Guess the rule and add the next number in the sequence.
6, 8, 12, 18, 26,

The expression −(4b)(4b)(4b) using positive exponents is -(4b)³

From the question, we have the following parameters that can be used in our computation:

−(4b)(4b)(4b)

Express properly

So, we have

−(4b) * (4b) * (4b)

5⁻¹² * 32⁻³ * 9⁻¹⁵

By using the definition of positive exponents, we have

−(4b) * (4b) * (4b) = -(4b)³

So, the solution is -(4b)³

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Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Answer:

104°

Step-by-step explanation:

\(\frac{sin~B}{18} =\frac{sin~29}{9} \\sin~B=\frac{18}{9} \times sin~29\\sin~B=2~sin~29\\B=sin^{-1}(2 ~sin~29)\\=104^\circ\)

Answer:

450 $ in tottle for every candle she sold.  

Step-by-step explanation:

By fraction method, 55/16 pounds of rice Belle purchased.

In math, what is a fraction?

Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                 Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

  = 2 3/4 * 5/4

   = 5/4 * 2 + 5/4 *  3/4

   = 5/2 + 5/4 * 3/4

  = 5/2 + 15/ 4 * 4

  = 5/2 + 15/16

  common denominator and write the numerators above common denominator   =   5 *8/16 + 15/16

         = 40/16 + 15/16

         = 40 + 15/16

          = 55/16

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Answer:

According to theorem 7.5

Π ABB'A' ≅ Π DEE'D'  

therefore by transitivity of equivalence  it is proven that triangle ABC and triangle DEF are triangles with equal defects and a pair of congruent sides

Step-by-step explanation:

To prove that triangle ABC and triangle DEF are triangles with equal defects and a pair of congruent sides :

Assume:  б(Δ ABC ) =  б(Δ DEF ) and also AB ≅ DE

let Π ABB'A' and DEE'D' be taken as the saccheri quadrilaterals that corresponds to Δ ABC and Δ DEF  respectively

Following the Lemma above; б(Π ABB'A' ) = б( Π DEE'D' ) given that

AB = summit of ABB'A' and DE = summit of DEE'D'  also  AB ≅ DE

According to theorem 7.5

Π ABB'A' ≅ Π DEE'D'  

therefore by transitivity of equivalence  it is proven that triangle ABC and triangle DEF are triangles with equal defects and a pair of congruent sides

Answer:

60 ounces.

Step-by-step explanation:

A chain weighs 9 pounds per foot.

We are to find the number of ounces 5 inches weigh.

First we find how many feet are in 5 inches.

1 foot = 12 inches

how many feet? = 5 inches.

Cross-multiplying gives;

\(\frac{5}{12} * 1 = \frac{5}{12}\)   feet

1 foot of the chain = 9 pounds

\(\frac{5}{12}\) feet = how many pounds?

Cross-multiplying gives;

\(\frac{5}{12} * 9 = 3.75\) pounds

1 pound = 16 ounces

3.75 pounds = how many ounces?

Cross-multiplying gives;

\(\frac{3.75 * 16}{1} = 60\) ounces.

The number of ounces will 5 inches weigh is 66.667 oz.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A chain weighs 9 pounds per foot.

We know that

1 foot = 12 inches.

1 pound = 16 ounces.

Now based on this,

= 5 inches 1/12 x foot/ inches x 10 x pound/ feet x 16

= 5 x 10 x 16 / 12

= 66.667 oz.

Hence, the chain weight 66.6667 oz.

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Step-by-step explanation:

Vertical angles are equal   r = 70 degrees

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Answer:

68°

Step-by-step explanation:

Okay, so m<8 is on the same plane as m<7 because line q is intersecting line t  and that's supposed to add up to 180° so:

180° - 112° = 68°

So, m<7 = 68°

hope this helps:)

Answer:

(0.5, 4.5)

Step-by-step explanation:

midpoint formula:

((sum of the two x values)/2, (sum of the two y values)/2)

= ((5+(-4))/2 , (6+3)/2)

= (0.5, 4.5)

Answer:

y=3x+5

Step-by-step explanation:

This is th eanswer because slope intercept form is always y=mx+b.

So, if you simplify the right side of the equation, you then get

y-6=3x-1, I got that because 3 multiplied by -1/3, you get -1.

