In ΔIJK, the measure of ∠K=90°, KJ = 65, IK = 72, and JI = 97. What is the value of the cosine of ∠J to the nearest hundredth?

Answer:

Fail to reject the null hypothesis

[tex]CI = (-4.278, 0.478)[/tex]

Step-by-step explanation:

Given

[tex]n_1=n_2 = 18[/tex]

[tex]\bar x_1 = 12.7[/tex]    [tex]\bar x_2 = 14.6[/tex]

[tex]\sigma_1 = 3.2[/tex]    [tex]\sigma_2 = 3.8[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test the hypothesis

We have:

[tex]H_o : \mu_1 - \mu_2 = 0[/tex]

[tex]H_a : u1 - u2 \ne 0[/tex]

Calculate the pooled standard deviation

[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]

[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]

[tex]s_p = \sqrt{12.34}[/tex]

[tex]s_p = 3.51[/tex]

Calculate test statistic

[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]

[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]

[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]

[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]

[tex]t = \frac{-1.9}{1.17}[/tex]

[tex]t = -1.62[/tex]

From the t table, the p value is:

[tex]p = 0.114472[/tex]

[tex]p > \alpha[/tex]

i.e.

[tex]0.114472 > 0.05[/tex]

So, the conclusion is that: we fail to reject the null hypothesis.

Solving (b): Construct 95% degree freedom

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom

[tex]df = n_1 + n_2 - 2[/tex]

[tex]df = 18+18 - 2[/tex]

[tex]df = 34[/tex]

From the student t table, the t value is:

[tex]t = 2.032244[/tex]

The confidence interval is calculated as:

[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]

[tex]CI = -1.90 \± 2.378[/tex]

Split

[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]

[tex]CI = (-4.278, 0.478)[/tex]

Answer:

23/26 is a greater percentage, it equals around 88% while 12/15 equals 80%

Step-by-step explanation:

Answer:2647.5

Step-by-step explanation:

Answer:

c 13 over 12

Step-by-step explanation:

it help I makeit

Answer:

[tex]2x^2y^3[/tex]

Step-by-step explanation:

The given expression is :

[tex]2x^2y^3+4x^2y^5[/tex]

We need to find the greatest common  factor of the expression.

The first term is [tex]2x^2y^3[/tex]

The other term is [tex]4x^2y^5[/tex]

[tex]2x^2y^3[/tex] is common in both terms. So,

[tex]2x^2y^3(1+2y^2)[/tex]

Hence, the greatest common factor of the expression is equal to [tex]2x^2y^3[/tex].

Answer:

x < 7

Step-by-step explanation:

the domain of a function defines the valid x values for the function.

as we go from left to right through all possible values of x, we see all values incl. x=-1 are creating a valid function result (y) for this function. until we reach x=7.

the empty ball indicates that there is no y value defined here. and for any value x>7 there is no y value defined.

so, x < 7 is the right one.

Answer: A

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Since the x values are the same

the distaance is simply the difference in the y values

23 - (-2) = 25

Answer:

Step-by-step explanation:

x = number of pounds

5x<30

x<30/5

so she can buy X<6 pounds

9514 1404 393

Explanation:

  -4h ≤ -14

in this context is a relation that would tell how many hours it would take for the temperature to be at or below -14 degrees.

He used 620 gallons of gas

Answer:

3/4

Step-by-step explanation:

because it is a linear function it means it has the same slope in every point

so you have to take 2 points and find the slope

I take points (0,1) and (4,4)

m = (y2-y1) / (x2-x1)

note that it does not matter which points you chose to be second or first

m = (4-1) / (4-0) = 3/4

you can solve it from the graph too 3/4 is y/x it means for every 4 unit right move 3 units up

Answer:

-1

Step-by-step explanation:

f(4) = 2.5(4) -11

f(4) = 10 -11

f(4) = -1

Answer:

A

Step-by-step explanation:

Did the quiz

Answer:

6

Step-by-step explanation:

The third digit to the right of decimal point is in the thousandths place. The fourth digit to the right of decimal point is in the ten thousandths place and so on.

In the decimal number 24.736, the digit which is at the thousandth place will be 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that the number starts from the tenths after the decimal.

....123.456..

The expansion of the number is given as,

... + 100 + 20 + 3 + 0.4 + 0.05 + 0.006 + ......

The expansion is written in form of words. Then

Hundreds + Tens + Ones + Tenths + Hundredths, Thousandths, and so on.

