Give the name (monomial, binomial,
trinomial, etc.) and the degree of the
polynomial.
2x - 4
Name? [?]
Degree? [ ]

Adding the difference between [tex]$\frac{9}{16}[/tex] and [tex]$\frac{5}{4}[/tex] we get [tex]$1 \frac{13}{16}[/tex].

Find the least common denominator or LCM of the two denominators:

LCM of 4 and 16 exist 16.

Subsequently, estimate the equivalent fraction of both fractional numbers with denominator 16.

For the 1st fraction, since 16 × 1 = 16,

9/16 = (9 × 1) / (16 × 1) = 9/16

For the 2nd fraction, since 4 × 4 = 16,

5/4 = (5 × 4) / (4 × 4) = 20/16

Add the two like fractions, then we get

(20/16) + (9/16) = (20 + 9)/16 = 29/16

So, [tex]$\frac{5}{4}+\frac{9}{16} =\frac{29}{16}[/tex]

In mixed form: [tex]$1 \frac{13}{16}[/tex].

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The profit margin required to achieve 15% targeted ROE is 9.0%

The ROE means return on equity, it is the return earned on shareholders fund or shareholders equity.

Based on the three-way DuPont approach to computing the ROE, the below formula is very relevant to this analysis:

ROE=net profit margin*assets turnover*equity multiplier

ROE=15%

net profit margin=the unknown now(assume it is X)

assets turnover=sales/total assets

assets turnover=$778,500/$468,500

assets turnover=1.6616862326574200

equity multiplier=total assets/total equity

Note the company is entirely financed by equity(zero debt) which means that total assets is the same as total equity

equity multiplier=$468,500 /$468,500

equity multiplier=1.00

15%=X*1.6616862326574200*1.00

15%=X*1.6616862326574200

X=15%/1.6616862326574200

X=9.0%

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Answer:

b

Step-by-step explanation:

(-4(-1)-8)(3(2)^2+2=4-8×12+2

-4×14=-56

The area between the two functions is 0

The functions are given as:

f₁(x)= 1

f₂(x) = |x - 2|

x ∈ [0, 4]

The area between the functions is

A = ∫[f₂(x) - f₁(x) ] dx

The above integral becomes

A = ∫|x - 2| - 1 dx (0 to 4)

When the above is integrated, we have:

A = [(|x - 2|(x - 2))/2 - x] (0 to 4)

Expand the above integral

A = [(|4 - 2|(4 - 2))/2 - 4] - [(|0 - 2|(0 - 2))/2 - 0]

This gives

A = [2 - 4] - [-2- 0]

Evaluate the expression

A = 0

Hence, the area between the two functions is 0

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Answer:

960 feet

Step-by-step explanation:

30×6=180

180×2=360

50×6=300

300×2=600

360+600=960

From the Δ YWZ we get c = 5 then the value of  [tex]$a= 5 \frac{1}{3}[/tex].

In the given Δ YWZ

WZ² = YW² + YZ²

c² = 4² + 3² = 16 + 9 = 25

c = 5

In the Δ XYW

b² = 4² + a²-----(1)

In the right-angle Δ WXZ

(a + 3)² = b² + c²

a² + 9 + 6a = b²+ c²

By putting the value of b² from (1)

a² + 9 + 6a = 16 + a² + 25

Simplifying the above equation, we get

6a + 9 = 41

6a = 41 - 9

6a = 32

[tex]$a = \frac{32}{6} = \frac{16}{3}[/tex]

[tex]$a= 5 \frac{1}{3}[/tex]

Therefore, the value of [tex]$a= 5 \frac{1}{3}[/tex].

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The values of x after the statement are:

This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.

Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false

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646 gallons of water are needed to fill the waterbed

The dimensions are given as:

8 ft long, 7 ft wide, and 1.5 ft tall

The volume is calculated as:

Volume = Length * Width * Height

So, we have

V = 8 * 7 * 1.5 cubic feet

Evaluate

V = 84 cubic feet

1 gallon = 0.13 cubic feet

So, we have:

V = 84/0.13 gallon

Evaluate

V = 646 gallons

Hence, 646 gallons of water are needed to fill the waterbed

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The equation of the median in standard form is; 9y - 38x = 179.

It follows from the task content that the point D is the midpoint of segment BC; Hence, the coordinates of point D given the coordinates of B and C above are given as; D(-13, -35).

The equation of the median which is the line joining points A and D is therefore determined as follows;

Slope = (-35-3)/(-13-(-4)) = 38/9

38/9 = (y-3)/(x+4)

9y -27 = 38x + 152

9y - 38x = 179.

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we can see that when they join with Carla, Carter and Isabella will get $200 less (individually).

When Carter and Isabella work together, they have a revenue of $6000, which is split in 50/50, so each one gets:

$6000/2 = $3000

Carter wins $3000 and Isabella wins $3000.

If they join with Carla, the revenue increases by $2400, so now the total revenue is:

$6000 + $2400 = $8400

And now they split it between 3, so each one gets:

$8400/3 = $2800

The difference of Carter's (Or Isabella's) part is:

$3000 - $2800 = $200

Then we can see that when they join with Carla, Carter and Isabella will get $200 less (individually).

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Answer:

3/10 as a decimal is expressed as 0.3.

Possible Dimensions of one prism are; 2cm, 3 cm and 4cm

Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm

We are told that volume of both rectangular prisms is; V = 24 cm³

Now, formula for Volume of a rectangular prism is;

V = lwh

where;

l is length

w is width

h is height

Thus, to solve this, we have to look for multiples of 24 which are;

1, 2, 3, 4, 6, 8, 12, 24.

Now, we must pick 3 numbers from the above in which their products will be equal to 24.

Thus;

Possible Dimensions of one prism are; 2cm, 3 cm and 4cm

Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm

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Answer:

Step-by-step explanation:

A) The median number is just the middle number so it should be 2.8

B) Bottom 30% are the six lowest amounts. The highest of the bottom six numbers is 2.3. Not sure what it means by calculating them. 1.8, 1.9, 1.9, 2.0, 2.1, and 2.3 are the lowest six. If you need to add them up the answer is 12.
C) I don’t know what your Q1 is.

Answer:

30 cans

Step-by-step explanation:

cross multiply

14x = 28 * 15

14x = 420

x = 420/14

x = 30 cans

By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.

From statement we have two lines in space, whose vector forms are described below:

(x, y, z) = (1, - 9, 1) + t · (4, 1, 2)     (1)

(x, y, z) = (1, 0, - 9) + s · (5, - 1, 5)     (2)

The point of intersection satisfies the following condition:

(1, - 9, 1) + t · (4, 1, 2) = (1, 0, - 9) + s · (5, - 1, 5)

(1, - 9, 1) - (1, 0, - 9) = s · (5, - 1, 5) + t · (- 4, - 1, - 2)

s · (5, - 1, 5) + t · (- 4, - 1, - 2) = (0, - 9, - 8)

There is a point of intersection if the resulting system of linear equations has at least a solution:

5 · s - 4 · t = 0      (2)

- s - t = - 9      (3)

5 · s - 2 · t = - 8     (4)

By (2):

s = 4 · t/5

(2) in (3):

- 4 · t/5 - t = - 9

- 9 · t/5 = - 9

t/5 = 1

t = 5

(2) in (4):

5 · (4 · t/5) - 2 · t = - 8

4 · t - 2 · t = - 8

2 · t = - 8

t = - 4

By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.

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Answer:

multiple triangles

Step-by-step explanation:

add the numbers up it adds to 180 which is the sum of a triangle and could create other triangles

The first three statements are not a negation. Only the last statement is a negation.

The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "P" is the statement's negation. The words negation is used to denote a statement's denial.

It's vital to know the opposite of a given mathematical statement from time to time in mathematics. This practice is known as "negating" a statement. Remember that if a statement is true, then its negation must be false (and if a statement is false, then its negation is true).

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The expanded form of the given exponential equation is 6718464

Exponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x

where

a is the base

x is the exponent

Given the expression below;

a = 4(6)^8​

Expand to have:

a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

a = 4 * 1679616
a = 6718464

Hence the expanded form of the given exponential equation is 6718464

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The energy is compared based on the information given below.

Energy released by burning 1 kilogram of element A = EA = 5.1 * (10)8

Energy released by fission of hydrogen in 1 kilogram of element B = EB = 1.3 * (10)10

Therefore,

Ratio = EB / EA = 1.3 * (10)10 / 5.1 * (10)8 = 25

Thus, the fission of 1 kg of element B releases 25 times as much energy as burning 1 kilogram of element A.

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The other part of the question:

Energy released by burning 1 kilogram of element A = 5.1 times 10 Superscript 8

Energy released by the fission of hydrogen in 1 kilogram of element B = 1.3 times 10 Superscript 10

The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. then the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be 15.1kg or less is 0.121 and 15.1kg or more is 0.879.

