What is the equivalent distance of 60,000 centimeters in kilometers?

1 m = 100 cm

1 km = 1000 m

Adding up all the data points during a specific period and dividing the sum by the number of time periods.

To compute a simple moving average, divide the number of prices during a time period by the total number of periods. A moving average is a technical indicator used by investors and traders to assess the direction of a security’s trend. It is determined by adding up all of the data points for a certain time period and dividing the total by the number of time periods.

For example, if we have the closing price data for the previous 30 days and need to estimate the price for the following day, we may add the 30 days’ closing price value and divide it by 30 to obtain the prediction of the next day.

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By calculating the given expression -1 1/2 minus -2.1​ we get 1.6

or 8/5 .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents.

Given expression,

-1 whole (1/2) minus -2.1

so -1 whole (1/2) can be written as = -2+1 / 2 = -1/2

so -2.1 can be written as = -21/10

-1/2 - (-21/10)

= -1/2 + 21/10

= 21/10 - 1/2

= 21-5/ 10

= 16/10

= 1.6

Hence , By calculating the given expression -1 1/2 minus -2.1​ we get 1.6

or 8/5 .

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a. sin(-60) = -(√3/2

cos (-60) = 1/2

b. sin ( 135) = 1/√2

cos (135) = -1/√2

c. sin (390) = 1/2

cos (390) = √3/2

A quadrant is a region defined by the two axes (x-axis and y-axis) of the coordinate system. When the two axes, x-axis and y-axis, intersect each other at 90 degrees, the four regions so formed are the quadrants. These regions include both positive and negative values of x-axis and y-axis, called coordinates.

. In the first quadrant,All the trigonometry functions are positive and in quadrant two, three and four respectively, sine , tan and cos are positive respectively.

sin ( -60) = sin(360-60) = sin 300= -(√3/2)

cos (-60) = cos 300 = 1/2

sin135= sin(180-135) = sin45 = 1/√2 = 1/√2

cos 135 = cos(180-45) = cos45 = -1/√2 ( cos in negative in second quadrant)

sin390 = sin( 360-390) = -sin-(30) = 1/2( sine is negative in fourth quadrant

cos 390 = cos (360-390) = cos(-30) = 1/2( cosine is positive in fourth quadrant).

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The exact values of the cosine and sine of each angle 135 and -390 is 0

To find the exact angles, we can also use the trig identities.

sin(135)    can be written as addition and subtraction angle identity.  Think of 2 angles we can easily find sine and cosine of on a unit circle, and the sum of the angle is 135

290 and 45  work because    45 +90 = 135

Therefore, we have an addition  angle identity.

sin(135) = sin(45 +90)

              = sin(45)cos(90) + cos(45)sin(90)

              = 0.7 * 0 + 0.7*1

               =0.7

sin(135) = 0.7 / 2)

Next, use the identity sin2(x) + cos2(x) = 1  to find cos(135).

cos(135) =  0.7 * 0 * 0.7*1

= 0

However, cosine is negative in the third quadrant, is 0

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Answer:

2(x+1)=3(4-x)

2x+2=12-3x

2x+2+3x=12-3x+3x

5x+2=12

5x+2-2=12-2

5x=10

5x/5=10/5

x=2

Step-by-step explanation:

The measure of the angle ∠K is 50° and the measure of the angle ∠M is 90°.

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.

Given that the external angle at point k is 130. By the property of supplementary angles, the value of the angle k will be,

k = 180 - 130

k = 50°

The measure of the angle M will be,

∠m + ∠L +∠k = 180

∠m = 180 - 40 - 50

∠m = 90

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By solving the system of linear equations we get x = 26 and y = 13.

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given,

Augustine and Raúl are selling tickets for a raffle. Together they sell 36 tickets. Augustine sells 10 more tickets than Raúl. The situation can be represented by the system of equations shown, where x is the number of tickets Augustine sells and y is the number of tickets Raúl sells.

x+y=36 ----- The total number of tickets they sell is 36.

x=y+10 ----- Augustine sells 10 more tickets than Raúl.

So substitute x = y+10 in x+y = 36

we get ,

y+10+y = 36

2y + 10 = 36

2y = 36 - 10

y = 26 / 2

y = 13

Substitute y = 13 in x= y+10

we get,

x = 13 + 10

x = 26

Hence, By solving the system of linear equations we get x = 26 and y = 13

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On solving the provided question, we can say that on subtraction we got 5 grams .

Along with addition, multiplication, and division, subtraction is one of the four arithmetic operations. An operation called subtraction simulates removing an item from a collection. As seen in the illustration below, there are 5 x 2 peaches. As a result, 2 of the 5 peaches are taken out, leaving 3 peaches. Subtraction in arithmetic refers to taking away from or adding to a group. The amount of items in a group is diminished or reduced by subtraction. A component of the subtraction problem is the minuend, subtrahend, and difference.

