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2 years ago

HURRY WILL GIVE BRANLIEST!!!!!!!

Mathematics

1 answer:

Ilia_Sergeevich [38]2 years ago

8 0

Answer:

√17

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a ratio of two integers. Or in other words, an irrational number can't be expressed as a fraction. You really cant divide one integer by another integer to get √17, so that makes it an irrational number.

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9x+2y-27z=-155 -11x-y+37z=208 19x+6y-52z=-304

Paladinen [302]

Answer:

(x,y,z)=( -2, -1 ,5)

Step-by-step explanation:

9x+2y-27z=-155 (1)

-11x-y+37z=208 (2)

19x+6y-52z=-304 (3)

(1) *3 ;(2) *6 ;(3)*1, you have

27x+6y-81z=-465 (1)

-66x-6y+222z=1248 (2)

19z+6y-52z=-304 (3)

(1) +(2), you have

-39x+141z= 783 (4)

(4) /3, you have

-13x +47z=261 (4)

(2) +(3), you have

-47x+170z=944 (5)

From ( 4) and (5), you have equations

-13x +47z=261 (4)

-47x+170z=944 (5)

(4)*(-47); (5)*13, you have

611x-2209z=-12,267 (4)

-611x+2210z=12,272 (5)

(4)+(5), you have

z=5

Replace z=5 in (4), you have

611x- 2209*5=-12,267

611x- 11,045 =-12,267

611x=-1222

x= -2

Replace x=-2, z=5 in (1) , you have

9*(-2) +2y -27*5=-155

-18+2y-135=-155

-18+2y=-20

2y=-2

y=-1

Result (x,y,z)=( -2, -1 ,5)

3 0

3 years ago

A university financial aid office polled a random sample of 670 male undergraduate students and 617 female undergraduate student

ahrayia [7]

Answer:

The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

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

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 $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Male undergraduates:

670, 388 were employed. So

$p_M = \frac{388}{670} = 0.5791$

$s_M = \sqrt{\frac{0.5791*0.4209}{670}} = 0.0191$

Female undergraduates:

Of 617, 323 were employed. So

$p_F = \frac{323}{617} = 0.5235$

$s_F = \sqrt{\frac{0.5235*0.4765}{617}} = 0.0201$

Distribution of the difference:

$p = p_M - p_F = 0.5791 - 0.5235 = 0.0556$

$s = sqrt{s_M^2+s_F^2} = \sqrt{0.0201^2 + 0.0191^2} = 0.0277$

Confidence interval:

The confidence interval is given by:

$p \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower bound of the interval is:

$p - zs = 0.0556 - 1.645*0.0277 = 0.01$

The upper bound of the interval is:

$p + zs = 0.0556 + 1.645*0.0277 = 0.1012$

The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).

5 0

3 years ago

A local pet shelter plans to sell pet calenders to raise money for food and other supplies. Anyone can submit a pocture of his o

Mama L [17]

Answer:

Step-by-step explanation:

We could consider the linear model of cost assumed that:

C(x) = $\frac{2250}{50}$ x when x is the number of calendars printed.

5 0

3 years ago

If a marble is randomly chosen from a bag that contains exactly 8 red marbles, 6 blue marbles, and 6 white marble, what is the p

omeli [17]

1. ok, so theres 8 red marbles, 6 blue marbles, and 6 white marbles so that makes

8 + 6 + 6 = 20 marbles in total 

the probability of the marble being white is 6/20 or 3/10 

so the probabilty of the marble NOT being white is 1 - (3/10) = 7/10 

and that matches up with choice e) 

2. so the ratio of the sides of a triangle is 12:14:15, and the second one is similar. for this one we have to set up a proportion 

since the shortest side of the second side is 8 inches, we can match it up with the shortest ratio of the first. and we kno the ratio of the longest side of the first triangle is 15, but we dont kno the the length of the longest side of the second triangle, so we can let that be our unknown, x. so the proportion we are going to set up is 

8 / 12 = x / 15 

now cross multiply 

12x = 120 

x = 10 

so the length of the longest side of the second triangle is 10 inches 

that matches up with choice b)

OR

1. 1 - 6/20 = 1 - 3/10 = 7/10
Answer: (e) 7/10 
---------- 
Ideas: Use complement set. 

2. x:8 = 15:12 = 5:4 
Answer: (b) 10.0

5 0

3 years ago

Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form.

m_a_m_a [10]

Answer:

Option C

y=5x-11

Step-by-step explanation:

We first find the gradient,m, of the line that passes through the points (3,4) and (2,-1)

Let

x=3

y=4

$x_1=2$

$y_1=-1$

$m=\frac{y - y_1}{x - x_1}$

By substitution,

$m=\frac{4-(-1)}{3-2}=\frac{4 + 1}{1} = \frac{5}{1}=5$

Putting that m=5, x=3 and y=4 into the general equation,

y=mx+c

This implies that

4=5(3)+c

4=15+c

4-15=c

c=-11

The equation of the line is given as

y=mx+c

where m=5 and c=-11

Hence y=5x-11

4 0

2 years ago