The coefficient of determination of a set of data points is 0.83 and the slope of the regression line is -1.38. Determine the linear correlation coefficient of the data.

Answer:

5.

Step-by-step explanation:

15.90 / 3.18 =

Answer:

-7.5

Step-by-step explanation:

Answer:-7.4

Step-by-step explanation:

Hopen helps ❤

The equation used to obtain the value of x in the right triangle is given as follows:

cos(58º) = 8/x.

The three trigonometric ratios are defined as follows:

For this problem, we have that the hypotenuse assumes a value of x, while the adjacent side to the angle of 58º has a length of 8 units, thus the cosine is used to obtain the value of x as follows:

cos(58º) = 8/x.

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Answer:

21 girls

Step-by-step explanation:

3 girls: 2 boys

multiply both sides by 7

21 girls: 14 boys

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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The two secants intersect at an exterior point and their

relationship is given by the intersecting secant theorem.

Correct response:

(a) (CG + GE) × CG = (CH + DH) × CH

(b) Yes, it is possible to find the length of DH

(a) According to the intersecting secants theorem, given the

two secants, CE  and CD drawn from the same exterior point

C, where the secant CE has the external segment CG, and

secant CD has the external segment CH.

The relationship between two secants is and their external

segments is presented as follows;

CE = CG + GE

CD = CH + DH

Therefore;

(b) Where; CG = 4 in., CH = 5 in., and GE = 6 in., it is possible to

find the length of DH, given that the number of unknowns in

the equation of the relationship are four, and the values of

three of the variables (CG, CH, and GE) are given, therefore;

The length of DH is given as follows;

Plugging in the values of the variables, gives;

(4 + 6) × 4 = (5 + DH) × 5

10 × 4 = 5² + 5 × DH

5 × DH = 10 × 4 - 5² = 15

\(DH = \dfrac{15}{5} = \mathbf{3}\)

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Answer:

33

Step-by-step explanation:

6x4+9= 33

The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

Herein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:

dy / dt = 3 · y · (1 - y / 14)

dy / [3 · y · (1 - y / 14)] = dt

dy / [- (3  / 14) · y · (y - 14)] = dt

By partial fractions we find the following expression:

- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt

- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.

y = 14 / [1 - C · tⁿ], where n = - 14² / 3.

If y(0) = 10, then the particular solution is:

y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

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The ordered pair (2,-1) is a solution the inequality.

Given the inequality is 3x-4y<12.

An inequality is a statement that compares two quantities and claims that one is greater or less than the other (the equation may also be included). These inequalities are linear if the variables are only linear.

By substituting each of the given option in the given inequality we will check which ordered pair satisfy the inequality.

1. (4,0)

Here x=4 and y=0

Substitute this in the inequality 3x-4y<12, we get

3(4)-4(0)<12

12<12

This is not true

2. (0,-3)

Here x=3 and y=-3

Substitute this in the inequality 3x-4y<12, we get

3(0)-4(-3)<12

12<12

This is not true.

3. (2,-1)

Here x=2 and y=-1

Substitute this in the inequality 3x-4y<12, we get

3(2)-4(-1)<12

6+4<12

10<12

This is true.

4. (4,-3)

Here x=4 and y=-3

Substitute this in the inequality 3x-4y<12, we get

3(4)-4(-3)<12

12+12<12

24<12

This is not true.

Hence, the ordered pair that satisfy the given inequality 3x-4y<12 is (2,-1).

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Answer:

- 4 / 9

Step-by-step explanation:

..........................

Answer:

15

Step-by-step explanation:

The measures of the angles are

Figure 1

The angle on a straight line is 180 degrees

So, we have

<1 + 70 = 180

Evaluate

<1 = 110 --- angle on a straight line

Also, we have

<2 + <2 + <1 = 180

This gives

2 * <2 + 110 = 180

So, we have

2 * <2 = 180 - 110

Evaluate

<2 = 25 --- base angle of an isosceles triangle

Figure 2

The angles in a triangle is 180 degrees

So, we have

<2 + 25 + 90 = 180

Evaluate

<2 = 65

The angles in a triangle line is 180 degrees

So, we have

<1 + <2 + 60 = 180

<1 + 65 + 60 = 180

This gives

<1  = 55

Corresponding angles are equal.

So, we have

<3 + 25 = <1

<3 + 25 = 55

Evaluate

<3 = 30

By the theorem of external angle of a triangle, we have

<4 = 90 + <3

<4 = 90 + 30

<4 = 120

Figure 3

By corresponding angles, we have

<2 = 75

The angle on a straight line is 180

So, we have

x = 180 - 75 - <2

x = 180 - 75 - 75

x = 30

By the sum of angles in a triangle, we have

<1 = 180 - 120 - x

<1 = 180 - 120 - 30

<1 = 30

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The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.

A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.

There are some characteristics that shows that a graph is of proportional relationship which include the following:

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The midsegment is half the length of the side parallel to it. In this case, BC is parallel to DE. So DE = (1/2)*BC = 0.5*64 = 32.

Note how AD = DB and AD+DB = AB. These facts can be used to prove that AD is half of AB. Similarly, we can prove AE is half of AC. To keep the same proportion, DE must be half of BC.

Answer: C). 32

Step-by-step explanation:

Taking the test right now

The length of AC is 12.5 and the length of AD is 3.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle ABC,

and D is a point on AB and E is a point on AC,

and forms a triangle ADE,

and  DE is parallel to AC,

taking ΔABC and ΔBDE

∠B = ∠B  (common angle)

because DE is parallel to AC, so corresponding angles are equal,

so ∠A = ∠D

and ∠C = ∠E

ΔABC ≈ ΔBDE (triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

AB/BD = AC/DE = BC/BE

given BD = 2, BE = 4, DE = 5 and EC = 6

BC = EC + BE = 4 + 6

BC = 10

AC/DE = BC/BE

AC = 5(10/4)

AC = 12.5

and AB/BD = BC/BE

AB = 2(10/4)

AB = 5

AD = AB - BD

AD = 5 - 2

AD = 3

Hence AC = 12.5 and AD = 3.

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The figure is in image.

At 95% confidence interval, we evaluate the critival value which is evaluated to be

The margin of error is expressed as

thus, we have

The confidence interval is expressed as

thus, we have

Hence, the confidence interval is between 58.5 and 61.3.

The numbers can be a solution for the inequality 32+a>44 is 13 and 14.

If the equation or inequality have variable terms, than there might be some values of those variables for which the equation or inequality might be correct. Such values are known as solution to that equation or inequality. To set of such values are called solution set to be considered equation or inequality.

Given that;

The inequality= 32+a>44

To solve the inequality 32 + a > 44, we need to isolate the variable "a" on one side of the inequality.

32 + a > 44

Subtract 32 from both sides:

a > 44 - 32

a > 12

This means that any number greater than 12 can be a solution to the inequality.

Therefore, the inequalities numbers 13 and 14 can be solutions, but 11 and 12 cannot.

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Answer:

Step-by-step explanation:

The least number of degree is 3 and the third root should be (4 - i) to make polynomial rational.

The polynomial is:

Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

Answer:

assuming symmetry x should be 10

Step-by-step explanation:

The fourth term of the arithmetic sequence will be -15.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given data is a₁ = -2, and the formula is an = 2a₁(n-1) - 3.

The fourth term will be calculated as below,

an = 2a₁(n-1) - 3.

an = -4 x (3 - 1 ) - 3.

an = -12 - 3

an = -15

Hence, the fourth term will be -15.

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Answer:

17822

Step-by-step explanation:

The number that are divisible by 7 between 30 and 500 are as follows :

35, 42,49,.....,497

It will form an AP with first term, a = 35 and common difference, d = 7

Let there are n terms in the AP.

nth term of an AP is given by :

\(a_n=a+(n-1)d\)

Putting all the values,

\(497=35+(n-1)7\\\\462=(n-1)7\\\\n-1=66\\\\n=67\)

Now, the sum of n terms of an AP is given by :

\(S_n=\dfrac{n}{2}[2a+(n-1)d]\)

Putting all the values,

\(S_n=\dfrac{67}{2}[2(35)+(67-1)7]\\\\S_n=17822\)

Hence, the sum of the numbers that are divisible by 7 between 30 and 500 is 17822.

Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For function f(x), the multiplication by -1 of the function is in the output, meaning that it was a reflection over the y-axis. For function g(x), the multiplication is in the input, the domain, hence the reflection was over the x-axis.

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Answer:

1/3

Step-by-step explanation:

divide each part by 11

Answer:

1/3 is the simplified fraction for 11/33 by using the GCD or HCF method. Thus, 1/3 is the simplified fraction for 11/33 by using the prime factorization method.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.