400 grams of water were used initially,

and Sue added salt to create a salt solution.

Sue has to add 5 grams of salt in order to make 405 grams of salt solution from 400 grams of water.

x = 405 - 400 = 5grams

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Answer:

4

Step-by-step explanation:

2+2=4

Answer:

Step-by-step explanation:

If x means times and 2 x 1 is equal to 2 because 2 x 1 is just saying I'd there was 2 ones so 2 x 2 is 4 because there is 2 two so it would be 2 +2 is

Two expressions joined by an equals sign form an equation.

a )B(-2, -5) and C(1, 1)

The point - slope form of the equation ,

y- y₁= m (x-x₁) --- (1)

(x₁, y₁) = (-2, -5)

The slope = m

[tex]m =\frac{y_{2}- y_{1}}{x _{2}- x _{1}} \\\\m = \frac{1+ 5}{1 +2} \\\\m = \frac{6}{3} = 2[/tex]

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

y- y₁=m (x-x₁)

y +5 = 2 (x + 2)

y +5 = 2x + 4a

y = 2x +4 - 5

y = 2x - 1

b ) B(-2, -5) and C(1, 1)

The slope- intercept form of the equation ,

y = mx +b ---- (1)

The slope = m

[tex]m =\frac{y_{2}- y_{1}}{x _{2}- x _{1}} \\\\m = \frac{1+ 5}{1 +2} \\\\m = \frac{6}{3} = 2[/tex]

(x₁, y₁) = (-2, -5)

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

-5 = 2(-2) + b

-5 = -4 + b

-5 +4 = b

b = - 1

The y- intercept , b is -1

Substituting b = -1  and m = 2 in (1)

y = 2x - 1

c )  B(-2, -5) and C(1, 1)

The general form of the equation,

Ax + By +C = 0 -- (1)

Here,

A = [tex]y_{1} -y_{2}[/tex]  

B = [tex]x _{2}- x _{1}[/tex]

C = [tex]x_{1}y_{2}- x_{2}y_{1}[/tex]

(-5 -1 )x + (1 +2)y + (-2 +5) = 0

-6x + 3y + 3 = 0

3y = 6x - 3

y = 2x- 1

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Two expressions joined by an equals sign form an equation.

a )B(-2, -5) and C(1, 1)

The point - slope form of the equation ,

y- y₁= m (x-x₁) --- (1)

(x₁, y₁) = (-2, -5)

The slope = m

m=y[tex]_{2}[/tex]-y[tex]_{1}[/tex]/x[tex]_{2}[/tex]-x[tex]_{1}[/tex]

m= 1+5/1+2

m=6/3 =2

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

y- y₁=m (x-x₁)

y +5 = 2 (x + 2)

y +5 = 2x + 4a

y = 2x +4 - 5

y = 2x - 1

b ) B(-2, -5) and C(1, 1)

The slope- intercept form of the equation ,

y = mx +b ---- (1)

The slope = m

m=y[tex]_{2}[/tex]-y[tex]_{1}[/tex]/x[tex]_{2}[/tex]-x[tex]_{1}[/tex]

m= 1+5/1+2

m=6/3 =2

(x₁, y₁) = (-2, -5)

Substituting (x₁, y₁) = (-2, -5)  and m = 2 in (1),

-5 = 2(-2) + b

-5 = -4 + b

-5 +4 = b

b = - 1

The y- intercept , b is -1

Substituting b = -1  and m = 2 in (1)

y = 2x - 1

c )  B(-2, -5) and C(1, 1)

The general form of the equation,

Ax + By +C = 0 -- (1)

Here,

A =y[tex]_{1}[/tex]-y[tex]_{2}[/tex]  

B = x[tex]_{2}[/tex] -x[tex]_{1}[/tex]

C = x[tex]_{1}[/tex]y[tex]_{2}[/tex] - x[tex]_{2}[/tex]y[tex]_{1}[/tex]

(-5 -1 )x + (1 +2)y + (-2 +5) = 0

-6x + 3y + 3 = 0

3y = 6x - 3

y = 2x- 1

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Using sampled data from a population (sample space) that has a definite size and follows a particular probability distribution, a Confidence Interval is a region is constructed.

A confidence interval shows the likelihood that a parameter will be between two values that are close to its mean. The level of certainty or uncertainty in a sampling process is measured by confidence intervals.

A Confidence Interval is a zone created using sampled data from a population (sample space) that has a fixed size and follows a specific probability distribution. The interval is built to include a selected population statistic with a certain probability.

A confidence interval in statistics is an educated prediction regarding a population trait. An original estimate plus or minus an error margin makes up a confidence interval (the amount by which you expect your results to vary, if a different sample were taken).

Therefore, the correct answer is option C. neither.

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a) find that x = 140/2 = 70.

b) side length [tex]x[/tex] the maximum area that the playground can have is x = 70

c)  The maximum area that the playground can have is 980 square meters

a. The playground is a rectangle, and the perimeter of a rectangle is given by 2(l + w) = 2x. The given information is that the perimeter is 280 meters, so we can set up the equation 2x = 280. Solving for x, we find that x = 140/2 = 70.

Now that we know the perimeter, we can find the area of the playground by using the formula A = lw. Since the perimeter is fixed at 280 meters, we can express the area of the playground as a function of x:

A(x) = lw = (x/2)(280 - x) = 140x - x^2

b. To find the side length x that gives the maximum area, we need to take the derivative of the area function and set it to zero.

A'(x) = 140 - 2x = 0

x = 70

c. Plugging x = 70 back into the area function, we get:

A(x) = 140x - x^2 = 140 * 70 - 70^2 = 140 * 70 - 4900 = 980.

The maximum area that the playground can have is 980 square meters.

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Answer:

hope it helps <3

Step-by-step explanation:

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in

Answer: Need more information to answer.

Step-by-step explanation:

Answer: 559.60$ before tax

              593.176$ or 593.18$

Step-by-step explanation:

Answer:

$46.63

Step-by-step explanation:

A dozen (12) computer disks costs $69.95

8 is two thirds of a dozen, and so 8 computer disks will cost two thirds of the price.

69.95 * [tex]\frac{2}{3}[/tex] = $46.63 (rounded to nearest cent)

Therefore the price of 8 disks is $46.63

By using the 68-95-99.7 Rule, the percent of scores in the data set that are expected to be below a score of 120 is 84.13%.

In Mathematics, the Empirical Rule is sometimes referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

At the middle 68% of the normal distribution, we have the following standard score:

μ - σ = 108 - 12 = 96.

μ - σ = 108 + 12 = 120.

Where:

At the middle 95% of the normal distribution, we have:

μ - σ = 108 - 2(12) = 84.

μ - σ = 108 + 2(12) = 132.

At the middle 99.7% of the normal distribution, we have:

μ - σ = 108 - 3(12) = 72.

μ - σ = 108 + 3(12) = 144.

Now, we can determine the percent (P) of scores in the data set that are expected to be below a score (x) of 120;

P(x < 120) = P((x - μ)/σ < (120 - 108)/12)

P(x < 120) = P((x - μ)/σ < 12/12)

P(x < 120) = P(z < 1)

P(x < 120) = 0.8413

P(x < 120) = 84.13%

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The coordinates of the other two vertices of the square are

Plotting the points shows that the coordinates given are diagonals of the square

The property of the square used now is that the diagonal are equal

Investigating the sets of vertices B (2, 5) and D (0, -3) &  (5, 0) and (-3, 2) will show that they will given equal length of diagonals

B (2, 5) and D (0, -3)

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(2 - 0)² + (5 + 3)²}

d =√{4 + 64}

d = √68

(5, 0) and (-3, 2)

d =√{(5 + 3)² + (2 - 0)²}

d =√{64 + 4}

d = √68

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Checkpoint 4 is 108 higher than Checkpoint 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Checkpoint 4 = -99

Checkpoint 3 = -207

The difference between the checkpoints.

= -99 - (-207)

= -99 + 207

= 108

This means,

-207 + 108 = -99

Thus,

Checkpoint 4 is 108 higher.

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The required perimeter of the given figure is Perimeter = 2 [length  + width].

Perimeter is the measure of the figure on its circumference.

here,
Questions seem to be incomplete, let's assume that the figure resembles a rectangle,
So,
the perimeter of the figure is given as,
Perimeter = 2 × length + 2 × width
Perimeter = 2 [length  + width]

Thus, the required perimeter of the given figure is Perimeter = 2 [length  + width].

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Answer:

1. Equivalent

2. Equivalent

3. Equivalent

Step-by-step explanation:

The length of the midsegment of the trapezoid with the vertices A(0, 3), B(2, 5), C(6, 4), D(2, 0) is 3√16.

The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, AB and CD

Step1:

Length of sides AB and CD

length = √(x2-x1)² + (y2-y1)²

AB =√(2-0)²+(5-3)²

AB = 2√16

Step2:

length = √(x2-x1)² + (y2-y1)²

CD = √(2-6)²+(0-4)²

CD = 4√16

Formula to use

midsegment = (AB+CD) / 2

                     = (4√16 + 2√6) / 2

                     = 3√16

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The equation of perpendicular is x+y=3

The equation perpendicular to ax+by+c=0 is bx-ay+c=0.

