Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about 13% of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York). The resulting relative frequency can be used as an estimate of the true probability of all Americans who can wiggle their ears. The resulting relative frequency can be used as an estimate of the true probability of all Americans who cannot wiggle their ears. The resulting relative frequency is the true probability of all Americans who can wiggle their ears. The resulting relative frequency cannot be used as an estimate of the true probability of all Americans who can wiggle their ears.

Answer:

Attachment 1 : Graph B

Attachment 2 : Option B

Step-by-step explanation:

( 1 ) The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.

( 2 ) We have the following system of equations at hand here.

{ x = 5 cot(t), y = - 3csc(t) + 4 }

Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,

x = 5 cot(t) ⇒ x - 5 = cot(t),

y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)

Now let's square these two equations, adding them --- Step #2

We know that csc²θ - cot²θ = 1, so let's subtract the equations

( y - 4 / - 3 )² = (csc(t))²

- ( x - 5 / 1 )² = (cot(t))²

___________________

(y - 4)² / 9 - x² / 25 = 1

And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.

Answer:

Q1= 2, Q2 = 4.5, Q3 = 7.5

Step-by-step explanation:

firstly, put the data is other;

0 1 1 1 2 2 2, 2 2 3 3 4 4 4, 5 6 7 7 7 7 7, 8 8 8 8 8 8 9

the Q1 = (2+2)/2 = 2

Q2 = (4 + 5)/ 2 = 4.5

Q3 = (7 + 8)/2 = 7.5

Answer:

[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]

Step-by-step explanation:

18d + 12

The greatest common factor is 6, So we need to factor out 6

=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]

Answer:

6(3d+2)

Step-by-step explanation:

6 is the gcd of the two terms.

Answer:

73%

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Hello, please consider the following.

For any a and b real numbers we can write.

[tex](a-b)(a+b)=a^2-b^2[/tex]

We apply this formula two times here, as below.

[tex](x+1)(x^{2}+1)(x-1)=(x+1)(x-1)(x^{2}+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1[/tex]

We have the coefficient of 1 for [tex]x^4[/tex] and the constant term is -1, so the sum of the coefficients is 0.

Thank you.

Answer:

1

Step-by-step explanation:

(x + 1)(x² + 1)(x - 1)

= (x³ + x + x² + 1)(x - 1)

= x^4 - x³ + x² - x - x³ - x² + x - 1

= x^4 - 1

Coefficient of x^4 = 1

Answer and Step-by-step explanation:

Suppose that we have a number y which is a positive integer and that:

y = [tex]x_n...x_5x_4x_3x_2x_1x_0[/tex]

Where;

[tex]x_{0}[/tex] = digit at 10⁰ => one's place (units place)

[tex]x_1[/tex] = digit at 10¹ => 10's place (tens place)

[tex]x_{2}[/tex] = digit at 10² => 100's place (hundreds place)

[tex]x_{3}[/tex] = digit at 10³ => 1000's place (thousands place)

.

.

.

[tex]x_{n}[/tex] = digit at 10ⁿ place

Then;

y = [tex]x_{0}[/tex] * 10⁰ + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ

Since 10⁰ = 1, let's rewrite y as follows;

y = [tex]x_{0}[/tex]  + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ

Now, to test if y is divisible by 11, replace 10 in the equation above by -1. Since 10 divided by 11 gives -1 (mod 11)     [mod means modulus]

y = [tex]x_{0}[/tex]  + [tex]x_1[/tex] * (-1)¹ + [tex]x_{2}[/tex] * (-1)² + [tex]x_{3}[/tex] * (-1)³ + [tex]x_{4}[/tex] * (-1)⁴ + [tex]x_5[/tex] * (-1)⁵ + . . . + [tex]x_{n}[/tex] * (-1)ⁿ

=> y =  [tex]x_{0}[/tex]  - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ (mod 11)

Therefore, it can be seen that, y is divisible by 11 if and only if alternating sum of its digits [tex]x_{0}[/tex]  - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ is divisible by 11

Let's take an example

Check if the following is divisible by 11.

i. 1859

Solution

1859 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (1 - 8 + 5 - 9) is divisible by 11.

1 - 8 + 5 - 9 = -11.

Since -11 is divisible by 11 so is 1859

ii. 31415

Solution

31415 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (3 - 1 + 4 - 1 + 5) is divisible by 11.

3 - 1 + 4 - 1 + 5 = 10.

Since 10 is not divisible by 11 so is 31415 not divisible.

