Which expression represents the correct form for the quotient and remainder, written as partial fractions, of

8x3-2x2-67x-24

It cannot be proven that the front faces are congruent triangles.

No, I cannot prove that the front faces of the two pyramids of Giza are congruent triangles. The exact dimensions and shapes of the pyramids have been lost to history, and the information we have today is based on estimates and interpretations of archaeological evidence.

The exact shape of the pyramids is still the subject of some debate among experts, and there is no consensus on whether the front faces are congruent triangles.

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2 minutes of time both the tanks have same amount of water and total amount of water at that minute will be 25 gallons.

Two or more expressions with an Equal sign is called as Equation.

The amount of water in Jason's dunk tank is represented by the equation below, where W represents the amount of water, in gallons, x minutes after he began to fill.

w=2x+1

The amount of water in Mark's dunk tank is represented by the equation

w=10x+5

The total amount of water in both dunk tanks will be the same.

2x+1=10x+5

8x=-4

Divide both sides by 4

x=-2

So at 2 minutes of time both the tanks have same amount of water.

Now plug in 2 value in any of equation

W=25

Hence, at 2 minutes of time both the tanks have same amount of water and total amount of water at that minute will be 25 gallons.

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Answer:

(4.44 + 0.55n) / n = p

(4.44 + 0.55 * 6) / 6 = p

(4.44 + 3.3) / 6 = p

(7.74) / 6 = p

1.29 = p

or

4.44 / 6 + 0.55 = p

Step-by-step explanation:

n = number of bottles

p = 1.29

-22 < 7x is the inequality that is equivalent to the given inequality.

What is inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Here, we have

Given: -4(x + 7) < 3(x - 2)

To find out which inequality is equivalent, you solve for x.

-4(x+7) < 3(x-2): distribute variables

-4x-28 < 3x-6: Add 6 to both sided

-4x-22 < 3x: add 4x to both sides

-22 < 7x

Hence,  -22 < 7x is the inequality that is equivalent to the given inequality.

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The probability that the test is negative for all people is: P = 0.9655 and probability that the test comes back positive for at least one of the five people is P = 0.0344.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

The probability that the test is negative for all people is:

[tex]P = (0.995)^7[/tex]

P = 0.9655

b. The probability that the test comes back positive for at least one of the five people:

P = 1 - P (Negative for all 5)

P = 1 - 0.9655

P = 0.0344

Hence, the probability that the test is negative for all people is: P = 0.9655 and probability that the test comes back positive for at least one of the five people is P = 0.0344.

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The required final balance on interest rate of 6%per annul is  $354.

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Simple interest is calculated as:

I = P * r * t

where I is the interest, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the number of years.

So, in this case:

I = 300 * 0.06 * 3

I = 300 * 0.06 * 3 = 54

The final balance would be the sum of the initial investment and the interest earned:

Final balance = P + I

Final balance = 300 + 54

Final balance = 300 + 54 = 354

Rounded to the nearest cent, the final balance is $354.

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The sample size based on the information is 30.

The probability is 0.1667.

From the information, Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value.

The Sample size , n = 30. The Probability of an event of interest, p = 0.1667

The Mean will be:

= np = 30 * 0.167

= 5.000

Standard deviation will be:

= √(np(1-p)) = √ 4.1667

= 2.04

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The logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).

Logical equivalence is the condition of equality that exists between two statements or sentences in propositional logic or Boolean algebra.

Given that, p → q ≡ ~p∨q and p ↔ q ≡ (~p∨q)∧(~q∨ p)

a) (p → r) ↔ (q → r)

Now, (p → r)≡ ~p∨r

(q → r)= ~q∨r

So, (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r)

Therefore, the logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).

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Answer:

15×24

times 15and24

giving you this answer

120

then divide 120 by 18

=20hrs would take the Baker

Answer:

28.8 hours

Step-by-step explanation:

[tex]\frac{24 .hours}{15 .bakers}[/tex] = 1.6 hours per baker

1.6 x 18 = 28.8 hours for 18 bakers to complete that order

Check the picture below.

