please answer thank you

Answer:

Proved all parts below.

Step-by-step explanation:

As given ,

|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]

To prove- a) For any real number x , | x | ≥ 0 . Moreover, | x | = 0 ⇒ x = 0

                 b) For any two real numbers x and y , | x | ⋅ | y | = | x y | .

                 c) For any two real numbers x and y , | x + y | ≤ | x | + | y | .

Proof -

a)

As given x is a real number

Also , by definition of absolute value of x , we get

| x | ≥ 0

Now,

if |x| = 0

⇒ x = 0 and -x = 0

⇒ x = 0 and x = 0

⇒ x = 0

∴ we get

| x | = 0 ⇒  x = 0

Hence proved.

b)

To prove - | x | ⋅ | y | = | x y |

As we have,

|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]

|y| = [tex]\left \{ {{y , y\geq 0} \atop {-y, y< 0}} \right.[/tex]

|xy| = [tex]\left \{ {{xy , x,y > 0 and x,y < 0} \atop {-xy, x > 0, y< 0 and x <0 , y > 0}} \right.[/tex]

We have 4 cases : i)  when x > 0 , y > 0

                              ii) when x > 0 , y < 0

                              iii) when x < 0, y > 0

                              iv) when x < 0, y < 0

For Case I - when x > 0 , y > 0

⇒ |x| = x, |y| = y

⇒|x|.|y| = xy

For Case Ii - when x > 0 , y < 0

⇒ |x| = x, |y| = -y

⇒|x|.|y| = -xy

For Case Iii - when x < 0 , y > 0

⇒ |x| = -x, |y| = y

⇒|x|.|y| = -xy

For Case IV - when x < 0 , y < 0

⇒ |x| = -x, |y| = -y

⇒|x|.|y| = (-x)(-y) = xy

∴ we get , from all 4 cases

| x | ⋅ | y | = | x y |

Hence Proved.

c)

To prove - | x + y | ≤ | x | + | y |

Let

|x| = |x + y - y|

    ≥ |x + y| - |y|     ( Triangle inequality)

⇒ |x| + |y| ≥ |x + y|

Hence Proved.

Answer:

No significant difference between mean and Expected value

Step-by-step explanation:

Hypothesis

H0 : u = 77.5

H1: u is not equal to 77.5

Alpha = 0.05

Mean = Σxi/n

= 77.09+75.37+72.42+76.84+77.84, +76.69+78.03+74.96+77.54+76.09+81.12+75.75/12

= 919.74/12

= 76.645

We get the variance s² = xi² -n(barx)²/n-1

= 77.09²+75.37²...75.75²-12(76.645)²/11

When we solve this out

We get 4.3486818182

T test = barx - u/(s/√n)

= (76.645-77.5)/√4.3486818182/12

= -1.420293

T critical = Tn-1, alpha/2

= 2.200985

The test statistic is less than 2.201 so we accept the null hypothesis at 0.05 level of significance. And then conclude that there is No significant difference between mean and Expected value.

Answer:

angle JKL is 21

Step-by-step explanation:

the angle of the two triangles are the same, so (2x + 1) = (3x - 9)

You would then find the x, which equals to 10.

Then replace x with ten with the equation.

Answer:

%18 tip

Step-by-step explanation:

The dinner cost was $29 before tip

after tip it was $32.22

34.22-29= $5.22  she tipped

$29 * %x = $5.22

After solving this equation, the x is %18

Answer:

[tex]\dfrac{w}{z}=\dfrac{2}{7}[/tex]

Step-by-step explanation:

Given that,

[tex]w=\dfrac{6}{7}[/tex]

z = 3

We need to find [tex]\dfrac{w}{z}[/tex].

Put w = 6/7 and z = 3 in the w/z

[tex]\dfrac{w}{z}=\dfrac{\dfrac{6}{7}}{3}\\\\=\dfrac{6}{7}\cdot\dfrac{1}{3}\\\\=\dfrac{2}{7}[/tex]

So, [tex]\dfrac{w}{z}=\dfrac{2}{7}[/tex]. Hence, the correct answer is 2/7.