Given Information:

Population mean, μ = 15.8 kg

Population standard deviation, σ = 4.2 kg

For finding the probability for the sample mean, we first need to find the standard score.

(a) For sample mean to be 15.1kg or less,

z = (x - μ) / (σ/√n)

Here, x = 15.1

⇒ z = (15.1 - 15.8) / (4.2/√49

z =-0.7 / (4.2/7)

z = -1.17

Now, we can use the z-table to find the probability of the sample mean to be 15.1kg or less.

∴ P(x ≤ 15.1) = 0.121

(b) Now, to find the probability of sample mean to be 15.1kg or more, we can simply subtract P(x ≤ 15.1) from 1.

⇒ P(x ≥ 15.1) = 1 - P(x ≤ 15.1)

P(x ≥ 15.1) = 1 - 0.121

P(x ≥ 15.1) = 0.879

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Answer:3/7

Step-by-step explanation:There are total 7 days in a week. 3 days were dry so the fraction is 3/7 . The dry days over the total days of the week

The equation of f(x) is f(x) = x + 4

The given parameters are

f(-1) = 3 and f(1) = 5

Start by calculating the slope (m) using:

[tex]m = \frac{f(1) - f(-1)}{1 - -1}[/tex]

This gives

[tex]m = \frac{5 - 3}{1 + 1}[/tex]

Evaluate

m = 1

The equation is then calculated as;

f(x) = m(x - x1) + f(-1)

This gives

f(x) = 1(x + 1) + 3

Expand

f(x) = x + 4

Hence, the equation of f(x) is f(x) = x + 4

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Answer:

6

Step-by-step explanation:

Assuming C lies on segment BD, we know that by the segment addition postulate,

[tex]BC+CD=BD \\ \\ 2+2x-6=x+2 \\ \\ 2x-4=x+2 \\ \\ x=6[/tex]

The values of BC = 2, CD = 2x - 6 and BD = x + 2 then the value of x = 6.

The algebraic expression should be any one of the conditions such as addition, subtraction, multiplication, and division.

In mathematics, an algebraic expression exists as an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c exists as an algebraic expression.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Given: BC = 2, CD = 2x - 6 and BD = x + 2 then

BC+CD= BD

2+2x-6=x+2

Simplifying,

2x-4=x+2

Thus,

x=6

Therefore, the value of x = 6.

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Answer:

8/3

Step-by-step explanation:

8/9

Answer:

6

Step-by-step explanation:

The mode is the number that is repeated the most in the data set. 6 is the only number that is repeated twice, so it is the mode.

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The 53,000 units produced and the increase in sales of 50,400 - 48,000 = 2,400 units, give an impact (increase) in profit of $168,000

Price per unit = $70

Number of units produced = 53,000

Number of units sold = 48,000

Material cost per unit = $21

Labour cost per unit = $10

Manufacturing overhead = $2

Selling and administrative overhead = $4

Fixed cost = $1,060,000

Administrative expenses = $557,000

Advertising cost = $43,000

Percentage increase in sales = 20%

Number of units sold in Year 2 = 1.2 × 12,000 = 14,400

Total cost = 53000×(21+10+2+4) + 1,060,000 + 557,00 = 3,578,000

Total revenue in Year 1 = 70 × 48,000 = 3,360,000

Profit in Year 1 = 3,360,000 - 3,578,000 = -218,000

Total revenue in Year 2 = 70 × (36,000+14,400) = 3,528,000

Profit in Year 2 = 3,528,000 - 3,578,000 = -50,000

The impact on the profit is therefore;

-50,000 - (-218,000) = 168,000

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Answer:

Step-by-step explanation:

First find the percentage of the ones that pass that study

.93 *(88)=88.84%

next find the ones that pass that did not study

.09*(100-88)=1.08

sum these to get the total passing percentage

88.84+1.08=82.92%

The probability is 82.9 per 100 or .8292 for student

E is the answer

Angles on straight line = 180

180 - 115 = 65

So, angle above 4 in the top corner is 65.

Co-interior angles add up to 180.

(180-65=115)

Thus, the value of 4 is 115 degrees.

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The steps to carry out scaling of a landscape drawing are; as detailed below

The steps to carry out if we want to scale landscape drawings are;

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Answer:

3x(10x10x10): 3x(1000): 3000-7000: -4000. (8x(-5)): -40. (4x4) +(2x2): (16 +4): 20