[tex]\textit{perimeter of a rectangle}\\\\ P=2(L+w) ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ P=88\\ L=w+8 \end{cases}\implies 88=2( ~~(w+8)+w ~~ ) \\\\\\ 88=2(2w+8)\implies 88=4(w+4)\implies \cfrac{88}{4}=w+4 \\\\\\ 44=w+4\implies \boxed{40=w}\hspace{5em}\stackrel{w+8}{\boxed{L=48}}[/tex]

Answer: The number of solutions for the system of linear equations depends on whether the lines are parallel or intersect at a single point. If the lines are parallel, there are no solutions, as they never meet. If the lines intersect at a single point, there is exactly one solution.

To determine the number of solutions, we need to find the point of intersection of the two lines. We can do this by solving for x in one equation and substituting it into the other equation:

2x + 3 = 8/4 x - 1/4

8x + 12 = 2x - 1/2

6x = - 12.5

x = -2.08

Then, substituting this value of x back into either equation to find the corresponding value of y:

y = 2 * (-2.08) + 3 = 0.16

So, the two lines intersect at the point (-2.08, 0.16), which means there is exactly one solution to the system of linear equations.

Step-by-step explanation:

The given triangle CDE is not Rectangular.

What are types of triangles ?

Acute triangle . . . all three angles are less than 90°

Right triangle . . . one angle is 90°

Obtuse triangle . . . one angle is greater than 90°

Equilateral triangle . . . all three sides are the same length

Isosceles triangle . . . two sides are the same length

Scalene triangle . . . all three sides are different lengths

Given:

CD = 36cm ; CE = 42cm and DE = 55

Hence , the given triangle CDE is not Rectangular.

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x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.

A interaction between two terms or concepts that is neither equal in mathematics is referred to as an inequality. Consequently, inequity results from imbalance. In algebra, an inequality establishes the connection between two non-equal numbers. Egality and inequalities are not the same. Use the not comparable symbol most usually when two components are really not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two aspects until only the variables are left, many straightforward inequalities can be solved. But, a variety of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.

given

11 < 3x-2 ≤ 19

11< 3x-2

3x-2 ≤ 19

11+ 2 < (3x-2)+ 2

(3x-2)+ 2 ≤ 19 + 2

x belongs to 13/3 and 7

x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.

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Elisa was charged a basic interest rate of 120% per year by the pawnbroker since she needed the money to fix her house air conditioner.

By dividing the initial by the interest income, the aging process, and other factors, simple interest is determined. Simple yield equals principal plus interest full days is the concept used in marketing. The easiest thing to compute interest is to employ this method. The most frequent method for calculating it is as a portion of the outstanding sum. For example, if he takes $100 from a buddy and undertakes to return the loan at 5% interest, he will only spend his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must make payments, and you must pay the interest whenever you lend it. Typically, interest is computed as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.

given

I = PRT/100

Simple interest (I) is calculated as follows: amount - principal ($279.90 - $270) = $9.90

P (principal) is the $270 loan made to Elisa.

R is the interest rate on a yearly basis.

The loan's amortisation period, or T (time), is 11 days, or 11/360 years.

9.9 = 270 × R × 11/360 × 1/100

R = (9.9×360×100)/(270×11) = 120%

120% is the annual simple interest rate.

Elisa was charged a basic interest rate of 120% per year by the pawnbroker since she needed the money to fix her house air conditioner.

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Answer:

28.26cm

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.

Plugging in r = 4.5 cm, we get:

C = 2π * 4.5 = 9π cm

To find the value of C to the nearest tenth, we can approximate π to 3.14:

C = 9 * 3.14 = 28.26 cm

The side length of a square with area of 7 units squared is given as follows:

2.65 units.

The area of a square of side length s is given by the side length squared, according to the equation given as follows:

A = s².

In this problem, we have that the output is of 7, that is, the area of the square is of seven, hence the side length of the square is given as follows:

s² = 7

s = sqrt(7)

s = 2.65 units.

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According to the question we have ,The area covered by the spotlight is 153.86 square feet. The correct option is c.

The diameter of a circle cuts through center whereas the radius extends from the center to the edges of the circle. A circle's diameter effectively splits the shape in half. The radius of a circle is the distance from the middle to any point on the edge. The diameter the radius are inversely proportional, or 2r=d2 r=d. A line connecting two points on either a circle is referred to as a chord.

We have the formula of Area of a circle: A = π[tex]r^2.[/tex]

According to the question we have ,there is a spotlight above the center of the ground that surrounds a 7-foot-radius lit area.

A = π[tex]r^2[/tex]. = π * [tex]7^2[/tex]

= 3.14 * 49 = 153.86 square feet.

So, the area covered by the spotlight is 153.86 square feet.

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Answer:

Step-by-step explanation:The equation for the nth term of an arithmetic sequence is given by:

an = a1 + (n-1)d

Where:

a1 is the first term of the sequence

d is the common difference

n is the number of the term we want to find

Using the given information, we have:

a1 = -9 and d = 2

Plugging these values into the formula, we get:

an = -9 + (n-1)2

To find the 12th term of the sequence:

n = 12

an = -9 + (12-1)2

an = -9 + 11 * 2

an = -9 + 22

an = 13

So the 12th term of the sequence is 13.

The value of the equations are

A =  0.93 x 2.6 = 2.418

B = 93 x 0.26 = 24.18

C = 9.3 x 26 = 241.8

D = 0.93 x 0.26 = 0.2418

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.

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 data ,

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

a)

A = 0.93 x 2.6   be equation (1)

On simplifying the equation , we get

A = 2.418

b)

B = 93 x 0.26   be equation (2)

On simplifying the equation , we get

B = 24.18

c)

C = 9.3 x 26   be equation (3)

On simplifying the equation , we get

C = 241.8

d)

D = 0.93 x 0.26   be equation (4)

On simplifying the equation , we get

D = 0.2418

Hence , the equations are solved

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the solutions of the equation are x = -1.5 and x = 2.

The solutions of the equation are x = -1.5 and x = 2.

Absolute value equation: |4/3x + 2| - 6 = 0

Equation inside absolute value must equal 0:

4/3x + 2 - 6 = 0

4/3x = -4

x = -4 * (3/4)

x = -1.5

Equation inside absolute value must equal 0:

4/3x + 2 + 6 = 0

4/3x = -8

x = -8 * (3/4)

x = 2

The absolute value quantity of four thirds times x plus 2 end quantity minus six equals zero can be written as:

|4/3x + 2| - 6 = 0

This equation can be rewritten as two separate equations as follows:

4/3x + 2 - 6 = 0

4/3x + 2 + 6 = 0

Solving the first equation:

4/3x + 2 - 6 = 0

4/3x = -4

x = -4 * (3/4)

x = -1.5

Solving the second equation:

4/3x + 2 + 6 = 0

4/3x = -8

x = -8 * (3/4)

x = 2

Therefore, the solutions of the equation are x = -1.5 and x = 2.

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The fraction pairs that are equivalent to 4 and 20 is given as follows:

Equivalent fractions are fractions that have the same denominator.

The fraction for this problem is given as follows:

4/20.

Dividing both the numerator and the denominator by 2, an equivalent fraction is given as follows:

2/10.

Dividing again by two, we have that:

1/5.

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The probability of F′∪A 0.9829

The probability can be defined as the likelihood that an event is going to happen.

We are to find the probability F′∪A.

What is F'

This is gotten as 1 - probability of F

F' = 1 - 0.2058

F' = 0.7942

Then we are to get the probability of event A from the question

P(A) = 0.1887

Hence the probability of F′∪A.

= P(A) + P(F`)

= 0.1887 + 0.7942

= 0.9829

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Answer: (21, 3)

Step-by-step explanation:

Answer: 485 is the answer.

Step-by-step explanation:

Answer: To find the value of w, we need to set the expressions equal to each other:

(4w-8) = (3w+6)

Subtracting 3w from both sides:

w - 8 = 6

Adding 8 to both sides:

w = 14

So the value of w is 14.

Step-by-step explanation:

Answer: Yes.

Step-by-step explanation: Follow PEMDAS.

P: PARENTHESIS

E: EXPONENTS

M: MULTIPLY

D: DIVIDE

A: ADDITION

S: SUBTRACT

Answer:

  ∆ABC is an isosceles triangle

Step-by-step explanation:

You have a triangle ABC such that the angle bisector of angle B also bisects side AC.

An angle bisector divides the sides of the triangle proportionally. This means the sides BA and BC will have the same ratio as the segments of AC on either side of the point of intersection with the angle bisector.

Since AC is bisected, that means those segments are congruent, hence sides BA and BC are congruent. The triangle is isosceles.