A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?

Answers

Answer 1

Answer:

= 18.2 miles per hour

Step-by-step explanation:

Speed = distance / time

            =82 miles / 4.5 hours

             =18.22222222 miles per hour

             Rounding

             = 18.2 miles per hour

Answer 2

Answer:

Given that

Distance = rate × time

82 = r × 4½

r = 18.2 mph


Related Questions

Determining the normal form of the equation of a line is like finding the equation of a tangent line to a circle of radius p.

Please select the best answer from the choices provided

True

False

Answers

Answer:

True

Step-by-step explanation:

The normal form of equation of a line is the radius of p. Tangent to a circle is the line that touches one point on the circle. The radius is the circumference of the circle. The tangent line on the circle is always perpendicular to the radius. The statement is correct.

When x=5 what would the value of expression

Answers

Answer:

46

Step-by-step explanation:

6 more than the product of 8 and a number x

6 more means 6+

product of 8 and a number x means 8x

6+8x

when x=5

6+8(5)=6+40=46

The data show the number of hours of television watched per day by a sample of 28 people. Use technology to answer parts​ (a) and​ (b) below. 1 1 2 8 8 4 8 7 8 3 1 2 8 2 4 7 4 0 5 7 7 8 9 3 6 2 2 7 a. Find the data​ set's first,​ second, and third quartiles. Upper Q 1 equals nothing Upper Q 2 equals nothing Upper Q 3 equals nothing

Answers

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

Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below.

HOURS OF TV AGE
1 45
3 30
4 22
3 25
6 15

a. Determine which variable is the dependent variable.
b. Compute the least squares estimated line.
c. Compute the coefficient of determination. How would you interpret this value?

Answers

Step-by-step explanation:

22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination.22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value How would22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value you interpret22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value this value22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value

22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of 22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination.22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination.22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination.22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value How22

3 25

6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you interpret this value would you interpret this value How would you interpret this value How would you interpret this value. How would you interpret this value of determination. How would you interpret this value of determination. How would you interpret this value this value interpret this value

How do you pronounce f(x)

Answers

Answer:

f of x

Or

f-function of x

Answer:

f(x) is pronounced in mathematics as if one were saying "f of x"

What is $121 divided into ratio of 7:4

Answers

Answer:

77:44

Step-by-step explanation:

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

Answer: 77:44

Explanation:

121 x 7/11 = 77

And

121 x 4/11 = 44

What is the domain of the set of ordered pairs?
(8, -13); ( 0,-5); (4, -9); (-3,2)

Answers

The domain is the input values, which are the x values.

The x values in the given pairs are: 8, 0,4,-3

The domain set is (-3, 0, 4, 8)

The required domain of the set of ordered pairs is [8, 0, 4, -3]

Given that,

Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).

We have to determine,

The domain of the set of ordered pair.

According to the question,

The domain refers to the set of possible input values.

The domain of a graph consists of all the input values shown on the x-axis.

A relation is a set of ordered pairs.

The domain is the set of all the first components of the ordered pairs.

Then,

Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).

Here, Set of all the input values on the x-axis.

Therefore,

The set of values of x is { 8,0,4,-3 }

Hence, The required domain of the set of ordered pairs is [8, 0, 4, -3]

To know more about Domain click the link given below.

https://brainly.com/question/19704059

Why is 12 * 10-8 is NOT a correct representation of scientific notation?

Answers

Answer:

see below

Step-by-step explanation:

Scientific notation is a * 10 ^b

a must be a number between 1 ( including 1 ) and less than 10

12 is greater than 10 so it is not scientific notation

I NEED HELP ASAP
FUND THE VALUE OF X

Answers

Answer:

2 sqrt(41) = x

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10 ^2 = x^2

64+ 100 = x^2

164 = x^2

Take the square root of each side

sqrt(164) = sqrt(x^2)

sqrt(4) sqrt(41) = x

2 sqrt(41) = x

The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)

a. $2,761.21


b. $3,583.83


c. $3,523.83


d. $3,722.47

Answers

Answer:

C). $3523.83

Step-by-step explanation:

loan of principles p= $9,300,

at rate R= 12 1 /8 % interest

Rate R = 12.125%

for duration year T = 37.5 months

T= 37.5/12 = 3.125 years

Interest I=PRT/100

Interest I =( 9300*12.125*3.125)/100

Interest I = (352382.8125)/100

Interest I = 3523.83

Interest I= $3523.83

What is 5 over 30= 3 over c

Answers

Answer:

c=18

Step-by-step explanation:

5/30=3/c

1/6=3/18

1✖️3=3

6✖️3=18

How many odd numbers with 4 different digits, can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8? (No repetition is allowed)
A. 71
B. 200
C. 210
D. 840
E.1680

Answers

Answer:

840 ( D )

Step-by-step explanation:

GIVEN DIGITS : 1,2,3,4,5,6,7,8  

Number of odd numbers = 4

Number of even numbers = 4

therefore the number of odd numbers with 4 different digits can be formed by the same way the number of even numbers ( without repetition )

Hence the number of ways odd numbers with 4 different digits = Total number of ways of forming 4 digit numbers / 2

8*7*6*5 = 1680 / 2 =  840 ways

Solve for x: the quantity of x plus 4 over 3 = 2.

Answers

Answer:

x =2

Step-by-step explanation:

(x+4) /3 = 2

Multiply each side by 3

(x+4) /3  *3= 2*3

x+4 = 6

Subtract 4

x+4-4 = 6-4

x =2

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 2

▹ Step-by-Step Explanation

[tex]\frac{x + 4}{3} = 2\\\\3 * 2 = 6\\\\x + 4 = 6\\\\x = 2[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

f(x)=6x+2 and g(x)=-9x-5 Find the product of f and g.

Answers

Answer: See below

Explanation:

(f • g)(x) = (6x+2)(-9x-5)
(f • g)(x) = 54x^2 - 30x - 18x - 10
(f • g)(x) = 54x^2 - 48x - 10

The product of the functions f(x) and g(x) will be negative 2 times (27x² + 24x + 5).

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = 6x + 2 and g(x) = -9x - 5

The product of the functions f(x) and g(x), then we have

⇒ f(x) × g(x)

⇒ (6x + 2) × (-9x - 5)

Simplify the expression, then we have

⇒ (6x + 2) × (-9x - 5)

⇒ 6x(-9x - 5) + 2(-9x - 5)

⇒ -54x² - 30x - 18x - 10

⇒ -(54x² + 48x + 10)

⇒ -2(27x² + 24x + 5)

The product of the functions f(x) and g(x) will be negative 2 times (27x² + 24x + 5).

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

I will name you Brainly hurryyyy What two integers are in between 0.7142

Answers

Answer:

0.71419 &0.71421 are the correct.

Apply the distributive property to factor out the greatest common factor. 18d+12 =18d+12=18, d, plus, 12, equals

Answers

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.

Twelve apples cost $2.00. How much will 50 apples cost?

Answers

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]

a radion station usa 1\6 of its time for the news. in a 12 hour day, how many hours are used for music & entertainment?

Answers

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

A household survey of 10 families was conducted by students of 4th year MBBS. In the collected data, the ages of heads of families were: 32, 34, 35, 36, 36, 42, 44, 46, 48, and 52. The mean age of heads of families is
a. 36
b. 38.5
c. 40
d. 40.5
e. 42

Answers

Answer:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14

Step-by-step explanation:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT

8 less than one-fourteenth of some number, w

Answers

Answer:

The answer is 1/14w-8

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.

Answers

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

     

       

Complete parts ​(a) through ​(c) below.

​(a) Determine 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. ​

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

​(c) Determine 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.

Answers

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.

Consider the following case and determine whether there is sufficient information to solve the triangle using the low of sines. Two angles and the side included between them are known.
A. There is insufficient information because to use the law of sines, one side and the angle opposite it must be known.
B. There is sufficient information because if two angles and a side included between them are known, the third angle and the remaining two sides can be determined using the law of sines.
C. There is insufficient information because to use the law of sines, two angles and a side opposite one of them must be known.
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.

Answers

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.

In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S

Answers

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a [tex]\triangle RST[/tex], RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

Using the cosine rule:

[tex]cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ[/tex]

Now, let us use Sine rule to find other angles:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

[tex]\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ[/tex]

[tex]\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ[/tex]

Smallest angle is [tex]\angle T[/tex]

Correct answer is option A. T

Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are not closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial. Reset Submit

Answers

Answer:

  f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.

Step-by-step explanation:

The set of all polynomials is closed under addition, subtraction, and multiplication, because performing any of these operations on a pair of polynomials will give a polynomial result.

__

Comment on the question

The wording is a bit strange, because f(x) and g(x) are elements of a set (of polynomials), so cannot be said to be "closed." "Closed" is a property of a set with respect to some function, it is not a property of an element of the set.

Answer:

f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.

Step-by-step explanation:

Its correct trust

X-6 greater then equal to 15 + 8x

Answers

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

price.
A shopkeeper marks the price of his her goods 40 % above the cost price and
allows 20% discount. If his her purchase price of an item is Rs 6.000. how much
should a customer pay for it levying 13 % VAT!
e 990 the honorariter​

Answers

Answer:

73%

Step-by-step explanation:

Help please!!! Tyyyyy

Answers

Answer:

D) 60 degree

Step-by-step explanation:

Let's connect the remaining diagonal, which forms a triangle containing angle x.

As a property of regular hexagon, all diagonals are equal.

=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.

show that an integer is divisible by 11 if and only if the alternating sum (add first digit, subtract the second, add the third, subtract the fourth etc) of its digits is divisible by 11
Need an answer by tomorrow if possible please

Answers

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.

Find the value of f (x)=x²-4 and g(x)=3x+2 Find the value of f (-1)g(-1)

Answers

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]

Other Questions
Given: ABC, AC = BC, AB = 3 CD AB, CD = 3 Find: AC Why was the war of 1812 victory victory for the United States even though neither side actually won A decline in the domestic real interest rate would cause a ________ in net exports and a ________ in the exchange rate. The diagonal of a square is 8 cm. What is the length of the side of this square? Give your answer as an exact surd in its simplest form. Mrs. Galindo decided to make Kool-Aid to serve along with the pizza at the Future Farmers of America party. The directions said to mix a half of a scoop of powdered drink mix with two gallons of water to make each pitcher of Kook-Aid. One of Mrs. Galindo's students said she will mix 4 scoops with 2 gallons of water to make 4 pitchers. Which choice best explains whether the student is correct and why. Question 1 options: The direction's constant of proportionality is 4. k = 2/0.5 There are 4 gallons of water per one scoop. The student is correct because 4 pitchers = 4 scoops times 2 gallons The direction's constant of proportionality is 4. k = 2/0.5 There are 4 gallons of water per one scoop. The student is incorrect because 4 pitchers does not equal 4 scoops times 2 gallons The direction's constant of proportionality is 0.25 k = 0.5/4 There is a quarter of a gallon of water per one scoop The student is correct because 4 pitchers = 4 scoops times 2 gallons The student is incorrect because 4 pitchers does not equal 4 scoops times 2 gallons A particle moves in a plane according to X=Rsinwt + wRt Y=Rcoswt+R where w and R constant this curved called cycloid path traced out by a point on rim of wheel that slipping with x-axis sketch the path calculate intantaneous velocity and acceleration when particle is its axis maximun and minimun value of Y Depending on the study, it is sometimes necessary for psychologists to be deceptive. Please select the best answer from the choices provided T F for the function y= -2+5 sin [pi/12(x-2)], what is the maximum value What is true about a scale (Music) Answer the question in attachment and can I ask from which country you are.I am new on this app. Select the correct answer.Which process is a physical change?A.iron rustingOB.milk turning to curdwater boilingD.paper burningE.hard water staining pipes Mr. Clifton was preparing for his upcoming birthday party. He ordered 51 white balloons and 47 red balloons. As he walked to his car 12 balloons flew away! With the remaining balloons, he mixed the colors to create bunches of 3 to decorate his party space. How many full bunches did Mr. Clifton have to decorate his party space? Two angles are complementary. One angle's measure is 3 more than 9times the other angle. What is the measure of each angle? Write eachangle's measure separately. Which equation represents a population of 300 animals that decreases at an annual rate of 23%? A. p=300(1.23)t B. p=300(1.77)t C. p=300(0.77)t D. p=300(0.23)t Suppose the 2020 adidas financial statements contain the following selected data (in millions). Current assets $4,575 Interest expense $200 Total assets 9,000 Income taxes 178 Current liabilities 3,050 Net income 236 Total liabilities 5,670 Cash 800 Compute the following values. (a) Working capital. $ millions (b) Current ratio. (Round to 2 decimal places, e.g. 6.25:1.) :1 (c) Debt to assets ratio. (Round to 0 decimal places, e.g. 62%.) % (d) Times interest earned. Bake Treats is a confectionery that makes cakes for special occasions and delivers them. They use gourmet ingredients while baking and deliver customized treats. In fact, they only start baking once they receive an official request from a customer. It is evident that Bake Treats has adopted a(n) _____ . As literature, the Bible contains an organized view of life that comprehends and subsumes even man's artistic creations.a) trueb) false You have a saturated solution of BaSO4, a slightly soluble ionic compound. What happens if you add Ba(OH)2, NaNO3, and CuSO4 to this solution The "TAO" approach to digital marketing analytics stands for. NEED HELP ASAPIn 1988, three gray whales were trapped in Arctic ice. Television crews captured the franticattempts of hundreds of people to save the whales. Eventually, a Soviet icebreaker and U.S.National Guard helicopters arrived to help free the whales. The cost of the rescue missionexceeded $5 million.i. Write a scientific question related to the whale story. (1 point)