-step explanation:

Here's proof

Answer:

38.7 units²

Step-by-step explanation:

4.6/SV = SV/8.1

SV² = 37.26

SV = 6.1

area = 1/2(8.1)(6.1) + 1/2(4.6)(6.1) = 38.7 units²

Answer:

A. 549.5

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:  13+18i

Step-by-step explanation:

(4-i)(2+5i)

8+20i-2i-5(i)^2

as we know that  i^2=-1

8+18i-5(-1)

8+18i+5

13+18i

Answer:

7

Step-by-step explanation:

13-6=7 compare maybe.....

Answer:

Ban has 9,000

Michel has 27,000

Bob has 36,000

Step-by-step explanation:

BA: MI: BO

1: 3: 4 (1+3+4 = total number)

BA:  [tex]\frac{1}{8}[/tex] of 72,000 (72,000 ÷ 8 x 1) = 9,000

MI: [tex]\frac{3}{8}[/tex] of 72,000 (72,000 ÷ 8 x 3) = 27,000

BO: [tex]\frac{4}{8}[/tex] of 72,000 (72,000 ÷ 8 x 4) = 36,000

Answer:

OB

Step-by-step explanation:

when we multiple 4 by 3 because they are like terms they give us 12

Answer:

a) 0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.

b) 0.9463 = 94.63% probability that Jodi will score 77% or lower.

c) 400 questions.

d) Yes, because the formula is the same, independently of the value of p.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.81[/tex]

Question a:

100 questions means that [tex]n = 100[/tex]

For the approximation, we have that:

[tex]\mu = p = 0.81[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]

This probability is the pvalue of Z when X = 0.77. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.77 - 0.81}{0.0392}[/tex]

[tex]Z = 1.02[/tex]

[tex]Z = 1.02[/tex] has a pvalue of 0.8461

0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.

Question b:

Now [tex]n = 250[/tex], so:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{250}} = 0.0248[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.77 - 0.81}{0.0248}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463

0.9463 = 94.63% probability that Jodi will score 77% or lower.

Question c:

The formula for the standard deviation is:

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Meaning that it is inversely proportional to the square root of the sample size.

So, to reduce the standard deviation by half, the number of question must be multiplied by (2)^2 = 4.

100*4 = 400

So 400 questions.

d. Laura is a weaker student for whom p = 0.76. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?

Yes, because the formula is the same, independently of the value of p.

Answer:

b=2sqrt14

A=33.7°(rounded to nearest tenth)

B=56.3°

Step-by-step explanation:

Pythagorean theorem= sqrt(c^2-a^2)=sqrt(9^2-5^2)=2sqrt14

angleA= sin^-1(5/9)=33.7°

angleB=90°-33.7°= 56.7°

Hopefully that makes sense

Answer:

c=7.180 miles. 2. Jack is on one side of a 200-foot-wide canyon and Jill is on the other. Jack and Jill can both ... a=2.947 miles. 5. Airplane A is flying directly toward the airport which is 20 miles away. The pilot notices ...

Answer:

x-fx-x*x

Step-by-step explanation:

Answer:

A. 107 kg

B. 49 kg

Step-by-step explanation:

Answer:

13/5

Step-by-step explanation:

The probability of (red) is the chance of drawing a red marble out of the red and blue marbles. As there are 13 red marbles and 5 blue marbles, the probability of drawing a red marble is 13 out of 5, or 13/5 in fraction form.

Answer:

Answer is 64.

Step-by-step explanation:

524288/8192 = 64

Answer:

3, 0

Step-by-step explanation:

first number is on the horizontal line and the second number on the vertical line

Answer: (3, 0)

Step-by-step explanation: To get to point B from the origin, we move 3 units to the right and 0 units up or down so our point has the coordinates (3, 0).

Remember to always go left or right first, which represents x,

then up or down, which represents y.