20. (06.07 )
The graph below plots the values of y for different values of
20
15
10
5
5
Which correlation coefficient best matches the data plotted on the graph? (1 point)
-0.5
0
0.25
0.90

Answer:

12

Step-by-step explanation:

First lets list all the factors of these numbers

72: 1,2 3,4,6,8,9,12,18,24,36,72

84: 1 , 2 , 3 ,4 , 6 , 7 , 12 , 14 ,  21 , 28 , 42 , 84

Now lets find the biggest number that is a factor of both 84 and 72  

as we can see the highest number that is the factor of both 84 and 72 is 12

12 is the hcf

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Fleet of 17 means that [tex]N = 17[/tex]

4 are carrying nucleas weapons, which means that [tex]k = 4[/tex]

9 are destroyed, which means that [tex]n = 9[/tex]

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]

In which

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294[/tex]

[tex]P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412[/tex]

[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588[/tex]

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Answer:

The first equation; x-2y=8

Step-by-step explanation:

Hi there!

We're told that Ty wants to isolate x in one of the equations. To do so in either, he will need to use inverse operations to cancel out values and leave just x remaining on one side of the equation.

In the second equation, he would need to subtract both sides by 6y and then divide both sides by 4 to isolate x. It's a two-step process.

However, in the first equation, he only needs to add 2y to both sides to isolate x.

I hope this helps!

Answer:

using the first equation

cause Being that the first equation has the simplest coefficients (1, -2, for x, and y respectively), it seems logical to use it to develop a definition of one variable in terms of the other

Answer: P = 4s

Step-by-step explanation:

P = 4s where s = the length of each side.  

Since each side of a square is the same length, the side length is multiplied by 4.

Answer:

157.8

Step-by-step explanation:

Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)

Some symbols and numbers are missing. I assume the system is supposed to read

2x - y + 2z + w = -3

x + 2y - 3z + w = 12

3x - y - z + 2w = 3

-2x + 3y + 2z - 3w = -3

In matrix form, this is

[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]

which we can strip down to the augmented matrix,

[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]

Now for the row operations:

• swap rows 1 and 2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]

• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]

• add 7 (row 2) to -5 (row 3), and row 3 to row 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]

• multiply through rows 3 and 4 by 1/2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]

• add -4 (row 4) to row 3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]

• swap rows 3 and 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]

• multiply through row 4 by 1/3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]

• add row 4 to row 3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]

• multiply through row 3 by 1/2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• add -8 (row 3) and row 4 to row 2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• multiply through row 2 by -1/5

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1

[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).

Answer:

The  weight that separate the top 8% by 5.2605 and the weight that separate bottom 8% by 5.1195.

Step-by-step explanation:

We are given that

Mean,[tex]\mu=5.19[/tex]

Standard deviation,[tex]\sigma=0.05[/tex]

We have to find the two weights that separate the top 8% and the bottom 8%.

Let x1 and x2 the two weights that separate the top 8% and the bottom 8%.

Z-value for p-value =0.08 =[tex]-1.41[/tex]

For 8% bottom

[tex]Z=\frac{x_1-\mu}{\sigma}=-1.41[/tex]

[tex]\frac{x_1-5.19}{0.05}=-1.41[/tex]

[tex]x_1-5.19=-1.41\times 0.05[/tex]

[tex]x_1=-1.41\times 0.05+5.19[/tex]

[tex]x_1=5.1195[/tex]

For 8% top

p-Value=1-0.08=0.92

Z- value=1.41

Now,

[tex]\frac{x_2-5.19}{0.05}=1.41[/tex]

[tex]x_2-5.19=1.41\times 0.05[/tex]

[tex]x_2=1.41\times 0.05+5.19[/tex]

[tex]x_2=5.2605[/tex]

(x1,x2)=(5.1195,5.2605)

Answer:

The correct answer is "[tex]0.300993e^{-0.300993x}[/tex]".

Step-by-step explanation:

According to the question,

⇒ [tex]P(x>4)=0.3[/tex]

We know that,

⇒ [tex]P(X > x) = e^{(-\lambda\times x)}[/tex]

⇒     [tex]e^{(-\lambda\times 4)} = 0.3[/tex]

∵ [tex]\lambda = 0.300993[/tex]

Now,

⇒ [tex]f(x) = \lambda e^{-\lambda x}[/tex]

By putting the value, we get

           [tex]=0.300993e^{-0.300993x}[/tex]

Answer:

S = v1 t1 = 7 t1    traveling downstream

S = v2 t2 = 5 t2    traveling upstream

7 t1 = 5 t2

7 (6 - t2) = 5 t2     since t1 + t2 = 6

42 - 7 t2 = 5 t2

t2 = 42 / 12 = 3.5 hrs so t1 = 2.5 hrs

S = 7 t1 = 7 * 2.5 = 17.5 mi

Also, S = 5 t2 = 5 * 3.5 = 17.5 mi

Answer:

The measure of the smallest angle is 30º

Step-by-step explanation:

Let the angles be:

[tex]x \to[/tex] the first angle (the smallest)

[tex]y \to[/tex] the second angle

[tex]z \to[/tex] the third angle

So, we have:

[tex]y = 2x[/tex]

[tex]z=x + 60[/tex]

Required

Find x

The angles in a triangle is:

[tex]x + y +z = 180[/tex]

Substitute values for y and z

[tex]x + 2x +x + 60 = 180[/tex]

[tex]4x + 60 = 180[/tex]

Collect like terms

[tex]4x = 180-60[/tex]

[tex]4x = 120[/tex]

Divide by 4

[tex]x = 30[/tex]

Answer:

[tex]-\frac{77}{24}[/tex]

Step-by-step explanation:

1. rewrite the equation in standard form: [tex]4\cdot \frac{3}{2}\left(y-\left(-\frac{41}{24}\right)\right)=\left(x-\left(-\frac{3}{2}\right)\right)^2[/tex]

2. find (h,k), the vertex. the vertex is [tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex]

3. find the 'focal length' of the parabola - the focal length is the distance between the vertex and the focus. from the vertex we can see that the focal length, p, = 3/2

4. Parabola is symmetric around the y-axis and so the asymptote is a line parallel to the x-axis, a  distance p from the [tex]\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex] y coordinate which is at  [tex]-\frac{41}{24}\right)[/tex]. Set up the equation:

[tex]y=-\frac{41}{24}-p[/tex]

5. substitute and solve:

[tex]y=-\frac{41}{24}-\frac{3}{2}[/tex]

[tex]y = -\frac{77}{24}[/tex]

hope this helps, ask me questions if you still don't understand.

Finding the line of best fit is something a Machine Learning Model would do.

This particular ML model is called "Linear Regressor" or "Linear Regression Model". Look it up and there are definitely calculators for it, as it is relatively simple.

You can also, if you know how to use ML libraries and code, use Python to determine the value of [tex]b[/tex].

Hope this helps.

Answer:

The solution to the equation  log3(x+2)=1 is given by x=1

Step-by-step explanation:

We are given that

[tex]log_3(x+2)=1[/tex]

We have to find the graph which shows the  solution to the equation log3(x+2)=1.

[tex]log_3(x+2)=1[/tex]

[tex]x+2=3^1[/tex]

Using the formula

[tex]lnx=y\implies x=e^y[/tex]

[tex]x+2=3[/tex]

[tex]x=3-2[/tex]

[tex]x=1[/tex]

Hi there!

[tex]\large\boxed{p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4}[/tex]

Recall a Taylor series centered at x = 0:

[tex]p(x) = f(0) + f'(0)(x) + \frac{f''(0)}{2}x^{2} + \frac{f'''(0)}{3!}x^{3} + ...+ \frac{f^n}{n!}x^n[/tex]

Begin by finding the derivatives and evaluate at x = 0:

f(0) = 7(0)e⁰ = 0

f'(x) = 7eˣ + 7xeˣ   f'(0) = 7e⁰ + 7(0)e⁰ = 7

f''(x) = 7eˣ + 7eˣ + 7xeˣ  f''(0) = 7(1) + 7(1) + 0 = 14

f'''(x) = 7eˣ + 7eˣ + 7eˣ + 7xeˣ    f'''(0) = 21

f⁴(x) = 7eˣ + 7eˣ + 7eˣ + 7eˣ + 7xeˣ   f⁴(0) = 28

Now that we calculated 4 non-zero terms, we can write the Taylor series:

[tex]p(x) = 0 + 7x + \frac{14}{2}x^2 + \frac{21}{3!}x^3 + \frac{28}{4!}x^4[/tex]

Simplify:

[tex]p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4[/tex]

Answer:

1.581

Step-by-step explanation:

Given the data:

13 15 14 16 12

The point estimate of the standard deviation will be :

√Σ(x - mean)²/n-1

Mean = Σx / n = 70 / 5 = 14

√[(13 - 14)² + (15 - 14)² + (14 - 14)² + (16 - 14)² + (12 - 14)² / (5 - 1)]

The point estimate of standard deviation is :

1.581

Hi there!  

»»————-　★　————-««

I believe your answer is:  

{7, -5, (2/3), 5.79}

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{\underline{\textbf{Some Examples of Rational Numbers Are...}}}}\\\\\rightarrow \text{Integers}\\\\\rightarrow \text{Perfect Squares}\\\\\rightarrow \text{Terminating Decimals}\\\\\rightarrow \text{Recurring Decimals}[/tex]

⸻⸻⸻⸻

⸻⸻⸻⸻

The rational numbers are {7, -5, (2/3), 5.79}.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

The quadrilateral is a rhombus

Step-by-step explanation:

Given

[tex]A = (2, 8)[/tex]

[tex]B = (3, 11)[/tex]

[tex]C = (4, 8)[/tex]

[tex]D=(3, 5)[/tex]

Required

The true statement

Calculate slope (m) using

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Calculate distance using:

[tex]d= \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]

Calculate slope and distance AB

[tex]m_{AB} = \frac{11 - 8}{3 - 2}[/tex]

[tex]m_{AB} = \frac{3}{1}[/tex]

[tex]m_{AB} = 3[/tex] -- slope

[tex]d_{AB}= \sqrt{(3 - 2)^2 + (11 -8)^2}[/tex]

[tex]d_{AB}= \sqrt{10}[/tex] -- distance

Calculate slope and distance BC

[tex]m_{BC} = \frac{8 - 11}{4 - 3}[/tex]

[tex]m_{BC} = \frac{- 3}{1}[/tex]

[tex]m_{BC} = -3[/tex] -- slope

[tex]d_{BC} = \sqrt{(4-3)^2+(8-11)^2[/tex]

[tex]d_{BC} = \sqrt{10}[/tex] --- distance

Calculate slope CD

[tex]m_{CD} = \frac{5 - 8}{3 - 4}[/tex]

[tex]m_{CD} = \frac{- 3}{- 1}[/tex]

[tex]m_{CD} = 3[/tex] -- slope

[tex]d_{CD} = \sqrt{(3-4)^2+(5-8)^2}[/tex]

[tex]d_{CD} = \sqrt{10}[/tex] -- distance

Calculate slope DA

[tex]m_{DA} = \frac{8 - 5}{2 - 3}[/tex]

[tex]m_{DA} = \frac{3}{- 1}[/tex]

[tex]m_{DA} = -3[/tex] -- slope

[tex]d_{DA} = \sqrt{(2-3)^2 + (8-5)^2}[/tex]

[tex]d_{DA} = \sqrt{10}[/tex]

From the computations above, we can see that all 4 sides are equal, i.e. [tex]\sqrt{10}[/tex]

And the slope of adjacent sides are negative reciprocal, i.e.

[tex]m_{AB} = 3[/tex]  and [tex]m_{CD} = -3[/tex]

[tex]m_{CD} = 3[/tex] and [tex]m_{DA} = -3[/tex]

The quadrilateral is a rhombus

Answer:

B. -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{(5.27+x)}{2} =-4.51[/tex],[tex]\frac{8.21+y}{2} = 1.37[/tex]

(3.75,-5.47)

Answer:

The sum of squared errors for the regression equation is 62.

Step-by-step explanation:

The sum of squared errors can be computed as follows:

X            Y           Y* = 2 + 3X         Y - Y*           (Y - Y*)^2

0            5                  2                      3                    9

3            5                  11                     -6                  36

7            27               23                     4                    16

10          31                32                    -1                     1  

20         68               68                     0                   62

From the above, we have:

Error = Y -  Y*

Error^2 = (Y - Y*)^2

Sum of squared errors = Sum of Error^2 = Total of (Y - Y*)^2 = 62

Therefore, the sum of squared errors for the regression equation is 62.

Answer:

TS = 12.7

Step-by-step explanation:

From the question given above, the following data were obtained:

QR = 9

QP = 6

TU = 19

TS =?

Since the triangles are SIMILAR, then,

QR / TU = QP / TS

With the above equation, we can obtain the value of TS as follow:

QR = 9

QP = 6

TU = 19

TS =?

QR / TU = QP / TS

9 / 19 = 6 / TS

Cross multiply

9 × TS = 19 × 6

9 × TS = 114

Divide both side by 9

TS = 114 / 9

TS = 12.7

Answer:

[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Answer:

a. 8.95

b. it is

c. yes it belongs

d. males are 2.574 taller than females on average.

Step-by-step explanation:

GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as

a. test statistic = 1.164/0.13

t test = 8.95

b. the regression coefficient of shoe size is 1.164, this is statistically significant

c. Yes the variable shoe size does belong to the model.

d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.

Answer:

C=25°

a=11

b=12

Step-by-step explanation:

Find angle c,since angles in a triangle add up to 180 and we know angleA andB angle C will be

65+90+C=180

C=180-155

C=25°

To find a

use trig ratios

tanA=opposite/adjacent

tan65=a/5

a=tan65×5

a=10.72 round off to 11

To find b

sinC=opposite/hypotenuse

sin25=5/b

sin25 b=5

b=11.8 or rather 12

Answer:

Step-by-step explanation:

First find  side a and to find this  calculate tan 65

Tan 65 = [tex]\frac{opposite \ side}{adjacent\ side}=\frac{a}{5}\\\\[/tex]

2.144 = a/5

a = 2.144 * 5

b² = a² + c²

   = 121+25

   = 146.

b = √146 = 12.08 = 12

a = 10.72 = 11

Now find Tan C

[tex]Tan \ C = \frac{5}{10.72}\\\\Tan \ C = 0.4664\\[/tex]

C = tan⁻¹ 0.4664

C = 25°

Answer:

Answer to the first question is D. Answer to the second question is also D.

Step-by-step explanation:

First question:

All the sides of the square are equal meaning you just have to multiply 1 side by 4 to get the perimeter(all the sides added together.) If one side is (s+3) then you either add that to itself 4 times or multiply it by 4. It's the same thing so it's 4(s+3) and (s+3)+(s+3)+(s+3)+(s+3).

Second question:

Adding a negative number is equivalent to subtracting a positive number. In this case, 59.2-84.7 = 59.2+(-84.7)

Answer:

The maximum value of the objective function is 112 when x = 0 and y = 7.

Step-by-step explanation:

Given the constraints:

5x+3y≤37, 3x+5y≤35, x≥0, y≥0

Plotting the above constraints using geogebra online graphing tool, we get the solution to the constraints as:

A(0, 7), B(7.4, 0), C(5, 4) and D(0, 0)

The objective function is given as E =2x+16y, therefore:

At point A(0, 7):  E = 2(0) + 16(7) = 112

At point B(7.4, 0): E = 2(7.4) + 16(0) = 14.8

At point C(5, 4): E = 2(5) + 16(4) = 74

At point D(0, 0): E = 2(0) + 16(0) = 0

Therefore the maximum value of the objective function is at A(0, 7).

The maximum value of the objective function is 112 when x = 0 and y = 7.

Answer:

The correct answer is =6.

Step-by-step explanation:

Solution,

Given;

11−17=49

or,11n-17=49

or,11−17+17=49+17

or,11=66

or,n=66/11

#n=6

HOPE IT HELPED♥︎

Answer:

1) x = 2

Step-by-step explanation:

Hope it helps. I'll try to solve the second one too

9514 1404 393

Answer:

Step-by-step explanation:

1. Substitution can work for this.

  2x +3(4x -5) = 13

  14x = 28 . . . . . add 15

  x = 2 . . . . . . . divide by 14

__

2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...

  x + y + 6 = 5

  x + y = -1

Only the 3rd choice satisfies this equation.

  (x, y, z) = (-5, 4, 6)

Answer:

7π/4 radians = 315°, Quadrant IV

sin(315°) = -√2/2

cos(315°) = √2/2

tan(315°) = -1

Step-by-step explanation: