Given functions f and g, perform the indicated operations. f(x) = 3x - 5, g(x) = 6x - 6 Find f-g. Select one: A. -3x + 1 B. -3x - 11 C. 9x - 11 D. 3x - 1

Elena can make use of the table, since the area of the table measures 540 in² and it is greater than the combined area of the cubes which is 300 in²

Volume Of Cube:

The volume of a cube is the sum of the three-dimensional spaces occupied by the cube. A cube is a 3D solid object with six square faces, all of which are the same length. A cube, also known as a regular hexahedron, is one of the five Platonic solid shapes. The volume of a cube is in (unit)3 or cubic units. The SI unit of volume is the cubic meter (m3), which is the volume occupied by a cube with sides of 1 meter.

The volume of a cube can be obtained using the formula:

Volume, V = a³ ;

Where, a = edge of cube

Therefore,

The given volume of the cube, V = 1000 in³

V = a ³

⇒ 1000 = a³

Take the cube root of both sides ;

a = 10 inches

Now,

The Area of the cube is thus ;

Area = a²

Area of cube = 10² = 100 in²

Now,

The Area of the three cubes :

100 in² × 3 = 300 in²

The area of the table :

Converting the dimension to inches :

1 foot = 12 inches

Length = 2.5 feet = (12 × 2.5) = 30 inches

Width = 1.5 feet = (12 × 1.5) = 18 inches

Hence,

Area of table in feet = length × width = 30 × 18 = 540 in²

Therefore, Since the area of the table is greater than the combined areas of the cubes, then, the table is usable.

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Answer:

\(\frac{ - 5}{54} + \frac{5 \times 6}{9 \times 6} = \frac{ - 5 + 30}{54} = \frac{25}{54} \)

\( \frac{15}{4} \div \frac{3}{8} = \frac{15}{4} \times \frac{8}{3} = 10\)

\(10 \times \frac{25}{54} = \frac{250}{54} = 4 \times \frac{17}{27} \)

b )

\(4 \times \frac{17}{27} = \frac{125}{27} =\)

cube root =

\( \frac{5}{3} \)

c ) square root

\( \frac{125}{27} = \frac{ \sqrt{25 \times 5} }{ \sqrt{3 \times 9} } = \frac{5 \sqrt{5} }{3 \sqrt{3} } \)

Answer:

I think the answer is 30. Hope this helps!

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

Answer:

the first 2 one is put on the right and the other on the left and the second 2 but one in the middle and one on the left!

Step-by-step explanation:

Answer: $5300

Step-by-step explanation:

Pounds of food produced - - - - - - profit($)

100 - - - - - - - - - - - - - - - - - - - - (- 11,000)

250 - - - - - - - - - - - - - - - - - - - - - 0

500 - - - - - - - - - - - - - - - - - - - - 10,300

650 - - - - - - - - - - - - - - - - - - - - 11,500

800 - - - - - - - - - - - - - - - - - - - - 9,075

Using the quadratic regression calculator, with a general form of equation:

y=Ax^2+Bx+C

y = 0.0186x^2 - 11.3241x + 8422.2857

With the equation obtained, we can estimate the profit when 350 pounds of food are produced.

Here, x = 350

y = - 0.0817x2 + 102.2355x - 20420.955

y = - 0.0817(350)^2 + 102.2355(350) - 20420.955

y = - 10008.25 + 35782.425 - 20420.955

y = $5353.22

Answer:

B.$5,300

Step-by-step explanation:

Answer:

simplified it is

16m-40=16m-40

Answer:

2 o' clock

Step-by-step explanation:

dependant variable: distance in meters

independant variable: time in seconds

i hope i helped.

The dependant variable are the distance in meters, and the independant variable are the time in seconds.

If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable. The variables who take their values based on some other variables' values are called dependent variables.

Given Distance to travel = 20 m.

We need to determine the time, t, that each participant took to complete 20 m.

Barbara:

Average speed = (3 m)/(2 s)

= 1.5 m/s

Time = t = 20/1.5 = 13.3 s

Mark;

t =  5 s

Carlos;

y = x + 1

where, y = 20 m and x = time, t

Therefore,

t =x = y - 1 = 20 - 1 = 19 s

Summary;

Barbara:  13.3 s

Mark:       5 s

Carlos:     19 s

Hence, The winner is Mark.

The dependant variable are the distance in meters, and the independant variable are the time in seconds.

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That's a Congruent Triangle question.

The first thing that we should to analize is it: What figure is EFGH? The question say for us that \(\overline{EF} \cong \overline{GH}\) and \(\overline{EH} \cong \overline{GF}\), therefore, EFGH is a parallelogram because its parallel sides are congruents (equals).

Now, we should to proof that \(\triangle EFH \cong \triangle GHF\). The simbol "≅" means congruence, that is, \(\triangle EFH \cong \triangle GHF\) means that the triangles EFH and GHF are equals.

Let's proof:

\(\overline{HF}\) is a diagonal of the parallelogram EFGH. When we have a diagonal in a parallelogram, the opposite angles are congruents (look at the picture: the blue angles are congruent and the red angles are congruents too). Therefore, \(E\hat{F}H \cong F\hat{H}G\) and \(E\hat{H}F \cong H\hat{F}G\).

Both triangle has a comum side: the diagonal \(\overline{HF}\). The diagonal \(\overline{HF}\) is between two angles that we know that are congruents, Therefore, by the case ASA (Angle, Side, Angle), we proof that \(\triangle EFH \cong \triangle GHF\).

the correct statement is:

b. The variance is 7.50 and the standard deviation is 2.98.

To find the correct answer, we need to calculate the variance and standard deviation of the given data set.

To calculate the variance, we use the formula:

Variance = (sum of squared deviations from the mean) / (number of data points)

The mean of the data set is given as 8, so we can calculate the deviations of each data point from the mean:

4 - 8 = -4

6 - 8 = -2

6 - 8 = -2

6 - 8 = -2

9 - 8 = 1

9 - 8 = 1

12 - 8 = 4

12 - 8 = 4

The sum of squared deviations from the mean is:

(-4)^2 + (-2)^2 + (-2)^2 + (-2)^2 + 1^2 + 1^2 + 4^2 + 4^2 = 64

The number of data points is 8, so the variance is:

Variance = 64 / 8 = 8

To calculate the standard deviation, we take the square root of the variance:

Standard deviation = sqrt(Variance) = sqrt(8) = 2.83 (rounded to the hundredths place)

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Answer:

65

Step-by-step explanation:

15*3+15=60

30*2+15=75

20*4+15=85

10*5+15=65

The midpoint is given by the following expression:

Where:

Therefore:

Replacing:

Mx= 5 and My=6

Qx= X1 =-1 and Qy= y1=3

Rx=X2 and Ry= Y2

Equating the x component and solving for X2:

Doing the same with the y component:

Answer: the coordinates of R are: (X2,Y2) = (11 , 9).

Answer:

This is because opposite sides of a parallelogram sum up to give 90°

(a) We can use a two-sample t-test to test the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.

The null hypothesis is that the mean weight of regular Coke is equal to or less than the mean weight of Diet Coke, while the alternative hypothesis is that the mean weight of regular Coke is greater than the mean weight of Diet Coke. Using a calculator or statistical software, we find that the test statistic is 4.013 and the p-value is 0.0001. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.

(b) Cans of regular Coke probably weigh more than cans of Diet Coke due to the sugar present in regular Coke but not Diet Coke. Sugar has weight and adds to the overall weight of the can. Diet Coke uses artificial sweeteners instead of sugar, which would result in a lower weight for the can.

Note: The answer choices provided are not accurate as they do not address the actual reason for the weight difference.

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For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = \(\sqrt{MK^2 + LK^2}\)

LM = \(\sqrt{8^2 + 3.56^2}\)

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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Answer:

Slope= 5

y intercept= (0,-3)

Step-by-step explanation:

The only exponential growth equation is the third one:

y = 2*(4)^x

A general exponential equation is:

y = A*(b)^x

if 0 < b < 1, then it is a decay.

if 1 < b, then it is a growth.

So any equation where the base, b, is larger than 1, represents a growth.

Then the correct option is the third one:

y = 2*(4)^x

All the other options are decays.

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The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Answer:

nose a qué se refiere con eso

The linear equations in two variables from the given options are ,Simple interest earned: I = 1000(0.02t), Price-demand: x = 1720 - 0.50p, Electricity cost: E = 14.00 + 0.10k, Cost per item: c = 0.10x + 1.30

The linear equations in two variables are equations that can be written in the form y = mx + b, where y and x are the variables, m is the coefficient of x (the slope), and b is the y-intercept.

Let's analyze the given equations to determine which ones are linear:

1.) Profit: P = x(45 - 0.05x) - 0.10x + 1.30

This equation is not linear since it contains a quadratic term (-0.05x^2), which means it does not have a simple linear relationship between the variables.

2.) Revenue: R = x(45 - 0.05x)

This equation is not linear either because it also contains a quadratic term (-0.05x^2).

3.) Simple interest earned: I = 1000(0.02t)

This equation is linear as it follows the form y = mx + b, where y is I, x is t, m is 0.02, and b is 0.

4.) Price-demand: x = 1720 - 0.50p

This equation is linear since it can be rearranged to the form y = mx + b, where y is x, x is p, m is -0.50, and b is 1720.

5.) Electricity cost: E = 14.00 + 0.10k

This equation is linear as it follows the form y = mx + b, where y is E, x is k, m is 0.10, and b is 14.00.

6.) Cost per item: c = 0.10x + 1.30

This equation is linear since it can be written in the form y = mx + b, where y is c, x is x, m is 0.10, and b is 1.30.

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Answer:

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

The greatest value of the function is - 3.

Answer:

y = 2x + 7

Step-by-step explanation:

When a line is parallel to another line, then the slopes of the lines are equal. If line A has an equation y = 3x + 5, then line B, parallel to line A, must also have a slope of 3. Therefore, we know that m (slope) is 2 in this case.

Next, let’s substitute the x and y coordinates and the slope value into y - y1 = m(x - x1). In this case, -4 is x1, and -1 is y1.

y - y1 = m(x - x1)

y + 1 = 2(x + 4)

Finally, simplify the equation and transform it into the slope intercept form, y = mx + b.

y + 1 = 2(x + 4)
y + 1 = 2x + 8

y = 2x + 7

Answer:  

32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5

============================================================

Explanation:

Let's use Pascal's Triangle

In the row that starts with 1,5,... we have the values 1,5,10,10,5,1

These will be the coefficients of the terms.

Let x = 2a and y = 2b

We want to expand out (x+y)^5

Using pascals triangle, we get the following expansion

(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5

The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.

Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.

At this point, we plug in x = 2a and y = 2b

Since this will clutter things a bit, I'll do it term by term

So in the end, the expression (2a+2b)^5 expands out to

32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5

The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.

Answer: \((2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5\).

Using Pascal's triangle we get:

\((x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5\)

Here, x = 2a and y = 2b

So the terms become:

\(1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\\)

Hence: \((2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5\)

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The number of ways the players can be selected is given by combination and the value of C = 364 ways

The number of ways of selecting r objects from n unlike objects is given by combination :

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of selecting players be C

Let the total number of players n = 14 players

The number of players to be chosen x = 3 players

So , the combination is

ⁿCₓ = n! / ( ( n - x )! x! )

Substituting the values in the equation , we get

¹⁴C₃ = ( 14 )! / ( 14 - 3 )! 3!

On simplifying the equation , we get

¹⁴C₃ = ( 14 )! / ( 11 )! 3!

¹⁴C₃ = ( 14 x 13 x 12 ) / ( 3 x 2 x 1 )

¹⁴C₃ = 14 x 13 x 2

¹⁴C₃ = 364 ways

Hence , the combination of ways is 364 ways

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Answer:w=−8

Step-by-step explanation:Step 1: Simplify both sides of the equation.

−2(w+3)=10

(−2)(w)+(−2)(3)=10(Distribute)

−2w+−6=10

−2w−6=10

Step 2: Add 6 to both sides.

−2w−6+6=10+6

−2w=16

Step 3: Divide both sides by -2.

−2w

−2

=

16

−2

w=−8

Answer:

Hi there!

Your answer is:

w= -8

Step-by-step explanation:

-2(w+3) = 10

First, distribute -2 to the parentheses

-2w -6 = 10

Next, isolate x by adding 6 to both sides

-2w = 16

Finally, divide both sides by -2

w = 16/-2

Simplify!

w= -8

Hope this helps

Answer:

b. $9.96

Step-by-step explanation:

To solve this problem, let's first calculate how much Nina charges for shipping per painting. We'll divide the total shipping cost by the number of paintings sold.

When Nina sells 4 paintings and charges a total of $9.96 for shipping:

Shipping cost per painting = $9.96 / 4 = $2.49

When Nina sells 8 paintings and charges a total of $19.92 for shipping:

Shipping cost per painting = $19.92 / 8 = $2.49

We can see that regardless of the number of paintings sold, Nina charges $2.49 for shipping per painting.

Now let's calculate how much Nina charges for shipping 20 paintings and 16 paintings:

Shipping cost for 20 paintings = $2.49 * 20 = $49.80

Shipping cost for 16 paintings = $2.49 * 16 = $39.84

The difference in shipping charges for 20 paintings and 16 paintings is:

$49.80 - $39.84 = $9.96

Therefore, Nina charges $9.96 more for shipping 20 paintings than for shipping 16 paintings. The correct option is (b) $9.96.

Answer:

These two triangles are similar triangles. This means that their side lengths are proportional to each other.

Thus, making line segment EC equal to "x", and BC equal to "y" we can write:

8/y = 28/(10+y)

The next step is to get rid of the fractions, which can be done by cross multiplying.

So we have:

8(10+y) = 28(y)

After distribution and some simplification, you should get the value of y.

80+8y = 28y

80 = 20y

80/20 = 20y/20

4 = y

y = 4

Knowing that y = BC, and y = 4, it is clear that BC = 4.

Since BC = 4, one can use the Pythagorean Theorem to solve for segment EC.

Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths of a right triangle, and c is the hypotenuse (in other words the longest side)

In our case, a and  b are 8 and 4 (the order doesn't really matter here).

So we have: 8^2 + 4^2 = c^2

64 + 16 = c^2

80 = c^2

c = sqrt 80

c  = 4 sqrt 5

And we arrive at the answer- EC = 4 sqrt 5, making B the correct choice.

Hope this helps!

Answer:

8s ≤ 100

Step-by-step explanation:

s = # shirts you can buy