In the decimal number 24.736, the digit which is at the thousandth place will be 6.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

Step-by-step explanation:

Let the Base of the  △  be  x

Then the Height will be  2 x + 4

Area of △ = 1 2 b h

Where, b = b a s e , h = h e i g h t , A r e a = 35

(in this case)

Substitute the values into the equation → 35 = 1 2 ( 2 x + 4 ) ( x ) → 35 = ( 2 x + 4 ) 2 ( x ) →

35 = ( x + 2 ) ( x ) → 35 = x 2 + 2 x

Subtract  35  both sides

→ 0 = x ^2 + 2 x − 35

Rewrite the equation in the Standard form

x ^2 + 2 x − 35 = 0

Factor the equation

→ ( x + 7 ) ( x − 5 ) = 0

So we have  

x = − 7 , 5

numbers So  x = 5

They have asked us to find the Height

So, ⇒ H e i g h t = 2 x + 4 = 2

Answer:

substitute that (6) in X so f(6) = 2(6) which is = 12

Answer:

41

Step-by-step explanation:

The angle were looking for is on the other side of the figure. It is also on the inside so we would divide 82 in half giving us 41.

Answer:

42n+108

Step-by-step explanation:

21(2n+8)

42n+108

Answer:-244

Step-by-step explanation:

I think you subtract -290 from -46.

Sorry If I am wrong.

========================================================

Explanation:

Imagine reflecting everything so that location A is above location B. Effectively all you're doing is erasing the negative signs.

That would place A at 290 feet and B would be at 46 feet. The difference in elevation is 290-46 = 244 feet

Instead of reflecting, you can turn the page upside down and just ignore the negative signs, and then subtract like normal.

This trick only works if both elevations A and B are below sea level.

--------

Or you could subtract like so:

|A-B| = |-290-(-46)| = |-290+46| = |-244| = 244

The absolute value is used to ensure the result is not negative. A negative difference makes no sense. In this case, "difference" and "distance" mean the same thing more or less.

Answer:

56 cm squared

Step-by-step explanation:

First things first: Cop one triangle off the rectangle, and attach it to the other one, so the shape looks like a L

Now I can actually solve this:

The left side is 8 cm (because y = 8 cm)

The top is 10 cm

The middle is 6 cm

The inside left is 3 cm

And the very bottom is 2 cm

First, we'll solve for the newly constructed rectangle: 3 x 2. That equals 6.

Next, solve for the longer rectangle: 10 x 5. That's 50.

Now, add the two areas, and we get 56. So the area of the whole thing is 56 cm squared.

(Please keep in mind that I could be wrong, so double check it for me, thanks!)

============================================================

Explanation:

First we need the arithmetic mean

Add up the values to get 1+2+4+4+5+6+6 = 28

Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4

The mean is 4.

Next, we subtract the mean from each data value and square the difference

Add up those results: 9+4+0+0+1+4+4 = 22

Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately

----------

Side note:

If you wanted the sample variance, then you divide over n-1 = 7-1 = 6

22/(n-1) = 22/6 = 3.67 is the approximate sample variance

Answer:

2.89, rounded to the nearest hundredth

Step-by-step explanation:

Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.

So, we start with math,

3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.

Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.

Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth

Answer:

I don't know sorry for your right question ok

Answer:

D. {3, 5, 7}

Step-by-step explanation:

Sets of y-values or outputs of a relation of a function = the range

The outputs/y-values of the relation mapped above are what we have on our right hand, which area {3, 5, 7}

Therefore,

Range = {3, 5, 7}

Answer:

Type I error (alpha error)

Step-by-step explanation:

Given that a TYPE 1 ERROR is a type of research error often referred to as false positive or alpha error and happens when a researcher wrongly rejects a true null hypothesis. This action by the researcher verifies a statistically significant difference even though there is no difference.

Hence, considering the situation described in the question above, the correct answer to the question is "TYPE 1 ERROR"

Answer:

inscribed

Step-by-step explanation:

For any given triangle, the circle inside of it is called the Inscribed circle

it think it is 10 or so but like just read or it and you will get it :)

9514 1404 393

Answer:

  $41,977.60

Step-by-step explanation:

Allison's average salary for the last 5 years is ...

  (70 +73.1 +75.2 +77.5 +79)/5 = 74.96 . . . . thousand dollars

Then her annual pension is ...

  1.75% × $74,960 × 32 = $41,997.60

Answer

Two fractions are equivalent fractions when they represent the same part of a whole. Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator.