In a recent poll of 500 13-year-olds, many indicated to enjoy their relationships with their parents. Suppose that 200 of the 13-year olds were boys and 300 of them were girls. We wish to estimate the difference in proportions of 13-year old boys and girls who say that their parents are very involved in their lives. In the sample, 93 boys and 172 girls said that their parents are very involved in their lives. What is a 96% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)?
(a) Calculate a 95% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)?
(b) Interpret your interval calculated above.

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)

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:

Line 3

Step-by-step explanation:

→ Calculate gradient

[tex]\frac{6-3}{4-2} =1.5[/tex]

Answer:

Line 3

Step-by-step explanation:

(0,0) & ( 4 , 6)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]

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:

[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:

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:

B. -3

Step-by-step explanation:

Answer:

7π/4 radians = 315°, Quadrant IV

sin(315°) = -√2/2

cos(315°) = √2/2

tan(315°) = -1

Step-by-step explanation:

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:

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:

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:

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:

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:

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:

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.5, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 1.9 feet.

This is the p-value of Z when X = 1.9. So

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

[tex]Z = \frac{1.9 - 2.5}{0.4}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a p-value of 0.0668

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

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]

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]

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]

Step-by-step explanation:

Double t

t+t=2t

Subtract v

2t-v

Subtract u

2t-v-u

You'll need 2 more lines to complete this two column proof.

---------------------

Line 4

For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

---------------------

Line 5

The statement is what you want to prove since this is the last line.

So the statement is [tex]p || q[/tex]

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

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:

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

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:

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:

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:)

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

Step-by-step explanation:

Given that,

The mass of a patient = 70 kg

A 70kg patient has approximately 8 pints of blood.

The patient donates 470mL of blood.

We know that,

1 pint = 568 mL

8 pints = 4544 mL

Required fraction,

[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]

So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].

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.