Simplify the expression:
31 – (5 – 3 x 4)^2 + 2^6 / 4

a. -2
b. 10
c. 0
d. -3

Answer:

Step-by-step explanation:

Given that:

population mean = 10

variance [tex]\sigma^2[/tex] = 25  ; [tex]\sigma[/tex] =[tex]\sqrt{ 25}[/tex] = 5

sample size n = 28

The standard deviation of the sample mean:

= [tex]{\dfrac{5}{\sqrt{28}}[/tex]

= 0.95

To halve the standard deviation of the sample mean, the size of how large the sample will be can be computed as follows:

[tex]\dfrac{sd_1}{sd_2} = \dfrac{\dfrac{\sigma}{\sqrt{n}} }{\dfrac{\sigma}{\sqrt{n}} }[/tex]

[tex]\implies \dfrac{\dfrac{5}{\sqrt{28}} }{\dfrac{5}{\sqrt{28}} }[/tex]

[tex]= \dfrac{5}{\sqrt{28}} \times \dfrac{\sqrt{28}}{5}[/tex]

= 2

n = 4 × 28

n = 112

The standard deviation is 0.95 and if the standard deviation is halved then the sample mean is 112.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

A normal population has a mean of 10 and a variance of 25.

A random sample of sizes n-28 is selected.

A.  The standard deviation will be

[tex]\sigma = \dfrac{\sqrt{Var(x)}}{n} \\\\\sigma = \dfrac{\sqrt{25}}{\sqrt{28}} \\\\\sigma = 0.95[/tex]

B.  The sample be if you want to halve the standard deviation of the sample mean

[tex]\rm \dfrac{SD_1}{SD_2} = 2 = \dfrac{\sqrt{n}}{\sqrt{28}}\\\\n = 4*28 \\\\n= 112[/tex]

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Answer:

9.25

Step-by-step explanation:

M₄ means the area using 4 rectangles with heights equal to the function evaluated at the midpoints.

The width of each rectangle is (4−0)/4 = 1.

The area of each rectangle is:

M₁ = (1) (1.12) = 1.12

M₂ = (1) (1.80) = 1.80

M₃ = (1) (2.69) = 2.69

M₄ = (1) (3.64) = 3.64

The total area is therefore:

M = 1.12 + 1.80 + 2.69 + 3.64

M = 9.25

3(2x+4),  2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12

An expression is combination of variables, numbers and operators.

The given expression is 6X +12

We have to find the equivalent expressions of 6x+12

Let us take 6 as a common factor we get

6(x+2)

so 6(x+2)  is equivalent expression of 6X +12

Now let us take 3 as common factor

3(2x+4)

so 3(2x+4)  is equivalent expression of 6X +12

Now let us take 2 as common factor

2(3x+6)

so 2(3x+6)  is equivalent expression of 6X +12

Hence,  3(2x+4),  2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12

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Answer: 991

square root of 982081 hope this helps

Answer:

299

Step-by-step explanation:

The expression equivalent to 6x + 18 is 3(2x + 6) thus option (B) is correct.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that are all constrained and create an equation.

Expression is very useful to determine the end or root value of constraint.

As per the given,

6x + 18

Take 3 as common,

3(2x + 6)

Hence "The expression equivalent to 6x + 18 is 3(2x + 6)".

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Answer:

Let x be the amount Nick's little sister is given.

x = 10 - 4

Answer:

C.0.1

Step-by-step explanation:

Because this is 10% confidence confirmed

Answer:

The equation of the tangent line

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

Step-by-step explanation:

Step(i):-

Given function y = x cot (x) ....(i)

Differentiating equation (i) with respective to 'x' , we get

[tex]\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)[/tex]

Step(ii):-

The slope of the tangent line

[tex]\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x[/tex]

[tex](\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}[/tex]

We will use trigonometry formulas

[tex]Cosec(\frac{\pi }{4} ) = \sqrt{2}[/tex]