Answer:

x = -6

y = 4

Step-by-step explanation:

Rewriting the equations :

Now, solving the two equations using substitution method, we get :

x = -6

y = 4

Answer:

y = 4

x = -6

Step-by-step explanation:

1/2 x + 1/4 y= -2        first equation

-2/3 x + 1/2 y = 6      second equation

solution:

from the first equation:

8(1/2 x + 1/4 y) = -2*8

8x*1/2 + 8y*1/4 = -16

8x/2 + 8y/4 = -16

4x + 2y = -16        third equation

from the second equation

6(-2/3 x + 1/2 y) = 6*6

6x*-2/3 + 6y*1/2 = 36

-12x/3 + 6y/2 = 36

-4x + 3y = 36        fourth equation

from the third & fourth equation:

 4x + 2y  = -16

-4x + 3y  = 36

   0  + 5y = 20

5y = 20

y = 20/5

y = 4

from the fourth equation:

-4x + 3y = 36

-4x + 3*4 = 36

-4x + 12 = 36

-4x = 36 - 12

-4x = 24

x = 24/-4

x = -6

Check:

from the first equation:

1/2 x + 1/4 y = -2

1/2 *-6 + 1/4 * 4 = -2

-3 + 1 0 -2

from the second equation:

-2/3 x + 1/2 y = 6

-2/3 * -6  +  1/2 * 4 = 6

4 + 2 = 6

Answer:x ≤ 3

Step-by-step explanation:

Answer:

x ≥ -3

Step-by-step explanation:

x - 6 ≥ 15 + 8x

x - 8x ≥ 15 + 6

-7x ≥ 21

x ≥ 21/-7

x ≥ -3

x greater than equal to -3

check:

-3 - 6 ≥ 15 + 8*-3

-9 ≥ 15 - 24

Answer:

[tex]\huge \boxed{\mathrm{\$ \ 7,533.33}}[/tex]

Step-by-step explanation:

There are 12 months in one whole year.

In one year, the person earns $96,600 with bonus.

The person gets a bonus of $6,200 during Christmas.

96,600 - 6,200 = 90,400

The person earns $90,400 yearly.

[tex]\frac{90,400}{12}[/tex] = 7,533.3333

Each month, the person earns $7,533.33, to the nearest cent.

Answer:

(a) 1.341

(b) -2.539

(c) -2.160 and 2.160

Step-by-step explanation:

(a) We have to find the critical​ value(s) for a​ right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%

Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.

(b) We have to find the critical​ value(s) for a​ left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%

Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.

(c) We have to find the critical​ value(s) for a​ two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.

Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.

Answer:

  10 hours

Step-by-step explanation:

In order to answer this question, you must assume that all air time not spent on news is spent on music & entertainment. That would usually not be the case, as there would usually be advertisements and public service programming along with everything else.

The time spent on news is ...

  (1/6)(12 hours) = 2 hours

If the rest is spent on music and entertainment, then ...

  12 -2 = 10 . . . hours are used for music and entertainment

Answer:

The answer is 1/14w-8

Answer: The value of x- 2y is a. [tex]\pm 3[/tex].

Step-by-step explanation:

Given:  x and y are two positive real numbers such that [tex]x^2+4y^2=17[/tex]   and [tex]xy= 2[/tex] .

Consider [tex](x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)][/tex]

[tex]=x^2-4xy+4y^2[/tex]

[tex]=x^2+4y^2-4(xy)[/tex]

Put  [tex]x^2+4y^2=17[/tex]   and [tex]xy= 2[/tex] , we get

[tex](x-2y)^2=17-4(2)=17-8=9[/tex]

[tex]\Rightarrow\ (x-2y)^2=9[/tex]

Taking square root on both sides , we get'

[tex]x-2y= \pm3[/tex]

Hence, the value of x- 2y is a. [tex]\pm 3[/tex].

Complete Question

Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.the correct conclusion at [tex]\alpha =0.001[/tex] is?

Answer:

There is no sufficient evidence to support the professor believe

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 18[/tex]

     The sample size is  [tex]n = 15[/tex]

      The sample mean is  [tex]\= x = 19[/tex]

      The standard deviation is  [tex]\sigma = 1.7[/tex]

      The level of significance is  [tex]\alpha = 0.001[/tex]

The null hypothesis is  [tex]H_o: \mu = 18[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > 18[/tex]

 The critical value of the level of significance from the normal distribution table is    

         [tex]Z_{\alpha } = 3.290527[/tex]

The test hypothesis is mathematically represented as

           [tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]

substituting values  

         [tex]t = \frac{ 19 - 18}{ \frac{1.7}{ \sqrt{15} } }[/tex]

         [tex]t = 2.28[/tex]

Looking at the value of  t and  [tex]Z_{\alpha }[/tex] we can see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis.

This mean that there is no sufficient evidence to support the professor believe

Answer:

$25

Step-by-step explanation:

.5 * 50 = 25

25<27.5<30

The cheapest supplier is the first one.

Answer:

Step-by-step explanation:

First you have to find the medians which is when you put the numbers in number order and find the one in the middle.

Class A: 60,65,70,70,75,80,80,85,90,90

=77.5

Class B: 75,85,85,85,90,90,90,90,95,100

=90

That the class B is more advanced, and they probably studied.

Answer:

see below

Step-by-step explanation:

4x + 10 = 2(2x + 5)

Distribute

4x+10 = 4x+10

Since the left side is identical to the right side, there are infinite solutions

4x - 5 = 4x + 10

Subtract 4x from each side

-5 = 10

This is never true, so there are no solutions

4x-5 = -5

Add 5 to each side

4x = 0

x=0

There is one solutions

Answer:

c=18

Step-by-step explanation:

5/30=3/c

1/6=3/18

1✖️3=3

6✖️3=18

Answer:

3

Step-by-step explanation:

[tex]f(-1)g(-1) \text{ is the same thing as } f(-1)\cdot g(-1). \\\text{Therefore, find f(-1) and g(-1)}[/tex]

[tex]f(-1)=(-1)^2-4\\f(-1)=1-4\\f(-1)=-3[/tex]

[tex]g(-1)=3(-1)+2\\g(-1)=-3+2\\g(-1)=-1[/tex]

Therefore:

[tex]f(-1)\cdot g(-1)\\=(-3)(-1)=3[/tex]

Answer:  4 seconds

Step-by-step explanation:

x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)

0 = -12x² + 48x

0 = -12x(x - 4)

0 = -12x     0 = x - 4

0 = x          4 = x

x = 0 seconds is when the ball was kicked

x = 4 seconds is when the ball landed on the ground

Answer:

0.71419 &0.71421 are the correct.

Answer:

Answer is below

Step-by-step explanation:

The width of the CI is directly proportional to critical value. When t* is greater than z value, the t value would then cause the margin of error to be larger and this will in turn cause the width of the confidence interval to be larger.

Greater t*df than z* gives us a bigger margin of error. This would in turn give bigger width of confidence interval. t distribution has greater width confidence interval compared to z distribution.

The width of confidence interval is a function of the margin of error. If the critical value of t(t*) is slightly larger than the critical value of z(z*), then the width of the confidence interval will be larger.

The margin of error is the product of the critical value and the standard error. Therefore, given the same standard error value, the value of the margin of error will increases based on the value of the critical value.

Since, t* is slightly larger than z*, then the confidence interval, t will be wider.

Learn more : https://brainly.com/question/18405415

Answer:

-5

Step-by-step explanation:

Answer:

$8.33

Step-by-step explanation:

[tex]Solve \:using \: proportion\\\\12\:apples = \$ 2\\50\:apples = \$ x\\Cross \: Multiply\\\\12x = 100\\\\\\\frac{12x}{12} = \frac{100}{12} \\\\x = \$ 8.333[/tex]

Answer:

About $8.33.

Step-by-step explanation:

Write a proportion. Make sure the values line up horizontally:

[tex]\frac{12\text{ apples}}{\$2} =\frac{50\text{ apples}}{\$x}[/tex]

Cross multiply:

[tex]100=12x\\x=25/3\approx\$8.33[/tex]

Answer:

y=3

Step-by-step explanation:

-5y+8=-7

Minus 8 from each side.

-5y=-15

Divide -5 from each side.

y=3

Answer:

D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.

Step-by-step explanation:

A triangle is a plane shape that consists of 3 sides and 3 angles. There are different ways of solving for any unknown sides or angles of a triangle.

If any two angles and just one side of a triangle are known, then other angles and sides can also be determined using the sine rule.

For example, if a, b and c are the sides of the triangle and <A, <B and <C are the angles. The sine law is expressed as shown;

a/sinA = b/sinB = c/sinC

Any two can be equated to get any unknown sides and angles.

Also, if two of the angles are known, the third angle can be determined since the sum of angle in a triangle is 180°. If <A and <B are known for example, the third angle <C can be determined using the expression.

<C = 180°-(<A+<B)

Based on the explanation, option D is therefore the correct option i.e There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.

Answer:

the answer is A

Step-by-step explanation: i have calculated this problom

Answer:

77:44

Step-by-step explanation:

Since 7:4 is equal to 11 and 121/11, each ratio can be multiplied by 11.

Step-by-step explanation:

Hello, there!!!!

It's simple lets get started with simple solution.....

Given,

AC= 7cm

BC= 25cm

let AB be x.

Now, As it is a Right angled triangle, taking angle B as a refrence angle. we get,

h= BC= 25cm

p= AC= 7cm

b= AB= x

now, by Pythagoras relation we get,

[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]

[tex]or \: b = \sqrt{ {25}^{2} - {7}^{2} } [/tex]

By simplifying it we get,

b= 24cm

Therefore, the value of AB is 24 cm.

Hope it helps...