Solve the following system of equations. 6x 5y = −5 3x 5y = 10

What is the critical value for a chi-square test with 13 degrees of freedom at the 1 percent level of significance

vagabundo [1.1K]

Answer: 27.688

Step-by-step explanation:

The critical chi-square value $\chi^2_{(df,\alpha)}$ depends on significance level ( $\alpha$ ) and degrees of freedom (df) .

Given significance level: ( $\alpha$ ) = 1% = 0.01

Degrees of freedom (df)= 13

From the chi-square table, the critical chi-square value for df = 13 and $\alpha =0.01$

is $\chi^2_{(df,\alpha)}=27.688$

Hence, the required critical value = 27.688

4 0

4 years ago

In RSM camp, there are four counselors for every fifty seven students and three teachers for every five counselors.

Ray Of Light [21]

Answer:

Students : Counselors : Teachers = 285: 20 : 12

Step-by-step explanation:

In the camp, the ratio of:

( C: S ) Counselors : Students is 4 : 57

( T: C ) Teachers : Counselors is 3 : 5

To determine the ratio of - Students : Counselors : Teachers

Here given - C : S = 4 : 57

Multiplying both sides by 5, we get

C: S = 4 x 5 : 57 x 5 = 20 : 285

So, for every 20 counselors, there are 285 students ...... (1)

Similarly, given Teachers : Counselors is 3 : 5

Multiplying both sides by 4, we get

T : C = 3 x 4 : 5 x 4 = 12 : 20

So, for every 12 teachers, there are 20 Counselors ...... (2)

Hence, in both equation 1 and 2 the number of counselors is same = 20 .

Hence, both the ratios acne be combined.

So we get C : S = 20 : 285 and T : C = 12: 20

Inverting the values

⇒ S : C = 285 : 20 and C : T = 20 : 12

or, S : C : T = 285: 20 : 12

or, Students : Counselors : Teachers = 285: 20 : 12

Hence, for every 285 students there are 20 counselors and 12 teachers.

4 0

3 years ago

Given the function h(x)=x^2-7x+6h(x)=x

Goryan [66]

Answer:

$0$ (no change)

Step-by-step explanation:

Recall that the average rate of change of a function $f(x)$ over the interval $[a,b]$ is equal to $\frac{f(b)-f(a)}{b-a}$ :

$\frac{h(b)-h(a)}{b-a}\\ \\\frac{h(6)-h(1)}{6-1}\\\\\frac{0-0}{5}\\ \\0$

Hence, the average rate of change of the function $h(x)$ over the interval $[1,6]$ is $0$ , or no change.

3 0

2 years ago

When a grizzly bear hibernates, its heart rate drops to 10 beats per minute, which is %20, percent of its normal value. What is

dybincka [34]

Answer:

50 beats/min

Step-by-step explanation:

normal heart rate = h

20% of h = 10

20/100 * h = 10

h = 10*5

= 50 beats/min

Hope this help!

5 0

3 years ago

The population of a type of local frog can be found using an infinite geometric series where a one equals 84 and the common rati

kodGreya [7K]

A=84 and r=1/5

Since r, the common ratio squared is less than one, the sum will converge to a limit. Rule: if r^2<1 infinite series converges, otherwise it diverges.

Since the sum of any geometric sequence is:

s(n)=a(1-r^n)/(1-r)

And if r^2<1, (1-r^n) becomes 1-0=1 as n approaches infinity.

So whenever r^2<1 the sum of the infinite series is just:

s(n)=a/(1-r)

Since a=84 and r=1/5 this infinite series has a sum of:

s(n)=84/(1-1/5)

s(n)=84/(4/5)

s(n)=5(84)/4

s(n)=105

5 0

3 years ago