[tex]sec(\frac{\pi }{4} ) = \sqrt{2}[/tex]

[tex]Cot(\frac{\pi }{4} ) = 1[/tex]

Now the slope of the tangent

[tex]\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1[/tex]

[tex]\frac{dy}{dx} =-\frac{\pi }{2} +1[/tex]

Step(iii):-

Given

Substitute [tex]x=\frac{\pi }{4}[/tex] in y = x cot (x)

               [tex]y = \frac{\pi }{4} cot (\frac{\pi }{4} )[/tex]

              [tex]y = \frac{\pi }{4}[/tex]

The point of the tangent line  [tex](x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )[/tex]

The equation of the tangent line

[tex]y - y_{1} = m ( x - x_{1} )[/tex]

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

Answer:

$5 each week

Step-by-step explanation:

$40 a month

$10 a week

$10-$5 is $5 each week

If you want to be paid $5 less, then every month you will be paid $35

There the amount that you get paid every week will be:

35 ÷ 4 ( 1 month have 4 weeks )

= $8.75

Answer:

6.79

Step-by-step explanation:

6.79 x 10 = 67.9

The unknown number z would be 6.79

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

WE have been given that 67.9 is ten times as much as unknown number;

Let the unknown number be z;

Z x 10 = 67.9

Now divide by 10 on both sides, we get;

Z = 67.9/10

Z = 6.79

Therefore,

6.79 x 10 = 67.9

Hence, the unknown number z would be 6.79

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Answer:

Lydia must sell 552 burritos

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is not too clear. check the attachment for better view of the question.

From the options The set A = {2, 3, 4} will be compared to other options to determine which of the remaining set is equivalent to the set A.

x e R means the values in the set are real numbers and real numbers can either be rational or irrational. R= Hence the real numbers between  1 and 5 are not restricted to only positive integer values but also decimal numbers. and since set A does nit contain ant rational number, hence both set B and C are not equivalent to set A.

Also, set B is not equivalent to set C even though the values in both sets are integers. They are not equal because 1 is included in set B but not in set C.

Set D and E are equivalent because they both contains integers between 1 and 5. Integers are positive whole numbers between 1 and 5 since the both sets doesn't contain any negative value. Hence the set A = set D = set E

Given :

A line 2x + 1 =0 .

To Find :

The slope of the given line .

Solution :

We know , slope of line is given by the tangent of the angle between the x-axis and the line .

Now, for line 2x + 1 =0 i.e [tex]x=\dfrac{-1}{2}[/tex] .

The line is perpendicular to x-axis and cuts the x-axis at [tex]\dfrac{-1}{2}[/tex] .

Therefore , the angle between the line and x-axis is [tex]90^o[/tex] .

So , slope [tex]m=\tan\ 90^o[/tex] i.e undefined .

Therefore , the slope of given line is not defined .

Hence , this is the required solution .

Answer:

x = 1

Step-by-step explanation:

Solve for x:

4 (2 x + 6) = 5 (x + 5) + 2

Hint: | Distribute 5 over x + 5.

5 (x + 5) = 5 x + 25:

4 (2 x + 6) = 5 x + 25 + 2

Hint: | Group like terms in 5 x + 2 + 25.

Grouping like terms, 5 x + 2 + 25 = 5 x + (25 + 2):

4 (2 x + 6) = 5 x + (25 + 2)

Hint: | Evaluate 25 + 2.

25 + 2 = 27:

4 (2 x + 6) = 5 x + 27

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

8 x + 24 = 5 x + 27

Hint: | Move terms with x to the left hand side.

Subtract 5 x from both sides:

(8 x - 5 x) + 24 = (5 x - 5 x) + 27

Hint: | Combine like terms in 8 x - 5 x.

8 x - 5 x = 3 x:

3 x + 24 = (5 x - 5 x) + 27

Hint: | Look for the difference of two identical terms.

5 x - 5 x = 0:

3 x + 24 = 27

Hint: | Isolate terms with x to the left hand side.

Subtract 24 from both sides:

3 x + (24 - 24) = 27 - 24

Hint: | Look for the difference of two identical terms.

24 - 24 = 0:

3 x = 27 - 24

Hint: | Evaluate 27 - 24.

27 - 24 = 3:

3 x = 3

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 3 x = 3 by 3:

(3 x)/3 = 3/3

Hint: | Any nonzero number divided by itself is one.

3/3 = 1:

x = 3/3

Hint: | Any nonzero number divided by itself is one.

3/3 = 1:

Answer:  x = 1

Answer:

  4x +3y = -1

Step-by-step explanation:

To find the new constant for the equation, use the given x- and y-values:

  4(5) +3(-7) = 20 -21 = -1

The equation of the parallel line in standard form is ...

  4x +3y = -1

this is the answer

Step-by-step explanation:

2x+3

Answer:

2x+3x

Step-by-step explanation:

Answer:

0.9

Step-by-step explanation:

I am not sure how to really explain but the 2 negatives equal a positive. So if there is 2 Negatives also know as -     = a positive. And a positive is just the the opposite of a negative

The product of the given fractions is 3/25.

The given fractions are -3/5 and -1/5.

The product of two fractions can often be expressed by an equivalent fraction where the numerator and denominator have been divided by a common factor. The product of two fractions is the product of the numerators and the product of the denominators.

Now, multiply the given fractions

-3/5 × -1/5

Multiply numerators and write the result in numerator and multiply denominators and write the result in denominator.

That is, -3/5 × -1/5 = 3/25

Therefore, the product of the given fractions is 3/25.

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Answer:

4x= 14

Step-by-step explanation:

let the nisha be x and nishan be y

Step-by-step explanation:

ATQ

your statement is x=2y

Answer:

1.39

Step-by-step explanation:

Answer:

36 and 49

Step-by-step explanation:

6x6 and 7x7

I will assume you want it in the form of y>mx+b

0.5x-2y>3

0.5x-3>2y

0.25x-1.5>y

Answer:

[tex]x>4y+6[/tex]

Step-by-step explanation:

[tex]0.5x-2y>3[/tex]

First, we will have to add 2 to both sides.

[tex]0.5x-2y+2y>3+2y[/tex]

This equals to

[tex]0.5x>2y+3[/tex]

Now, we will make this into a fraction and divide. We will divide by 0.5.

[tex]\frac{0.5x}{0.5} >\frac{2y+3}{0.5}[/tex]

Now that we divided, we got our answer!

[tex]x>4y+6[/tex]

Hope this helps!

Answer:

[tex]y = \frac{z}{2} -3x[/tex]

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents & roots

Multiplication

Division

Addition

Subtraction

& is the order of operation.

First, subtract 6x from both sides:

6x (-6x)  + 2y = z (-6x)

2y = z - 6x

Next, divide 2 from both sides:

(2y)/2 = (z - 6x)/2

y = (z - 6x)/2

y = (z/2) - 3x

[tex]y = \frac{z}{2} -3x[/tex]  is your answer.

~

Answer:

a. g(0)= 1

b. f(-2)= 0

d. g(x-2)= 5x-9

Step-by-step explanation:

a. g(x)=5x+1  *substitute 0 for x*

g(0)= 5(0)+1

g(0)= 1

b. f(-2)= [tex](-2)^2-4[/tex]   *substitute -2 for x*

f(-2)= 4-4 =0

c. g(x-2)= 5(x-2)+1 *substitute x-2 for x*

 g(x-2)= 5x-10+1    *distributive property*

g(x-2)=5x-9          *simplify*

Answer:Line BD

Step-by-step explanation:

The top is shorter than the bottom, so it can't be AC. EF will only have about half of the section covered. BD is symmetrical so it can't be no lines. So it must be BD.

Answer:

The weight is 4 pounds :D

Step-by-step explanation: