Choose the four expressions that are equivalent to 6^−2.

We need to know about density to solve this problem. The density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex], so option (c) is the correct answer.

Density is a substance's mass per unit volume. The symbol commonly used for density is ρ. Density can be calculated by dividing the mass by volume. In this question we know that mass of the metal piece is 124 grams and the volume is given to be 21 cubic centimeters. The density can be calculated by dividing the mass by volume of the metal piece.

density =mass/ volume= 124/21=5.90 g/[tex]cm^{3}[/tex]

Therefore the density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex] , so option (c) is the correct answer.

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Answer: 1/2

Step-by-step explanation:

If we have an equaton in a standard form, that is y = mx + b, our slope is m (the coefficient of x). So, let's transform 3x - 6y = 144 into the standard form.

3x - 6y = 144

-6y = - 3x + 144

y = -3/(-6)x - 144/6

y = (1/2)x - 24

As I mentioned above, the slope is the coefficient of x. Here our slope is 1/2.

The number of different samples possible when the shopper selects a sample of 4 apples from the bag is 126.

Combinations are a method of calculating the overall results of an event where the order of the results is irrelevant. From the information, the bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.

It should be noted that the question has to do with a combination. The number of different samples that are possible will be:

Number of apples = 9

Number to be selected = 4

= ⁹C₄

= 9! / (9 - 4)! 4!

= 9 × 8 × 7 × 6 / 4 × 3 × 2

= 126

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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. How many different samples are possible?

The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%

To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room

The probability of an unlocked room being robbed is therefore:

= 0.75 x 0.03 x 0.842

= 0.0225 x 0.842

= 0.018945

= 1.89%

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The absolute change or the car's value decreased by $1500.

The relative change: The value of the car decreased by 6.302 %.

The car's value dropped from $23,800 to $22,300 over the last year.

So, the initial price of the car is I = $23,800, and the final value of the car after a year is F = $22,300.

Therefore,

The Absolute change will be:

= I - F

= $23,800 - $22,300

= $1500

Hence, the car's value decreases by $1500.

Now, the relative change is the percentage by which the price decreased over the year.

So,

As the price decreased by $1500.

Let x be the relative change.

Then,

$ 23,800 × x/100 = $1500

238x = 1500

x = 6.302

Hence, the car's value decreased by 6.302% last year.

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Answer:

Using a class size of 6.

Range = Highest value - Lowest value = 100 - 1 = 99

No. Of class = range/class size = 99/6 = 16.5 ~ 17/classes.

Upper-class limit of class (1) = Lower class limit of class (1) + class size - D

=> 1 + 6 - 1 = 7 - 1 = 6

.: UCL1 = 6

The table is shown below:

Answer:

a: undefined

b: -15

c: 20

d: 25

Step-by-step explanation:

a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined

b: look at x 0 on graph, there is open dot at -15 meaning the limit is there

c: look at x -7 on graph, there is open dot at 20 meaning the limit is there

d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)

answer:

the third one

To find the area of a rectangle, we can use the following formula

Therefore, to find the total area we have to multiply his length by his width.

Using the data given in the question, we know that the length is 21 yards and the width is 5 yards. Therefore we find that:

we conclude that the area of the rectangle is 105 yards^2.

Note that the units of the area are square units

Answer:4

Step-by-step explanation:

The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275

The given parameter is in the attached figure

Also from the question, we have:

House price decreases by approximately every mile

The above implies that the relationship is an approximately linear relationship

From the table, we have

Coefficient constant = 301.7

Coefficient distance = -2.158

This means that

y-intercept = 301.7

Slope = -2.158

So, the equation is

y = y-intercept + slope * x

This gives

y = 301.7 - 2.158x

The interpretation of the slope and y-intercept in context are:

Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7

Here, we have

Residual =  -2.962

Miles = 11

This means that

Predicted price = 301.7 - 2.158 * 11

Evaluate

Predicted price = 277.96

So, we have

residual = actual - predicted

This gives

actual = residual + predicted

So, we have

actual = -2.962 +  277.96

Evaluate

actual = 275

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The prices p that would yield a revenue of 7110 dollars are;

Lowest price = $0.895

Highest price = $119.105

We are told that the total revenue obtained by producing and selling x units is given by; R = xp.

Now, we are told that the demand equation for a certain product is given by p = 120 - 0.015x.

where;

p is the unit price (in dollars) of the product.

x is the number of units produced.

At a revenue of $7110, we will have;

(120 - 0.015x)x = 7110

120x - 0.015x² = 7110

0.015x² - 120x + 7110 = 0

Using quadratic equation calculator, we have;

x = 59.695 and 7940.305

Thus;

Lowest price = 120 - 0.015(7940.305) = $0.895

Highest price = 120 - 0.015(59.695) = $119.105

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Answer:

n / 9  + 5 = 3

Step-by-step explanation:

The simplified form of the given expression is x + a - 4

From the question, we are to simplify the given expression

From the given information, we have that

g(x) = x² - 4x,

Now,

We are to simplify

[tex]\frac{g(x)-g(a)}{x -a}[/tex]

First, we will determine g(a)

From the given function,

g(x) = x² - 4x

∴ g(a) = a² - 4a

Thus,

[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes

[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]

[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]

[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]

Factoring

[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]

Further factorization

[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]

Dividing

((x +a) -4)

x + a - 4

Hence,

The simplification gives x + a - 4

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nswer:

Explanation:

ere, we want to solve the given composuite function

What we have to do is to replace the x in f(x) with the entirety of g(x)

We have that as:

Now, we replace x in f(x) with 2x+9 as stated

We have that as:

The length of the target is 4cm and the width of the target is 6cm.

A rectangle is an object that has four sides and four right angles. The sum of angles in a rectangle is 360 degrees.  The perimeter of a rectangle is the distance round the rectangle.

Perimeter = 2( length + width)

20 = 2(w - 2 + w)

20 = 2(2w - 2)

20 / 2 = 2w - 2

10 = 2w - 2

10 + 2 = 2w

12 = 2w

w = 12/2

w = 6

Length = 6 - 2 = 4

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Answer:

$3,312.00

Step-by-step explanation:

If we add up her sales we get 207,000

We multiply that by .016 to get $3,312.00

step 1

Find out the scale factor

Remember that

If two figures are similar, then the ratio of their volumes is equal to the scale factor elevated to the cubic

so

Let

s ----> scale factor

s^3=11,000/8,019

s=1.11

step 2

Remember that

If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared

so

s^2=SA/1,134

s=1.11

1.11^2=SA/1,134

SA=(1.11)^2*(1,134)

SA=1,400 yd2

The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.

As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.

We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:

Where (t,C) is any point on the line, m is the slope and b is the C-intercept.

By replacing the know values we can solve for b:

Therefore,

The graph of the function H(x) = "x+5" and the graph of the function t(x) = "2x+5" are displayed in the picture that is attached below.

This is further explained below.

Generally, The set of ordered pairings that satisfy the condition [tex]"\displaystyle f(x)=y"[/tex] is the graph of the function f.

These pairings, which are Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane, are found under the usual scenario in which both x and f(x) are real values.

In conclusion, The Graph of the function H(x) =|x+5| and t(x)=|2x+5| is given in the image attached below.

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The graph of the function gives the type of function, (continuous or discrete function) the domain and the range as follows;

(A, 2A)

First graph;

Discrete function

Domain; {x| x = -8, -2, 3, 6}

Range; {y| y = 5, 4, -2, 7, }

Second graph

Continuous function

Domain; -4 < x < ∞

Range; 1 ≤ y < 9

(A3.A) 1. The slope of the graph is -1.5

2. The slope of the graph is 1.5

A function is an equation defining the relationship between input and output variables

(A, 2A)

A continuous function is one in which a continuous variation in the input values produces a continuous variation in the output. Therefore, a continuous function does not have discontinuity and it has a defined output within the interval in which it is contagious

A discrete function is one that have input values and output only at specified points, such that the function does not have inputs, and therefore, outputs at certain points.

The points in the scatter plot of the first graph are separate and not linked, such that the function is not contagious between any two x–values, which gives;

The function is a discrete function

The domain, which is the set of possible x–values is; {x| x = -8, -2, 3, 6}

The range is {y|y = 5, 4, -2, 7, }

The line joining the points on the second graph, indicates that the graph has values for all input or x–values

Therefore, the function of the graph is a continuous function

(A3. A) 1. Points on the graph are:

(0, 2), (2, -1)

The slope is given by the equation;

Slope = ∆y ÷ ∆x

Which gives;

2. The given function is; -3•x + 2•y = -6

To find the slope, the function is expressed in the slope and intercept form, y = m•x + c, as follows;

-3•x + 2•y = -6

2•y = 3•x - 6

Therefore;

2•y = 3•x - 6

y = (3•x - 6) = 1.5•x - 3

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The reciprocal of 3 7/8 is 8/31.

To find the reciprocal of a number, we invert the fraction by swapping the numerator and denominator.

Let's calculate the reciprocal of 3 7/8.

First, we need to convert the mixed number into an improper fraction. To do this, we multiply the whole number (3) by the denominator (8) and add the numerator (7). This gives us:

3 7/8 = (3 x 8 + 7) / 8 = 31/8

Now, to find the reciprocal, we invert the fraction:

Reciprocal of 31/8 = 8/31

Therefore, the reciprocal of 3 7/8 is 8/31.

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Answer:

350'000

Step-by-step explanation:

The real # is 369,852, so 350,000 is closest to all the other options.

To solve the equation;

To solve for t, we shall take the following steps;

ANSWER:

The correct answer is option (b)

The value of x in the equation is 18. 98

Trigonometric identities are defined as mathematical equations relating to several trigonometric functions, holding true for all the values in the domain of the functions.

The several types of trigonometric identities includes;

It is important to note that the trigonometric ratios for major identities are;

sine = opposite/hypotenuse

tangent = opposite/adjacent

cosine = adjacent/hypotenuse

Given the equation;

x/25.75=sin47.5 degrees

Take the following steps to determine the value of 'x'

We have;

cross multiply

x = sin47.5  × 25. 75

Find the value of sin 47. 5 and substitute the value

x = 0. 7373 × 25. 75

multiply through

x = 18. 98

Hence, the value of x is  18. 98

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The complete question:

x/25.75=sin47.5 degrees

Find the value of x

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Find gradient of the line first.

Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.

Gradient = (-3-0) ÷ (-2-5) = 3/7

Eqn is y = 3/7x + c

Substitute either one of the coordinates into the equation to find c.

0 = 3/7(5) + c

c = -15/7

Hence, the equation of the line is y = 3/7x - 15/7

The actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.

The minimal amount of coordinates required to specify any point within a mathematical space (or object) is known as the dimension in physics and mathematics. As a result, a line has one dimension (1D), since only one coordinate is required to specify a point on it, such as the point at 5 on a number line.

A surface, like the perimeter of a cylinder or sphere, has two dimensions (2D) because two coordinates are necessary to specify a point on it. For instance, both a latitude and a longitude are necessary to pinpoint a point on the surface of a sphere.

The dimensions are 3cm by 5 cm meaning length = 5cm and breadth = 3cm

Given that ½ cm = 2 ft, that is

1 cm = 4 ft

Using the conversion method

3 cm = 3 × 4

        = 12 ft

5 cm = 5 × 4

        = 20 ft

Actual area = 20 × 12 ft

                    = 240 square ft

Thus, the actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.

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