At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?
0.029
0.050
0.120
0.091

Answer:

74.52

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]

We need to determine if the figures are congruent and if one or more of the given transformations map A onto B.

Notice that figure A is a trapezium with bases' lengths 1 and 3.

And figure B is a trapezium with bases' lengths 2 and 4. And both trapeziums have the same height 2.

Thus, the figures are not congruent, not even similar.

Since the listed transformations map to congruent images of A, none of them maps A onto B.

Therefore, they are NOT congruent and NONE of the transformations maps A onto B.

the coordinates of the image after a reflection in the y- axis are =A (5,2), B (2,1) and C(1,3)

A pair of number that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x ,y)the x-value and y- value

Firstly, we want to reflect across the x-axis When we reflect a point (x,y) over x-axis, we get (x,-y)

So;

A ( 2,5) becomes (2,-5)

B (1,2) becomes (1,-2)

C ( 3,1) becomes (3,-1)

Then we proceed to rotate 90 degrees counterclockwise about the origin

Here we have;

(x, y) becomes (-y ,x)

(2,-5) becomes (5,2)

(1,-2) becomes (2,1)

(3,-1) becomes (1,3)

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By theorem we have that if two sides of a triangle are equal, then the angles opposite to those sides are equal, with this or with knowing that the angle between the known sides are equal we conclude that both triangles are equal [the latter solution is using congruency SAS for the triangles, where S is side and A angle.]

Solution

For this case we need to remember that the point-slope formula is given by:

y= mx+b

And in order to find the slope we just need to have two points (x1,y1) and (x2,y2) and we can find m like this:

Then if we look at the graph we have two points:

x1= -2, y1= 3

x2= 0, y2= -1

And replacing we got:

And using the second point we can find the intercept

3= -2(-2)+b

b= 1

Our solution for this case :

y-3=-2(x+2)

The graph of the equation defined by; y = f(x) = x² + 20 as represented in the task content is symmetrical about the y-axis.

It follows from the task content that the axis about which the given graph is symmetrical be determined as follows.

Since it follows that for a function to be symmetric about the y-axis;

f(-x) = f(x).

Therefore, we have;

f(-x) = (-x)² + 20.

f(-x) = x² + 20 = f(x).

Hence, the graph is symmetrical about the y-axis.

Also; Since; f(-x) = x² + 20 ≠ - f(x).

It follows that the graph is not symmetrical about the origin and hence, the graph is only symmetrical about the y-axis.

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[tex]-1\frac{3}{4}[/tex] is located at a point 1.

1.1125 is located at point 6.

14 / 8 is located at point 8.

-0.875 is located at point 3.

The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator. An example of a mixed number is 1 3/4. An improper fraction is a fraction in which the numerator is greater in value than the denominator. An example of an improper fraction is 14/8.

A negative number is a number that is less than 0. This numbers would be located to the left of 0 on the number line. An example of a negative number is -1.2. A positive number is a number that is greater than 0. These numbers are located to the right of 0 on the number line. An example of a positive number is 1

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The number of citizens choosing cats, fish and dogs are 3360, 1820 and 3500 respectively.

Given, from the data which is represented by the pie chart, the percentage of citizens of a certain community choosing their favorite pet is listed below:

Fish = 13%

Dogs = 25%

Birds = 21%

Cats = 24%

Hamsters = 9%

Snakes = 8%

Altogether there are 14,000 citizens in the community.

we are asked to determine how many citizens have chosen cats, fish or dogs.

we use the method of percentage over here:

total citizens = 14000

percentage of citizens choosing cats = 24%

hence 24% of 14000 = 24/100 × 14000

= 24×140

= 3360

now, percentage of citizens choosing fish = 13%

hence 13% of 14000 = 13/100 × 14000

= 13×140

= 1820

And, percentage of citizens choosing dogs = 25%

hence 25% of 14000 = 25/100 × 14000

= 25 × 140

= 3500

hence the number of citizens choosing cats, fish and dogs are 3360, 1820 and 3500 respectively.

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The given function is,

The domain can be determined as,

Thus, the domain is the set of real numbers excluding the number 2.

The graph can be drawn as,

The vertical asymtotes is x=2 as the fuction attains the value of infinty and negative infinity at x=2.

The horizontal asymtotes is y=1 as at this value of function the value of x is either infinity or negative of infinity.

The range of the function is,

Thus, the required range of the function is set of all real numbers excluding 1.

The price relative of a new Explorer compared to the cost of Explorer in 1990 is 1.66.

The price relative is the ratio of the price of the Explorer today to the price of the Explorer in 1990. In order to determine the price relative, divide the price of the Explorer today to the price of the Explorer in 1990.

Division is the operation that is used to determine the quotient of two or more numbers. The sign that is used to represent division is ÷.

Price relative = price of the Explorer now / price of the Explorer in 1990

$39,900 / $24,00 = 1.66

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Julia sent 880 text messages in the moth of May .

In the question ,

it is given that

Cost for first 650 messages = $15

additional text message charge = $0.15

Amount owed by Julia for the month of May = $49.50

Let the number of Additional messages be x.

So, according to the question

15 + 0.15x = 49.50

0.15x = 49.50 - 15

0.15x = 34.5

x = 34.5/0.15

x = 230

number of extra messages = 230

total messages = first 650 messages + extra messages

= 650+230

= 880

Therefore , Julia sent 880 text messages in the month of May .

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The number is given to be n.

4444 is ratio of ojo’s share and 355.2 is the ratio of olu’s share .

What does a math ratio mean?

the ratio of olu’s share and ojo’s = 4:5

total Shared = 8000

the ratio of olu’s share =  8000 * 4/9

                                      =  888.8 * 4 = 355.2

the ratio of ojo’s share  = 8000 * 5/9

                                       = 888.8 * 5 = 4444

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Step-by-step explanation:

gradient means slope.

the slope is anyways the factor a of x on the slope-intercept form

y = ax + b

and in the point-slope form

y - y1 = a(x - x1)

"a" is as mentioned the slope. b is the y-intercept (the y- value when x = 0).

(x1, y1) is a point on the line.

a)

y = (1/2)×x - 2

b)

y - 2 = 3(x - -2) = 3(x + 2) = 3x + 6

y = 3x + 8

c)

remember, the slope is defined as ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

so, let's go from (1, -2) to (-2, 1)

x changes by -3 (from 1 to -2)

y charges by +3 (from -2 to 1)

the slope is +3/-3 = -1/1 = -1

so, we pick one point, e.g. (1, -2), and the line is

y - -2 = -(x - 1) = -x + 1

y + 2 = -x + 1

y = -x - 1

d)

x = -1

this is a vertical line (parallel to the y-axis) representing all points on the grid for which x = -1.

the slope is undefined, as it is y/0 (because x never changes at all). and there is no y-intercept, as x can never be 0, and the line is parallel to the y-axis, so, there cannot be any intersection point.

Answer:

[tex]\textsf{a) \quad $y=\dfrac{1}{2}x-2$}[/tex]

[tex]\textsf{b) \quad $y=3x+8$}[/tex]

[tex]\textsf{c) \quad $y=-x-1$}[/tex]

[tex]\textsf{d) \quad $x=-1$}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

Given values:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y=\dfrac{1}{2}x-2[/tex]

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

Point-slope form of a linear equation:  

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

where:

Given:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y-2=3(x-(-2))[/tex]

[tex]\implies y-2=3(x+2)[/tex]

[tex]\implies y-2=3x+6[/tex]

[tex]\implies y=3x+8[/tex]

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

Slope formula:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

where (x₁, y₁) and (x₂, y₂) are points on the line.

Given points:

Substitute the points into the slope formula to calculate the slope of the line:

[tex]\implies m=\dfrac{1-(-2)}{-2-1}=\dfrac{3}{-3}=-1[/tex]

Substitute the found slope and one of the points into the point-slope formula to create the equation of the line:

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

[tex]\implies y-(-2)=-1(x-1)[/tex]

[tex]\implies y+2=-x+1[/tex]

[tex]\implies y=-x-1[/tex]

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

If the line is parallel to the y-axis, it is a vertical line.

The equation of a vertical line is x = c.

Therefore, as the line intersects the x-axis at -1, the equation of the line is:

[tex]\implies x=-1[/tex]

There are several ways that you can follow to from two binomials from this trinomial, for example, you can do it by following these steps:

1.write two sets of parenthesis, both with the term x

2. write a list of all the factors of 36

3. find the sum of the factors of 36

4. choose the factors whose sum equals 7 and write them into the two parenthesis

Then, the second step in the process of factoring this trinomial is: option D, to write a list of all the factors of 36

Given data:

The value of the socks are x+y=$40,000.

The total interest is I=$2100.

The interest on first stock is,

i=x(4%)(1)/100

i=0.04x

The interest on second stock is,

i'=y(6%)(1)/100

=0.06x

0.04x+0.06y=2100

Substitute 40,000-x for y in the above expression.

0.04x+0.06(40,000-x)=2100

0.04x-0.06x=-300

-0.02x=-300

x=$15000

The value of second stock is,

y=40,000-15,000

=$25,000

Answer: 268435456

Step-by-step explanation:

please mark brainliest if this helped :)

Answer:

Use order of operations,

1. 4^5 = 1024

2. 4^3 = 64

3. 4^2 = 16

4. 1024 * 64 = 65,476

5. 65,476 * 16 = 696,616

6. 16 * 4 = 64

7. 64 * 16 = 1,024

8. 696,616 / 1,024 = 680.2890625

The value of the functions are given as;

(f. g)(x) =  9x² + 5  

(g . f)(x) = 3x² + 15

A function can simply be described as an expression, law, or rule showing  or explaining relationship between two variables in an equation.

The variables are namely;

Given the functions;

To determine  ( f. g)(x), we have to substitute the value of g(x) as x  in the function, we get;

(f. g)(x) = (3x)² + 5

expand the bracket

(f. g)(x)  = 9x² + 5

To determine (g . f )(x), we have to substitute the value of x in the function

(g . f(x) = 3(x² + 5)

expand the bracket

(g . f)(x) = 3x² + 15

Hence, the values are  9x² + 5 and  3x² + 15

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Given,

The radius of the cylinderis 5unit.

Required

The measure of CD.

The length of the CD is equal to the circumference of the base of circle.

So, the length of the cylinder is,

Hence,the length of CD is 10 pi.

Given:

Increased rate = 15%

One month bill = $130

Find-:

What was the monthly food bill after three​ months?

Explanation-:

Formula:

Where,

The given value is:

Amount after 3 months.

So, the food bill after three months is $197.714

The area of the Great Lakes is 988 square miles.

According to the question,

We have the following information:

The area of the Great Lakes is about 9.5 x 104 square miles.

Now, the area of the Great Lakes can simply be found by multiplying the given two numbers.

Now, in the multiplication involving numbers with decimal points, we know that the numbers are multiplied first as if there is no decimal point but in the result obtained we put the decimal point to exactly counting the digits where the decimal point was placed in the input. We move the decimal point to the left hand side according to the number of digits.

In this case, point is after 1 digit.

9.5*104 square miles

988.0 square miles

988 square miles

Hence, the area of the Great Lakes is 988 square miles.

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The probability that fewer than three of the selected consumers believe that cash will be obsolete in the next 20 years is 0.538.

The following can be deduced:

p = 40.3% = 0.403

1 - p = 1 - 0.403 = 0.597

n = 6

Therefore X follows the Binomial (6 , 0.403)

The PMF of the Binomial distribution is

P(X = x) = (n C x) * px * (1 - p)n - x ; x = 0 ,1 , 2 , ....., n

Now ,

P(fewer than 3)

= P(X < 3)

= P(X = 0) + P(X = 1) + P(X = 2)

= 0.0453+0.1834+0.3095

= 0.538

The probability is 0.538

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Given:

The size of a rectangular TV screen is given by the length of its diagnol.

THe diagonal length is 27 inches.

The height is 16.2 inches.

Required:

To find the width.

Explanation:

From the given data

Let x be the width.

From the above figure

Final Answer:

The width of the TV screen is 21.6 inches.

The given inequality is

First, we subtract 1 on each side

Now we use the property of inequalities with absolute values, which states

Using this property, we have

We solve the compound inequality now

Therefore, the solution is the interval [-2,7], and the graph of it would be

The expected value is given by:

In this case we have:

Therefore the expected payoff is $4.16

The equation using the variable m to represent the cost of a Big Mac is

m + 1.07 = 15.07.

The cost of a Big mac is $14.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Let the cost of Big macs = m

cost of fries = $1.07

The total cost of Mig macs and fries = $15.07

This can be written as an equation:

m + 1.07 = 15.07

Subtract 1.07 on both sides.

m + 1.07 - 1.07 = 15.07 - 1.07

m = 14

The cost of a Big mac is $14.

Thus,

The equation using the variable m to represent the cost of a Big Mac is

m + 1.07 = 15.07.

The cost of a Big mac is $14.

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the expression (x - 3)², has one term

the expression (x + 3)(x - 3), has two terms (x- 3) and (x + 3)

Least common denominator is the smallest number that can be divided by both given denominators.

From the problem, we have :

The denominators are 6 and 2.

The smallest number that can be divided by 6 and 2 is 6.

6/6 = 1 and 6/2 = 3

So we need an equivalent fraction with a denominator of 6.

For 5/6, multiply this by 1/1 since the denominator is already 6.

For 1/2, multiply this by 3/3 to make the denominator equal to 6.