Here we are given x-y+3=0

a=1,b=-1c=3

the equation is -1x-y+3=0

x+y=3

The equation of perpendicular is x+y=3.

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Answer: ±i-4

Step-by-step explanation:

To solve this equation by completing the square, we first have to adjust the equation.

Let's rewrite it in this form:

x^2+8x+16+1=0

Then we can complete the square.

(x+4)^2+1=0

(x+4)^2 = -1

x+4 = ±i

x = ±i-4

Answer:

0.05x + 0.25y = 4.65

Step-by-step explanation:

Let x = number of nickels.

Let y = number of quarters.

0.05x + 0.25y = 4.65

for the given function the value of k=6

What is a function?

A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph since one is mapped to two different values. However, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.

The function machine receives the x-values as input. After finishing its operations, the function machine produces the y-values. Any function may be the one within.

function f(x)=2x^3-kx^2+8

For x=2

f(2)=2*8-k*4+8 = =

4k = 24

k = 6

Hence, for the given function the value of k=6

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This measurement written in scientific notation is 4.75 x 10-5 centimeters.

Solution:

Step 1: The given wavelength of blue light is 0.0000475 centimeters.

Step 2: To convert this number into scientific notation, we need to move the decimal point 4 places to the left.

Step 3: This results in 4.75 x 10-5 centimeters.

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The forces result in a right triangle. To obtain the resultant force, one can simply use the Pythagorean theorem. 1250 lbf and 2650 lbf both act as the legs of the triangle. Obtaining the hypotenuse via the theorem would yield the resultant force. This is done below:

c^2 = a^2 + b^2

c^2 = (1250)^2 + (2650)^2

c = 2930.017 lbf

Therefore, the magnitude of the resultant force is approximately equal to 2930 lbf.

So, on solving the provided question we cans say that the three consecutive integers are -12,-11,-10.

Integers with no spaces between them are referred to as consecutive integers. Integers 15, 16, and 17 are examples of sequential numbers. Serial numbers are arranged in ascending order of least to largest. like in 1, 2, 3, 4, 5, 6, etc., which are all consecutive numbers. Therefore, there are three 7s in a row: 27, 28, 29, 30, and 33. In the event that n is an integer, then (n + 1) and (n + 2) are two subsequent integers: If n is 1, for instance, the subsequent integers are (1 + 1) and (1 + 2) or 2 and 3.

The sum of three consecutive integers is -33.

x +x+1+x+2 = -33

3x+3 =  -33

3x = -36

x = -12

so, three consecutive integers are -12,-11,-10.

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The intermediate step in the form (x+a)² = b as a result of completing the square for the following is  (x + 3 )² = 16.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Equation x²+6x = 7

This can also be written as:

x²+6x - 7 = 0

To complete the square of the expression, we will add the square of the half of coefficient of x in the equation to both sides

Coefficient of x = 6

Half of the coefficient =3

Square of the result = 9

Add 9 to both sides to have:

x²+6x - 7 + 9 = 0 + 9

x²+6x  +9 - 7 =  9

(x + 3 )² = 16

Hence,  the intermediate is (x + 3 )² = 16.

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The equation in slope-intercept form is y= 3x+2

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

(x1,y1)=(-1, -1)

(x2,y2)=  (-3, -7)

m = (y2-y1)/(x2-x1)

   = (-7-(-1))/(-3-(-1))

   = (-7+1)/(-3+1)

   = -6/-2

m = 3

y-y1=m(x-x1)

y-(-1)=3(x-(-1))

y+1=3(x+1)

y+1=3x+3

=> y= 3x+3-1

=> y= 3x+2

So, the equation in slope-intercept form is y= 3x+2

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Answer:

The first option

15, 900 grams

Step-by-step explanation:

Total number of bolts = 600

Out of these 35% are small bolts
35% of 600 = 0.35 x 600 = 210

Total mass of 210 small bolts = 210 x 20 = 4200 grams

The remaining number of bolts = 600 - 210 = 390 large bolds

Their total mass = 390 x 30 = 11,700 gms

Total mass of all 600 bolds = 4,200 + 11, 700 = 15, 900 grams

This is the first of the listed choices

The discriminant of the quadratic equation is zero, thus, we have a double root.

A general quadratic equation can be written as:

y = a*x^2 + b*x + c

The discriminant is defined as:

D = b^2 - 4ac

In this case, the quadratic equation is:

16x^2 + 8x + 1 = 0

So the discriminant is:

D = 8^2 - 4*16*1

D = 0

So we have a double root.

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