Answer:

yeah I would say deal #1 is better

Answer:

70-25=45

45+25=70

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Answer:

a)  f(5) = 24

b) The inverse of given function

              f⁻¹ ( x ) = √x+1

c)    f⁻¹ ( 8 ) = √9 =3

Step-by-step explanation:

Explanation:-

Given  f(x) = x² - 1

a)

      f(5) = 5² -1 = 25-1 =24

b)      

put y =  f(x) = x² - 1

   ⇒   y =  x² - 1

 ⇒     x² = y + 1

⇒     x = √y+1

⇒ f⁻¹ ( y ) = √y+1      ( ∵ f⁻¹ ( y) =x)

The inverse of given function

              f⁻¹ ( x ) = √x+1

c)   put x=8

             f⁻¹ ( 8 ) = √8+1 = √9 =3

Answer:

daaaaaaaaaa

Step-by-step explanation:

ssdddsss

Answer:

34

Step-by-step explanation:

Answer:

Area of rectangle =LXB

L=7m

B=3m

so 7m multiply by 3m gives 21 so the area is 21

Answer:

-3/4

Step-by-step explanation:

-1 1/4 = -5/4

1/2 = 2/4

-5 + 2 = -3

-3/4

Answer: The answer is -3/4

Step-by-step explanation: covert the mixed numbers to improper fractions, then find the LCD and combine.

Answer:

Step-by-step explanation:

1/6 x 1/5 + 1/30

= 1/30 + 1/30

= 2/30

=1/15

Solution :

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

This is a valid probability distribution.

In the question it is given that call for a response of Y for short of a sample of people aged between 19 years to 25 years.

Also the event that describes the value of call for response greater than 3 i.e. (Y < 3) is a randomly chosen people between the age 19 to 25 years old who has gone to fitness center or did exercise fewer than 3 days.

Valid probability models add up to 1

The probability is a valid probability model

The probability model is given as:

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

To determine if the model is a valid probability model, or not

We make use of:

[tex]\mathbf{\sum P(x) = 1}[/tex]

So, we have:

[tex]\mathbf{0.68 + 0.05 + 0.07 + 0.08 + 0.05 + 0.04 + 0.01 + 0.02 = 1}[/tex]

Add the probabilities

[tex]\mathbf{ 1= 1}[/tex]

The above equations shows that:[tex]\mathbf{\sum P(x) = 1}[/tex]

Hence, the probability is a valid probability model

Read more about probability models at:

https://brainly.com/question/9965602

Answer: 22

Step-by-step explanation:

Solve for x

   1/2x + 7 = 18

Combine 1/2 and x.

  x/2+ 7 = 18

Move all terms not containing x to the right side of the equation.

Subtract 7 from both sides of the equation.

  x/2= 18 − 7

  x/2 = 11

Multiply both sides of the equation by 2.

  2 ⋅ x/2 = 2 ⋅ 11

Simplify both sides of the equation.

Cancel the common factor of 2.

  x = 2 ⋅ 11

Multiply 2 by 11.

  x = 22

Answer: 829 3/4 or 829 75/100

Step-by-step explanation:

What was the answer

Answer:D

Step-by-step explanation:

Answer: The answer is -19.5

Step-by-step explanation: This is because 1/2 is .5 in decimal form. A negative PLUS a positive = is negative since the -20 is larger than .5

Answer:

the answer would be -19.5 :)

Step-by-step explanation:

Let the two number is a and b

so,

product =ab=20

sum of square=[tex]\bold{a^2+b^2=41 }[/tex]

Then,

[tex]\bold{(a+b)^2=a^2+b^2+2ab }[/tex]

[tex]\bold{ (a+b)^2=41+2×40 }[/tex]

[tex]\bold{ (a+b)^2=81 }[/tex]

[tex]\bold{a+b=\sqrt{81} }[/tex]

[tex]\bold{a+b=9 }[/tex]•••••••••(equation I)

Now,

[tex]\bold{(a-b)^2=a^2+b^2-4ab }[/tex]

[tex]\bold{ (a-b)^2=41-4×20 }[/tex]

[tex]\bold{(a-b)^2=41-40 }[/tex]

[tex]\bold{a-b=\sqrt{1} }[/tex]

[tex]\bold{a-b=1 }[/tex]••••••••(equation II)

Now,combine the equation I and equation II

we,get

[tex]\bold{a+b+a-b=9+1 }[/tex]

[tex]\bold{a+\cancel{b}+a\cancel{-b}=10 }[/tex]

[tex]\bold{ 2a=10 }[/tex]

[tex]\bold{a=\dfrac{10}{2} }[/tex]

[tex]\blue{\boxed{ a=5 }}[/tex]

Then,

put the value of a in equation II.

we get that,

[tex]\bold{5-b=1 }[/tex]

[tex]\bold{b+1=5 }[/tex]

[tex]\bold{b=5-1 }[/tex]

[tex]\bold{\boxed{\blue{b=4}} }[/tex]

so,

The two number is 5 and 4.

Answer:

Equation of straight line that passes through (-4, 2) and has slope 9/2 is

[tex]y-2=\frac{9}{2} (x+4)[/tex]

Step-by-step explanation:

Equation of straight line in point slope form is given as

[tex]y-y_1=m(x-x_1)[/tex] ---------(2)

Here

[tex]m = \frac {9}{2}[/tex]   and  [tex](x_1, y_1) = (-4, 2)[/tex]

Substituting values in equation (1)

[tex]y-2=\frac{9}{2} (x+4)[/tex]

Answer:

29.8÷3=9.93333333333

Step-by-step explanation:

*note* the 3 is a repeating number

Answer: P(4) - 4/12,1/3,33%,0.33

Step-by-step explanation:

My teacher went over the answers

Answer:

4/1

Step-by-step explanation:

g is 4

Answer:

0.1402

Step-by-step explanation:

For each baby elk, there are only two possible outcomes. Either they survive adulthood, or they do not survive. The probability of an elk surviving adulthood is independent of other elks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood.

This means that [tex]p = 0.44[/tex]

Suppose researchers choose 7 baby elk at random to monitor.

This means that [tex]n = 7[/tex]

What is the probability that more than 4 elk in the sample to survive to adulthood?

This is:

[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{7,5}.(0.44)^{5}.(0.56)^{2} = 0.1086[/tex]

[tex]P(X = 6) = C_{7,6}.(0.44)^{6}.(0.56)^{1} = 0.0284[/tex]

[tex]P(X = 7) = C_{7,7}.(0.44)^{7}.(0.56)^{0} = 0.0032[/tex]

[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1086 + 0.0284 + 0.0032 = 0.1402[/tex]

0.1402 probability that more than 4 elk in the sample to survive to adulthood.

Using the concept of binomial probability, the probability that more than 4 survive is 0.1402

Using the binomial probability formula :

The probability that more than 4 survive can be defined thus :

Using a binomial probability calculator :

[tex] P(x > 4) = 0.1086 + 0.0284 + 0.0032 [/tex]

[tex] P(x > 4) = 0.1402 [/tex]

Hence, the probability that more than 4 survive is 0.1402

Learn more : https://brainly.com/question/15929089

Answer:

p=5x+3y

solve for x, number of cupcakes. isolate x

5x=p-3y

divide by 5

x=(p-3y)/5

Step-by-step explanation:

D. x<15

Answer:

17 units

Step-by-step explanation:

Use distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], to find the distance between (-9, 5) and (8, 5):

Let,

[tex] (x_1, y_1) = (-9, 5) [/tex]

[tex] (x_2, y_2) = (8, 5) [/tex]

Plug in the values into the distance formula:

[tex] d = \sqrt{(8 - (-9))^2 + (5 - 5)^2} [/tex]

[tex] d = \sqrt{(17)^2 + (0)^2} [/tex]

[tex] d = \sqrt{(289 + 0)} [/tex]

[tex] d = \sqrt{289} [/tex]

[tex] d = 17 [/tex]

Step-by-step explanation:

[tex]x ^{1} = - 5 \\ y ^{1} = - 2 \\ x {}^{2} = - 2 \\ y {}^{2} = 1 \\ then \: you \: solve \: with \: that \: formula \: you \: know[/tex]

[tex]16 - 3 \times 5 {}^{2} \div 5[/tex]

[tex]16 - 3 \times 5 {}^{2} \div 5 {}^{1} [/tex]

[tex]16 - 3 \times 5 {}^{2} \div 5 {}^{ - 1} [/tex]

[tex]16 - 3 \times 5 {}^{2 - 1} [/tex]

[tex]16 - 3 \times 5 {}^{1} [/tex]

[tex]16 - 3 \times 5[/tex]

[tex]16 - 15[/tex]

[tex]1[/tex]

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