Then you add 6 to both sides to isolate y by itself. So, now you have

y=3x+5.

Hope this is helpful

Answer:

C their speeds are equal

Answer: C) Their speeds are equal

Step-by-step explanation:

Use the speed-distance equation

Dog - s=d/t = 100/4 = 25m/s

Lion - s=d/t = 250/4 = 25m/s

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer: V≈508.94m³

Step-by-step explanation:

V=π(d

2)2h=π·(18

2)2·2≈508.93801m³

V= 508.9m^3

Step-by-step explanation:

Use the equation for the volume of a cylinder which is \(V=\pi r^{2} h\)

r = 18/2 = 9m and h = 2m so \(V=\pi 81*2=162\pi =508.9380m^{3}\)

Answer:

\(5x+11\)

Step-by-step explanation:

Step 1: Distribute

\(3x+6+2x+5\)

Step 2: Add like terms

\(5x+11\) < your answer

Substitute \(x\mapsto\sqrt{1-x^2}\), which transforms the integral to

\(\displaystyle \int_0^1 \ln^{2k} \left(\frac{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}\right) \, dx = \int_0^1 \ln^{2k}\left(\frac{\ln\left(\frac{1-x}{\sqrt{1-x^2}}\right)}{\ln\left(\frac{1+x}{\sqrt{1-x^2}}\right)}\right) \frac{x}{\sqrt{1-x^2}} \, dx\)

and factoring \(\sqrt{1-x^2}=\sqrt{(1-x)(1+x)}\) reduces this to

\(\displaystyle = \int_0^1 \ln^{2k}\left(\frac{\ln\left(\sqrt{\frac{1-x}{1+x}}\right)}{\ln\left(\sqrt{\frac{1+x}{1-x}}\right)}\right) \frac x{\sqrt{1-x^2}} \, dx\)

The inner logarithms differ only by a sign, so that

\(\displaystyle = \int_0^1 \ln^{2k}(-1) \frac x{\sqrt{1-x^2}} \, dx\)

Using the principal branch of the complex logarithm, we have

\(\ln(-1) = \ln|-1| + i\arg(-1) = i\pi\)

and hence

\(\displaystyle \int_0^1 \ln^{2k} \left(\frac{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}\right) \, dx = (i\pi)^{2k} \underbrace{\int_0^1 \frac x{\sqrt{1-x^2}} \, dx}_{=1} = \boxed{(-\pi^2)^k}\)

where I assume k is an integer.

Answer:

To solve this problem, we need to subtract the cost of the book and the total amount donated to charities from the total amount of cash Katye received for her birthday. Here are the steps:

Add up the value of the gifts Katye received:

Total value of gifts = (value of gift 1) + (value of gift 2) + ... + (value of gift 15)

Add up the value of the cash Katye received:

Total cash = $100

Subtract the cost of the book from the total cash:

Cash remaining after buying the book = $100 - $23

Determine the maximum number of $10 donations that Katye can make:

Maximum number of $10 donations = (cash remaining after buying the book) / $10

Multiply the maximum number of donations by $10 to get the total amount donated:

Total amount donated = (maximum number of $10 donations) x $10

Subtract the cost of the book and the total amount donated from the total cash:

Cash remaining = $100 - $23 - (total amount donated)

The final answer will be the cash remaining after these calculations

Answer:

Statements:

- When (1, 2) is substituted into the second equation, the equation is true

- The ordered pain (1, 2) is a solution to the system of linear equations

- When (1, 2) is substituted into the first equation, the equation is true.

Step-by-step explanation:

Statement 1:

y= 7/2x - 3/2

2= 7/2 * 1 - 3/2

2= 7/2 -3/2

2=4/2

2=2

Statement 2:

y= -2x + 4

2= -2 ( 1 ) + 4

2= -2 + 4

2 = 2

Statement 6:

y= 7/2x - 3/2

2= 7/2 * 1 - 3/2

2= 7/2 -3/2

2=4/2

2=2

y= -2x + 4

2= -2 ( 1 ) + 4

2= -2 + 4

2 = 2

The iterative rule for each sequence in the table will be to use the slope-intercept form of the equation of a line y=mx+b.

In this situation, x is the week, and y is the amount paid. Basically, you need to find the slope, represented by m, which is the amount the amount paid increases by each week, and the y-intercept, b, which is the "amount paid" at week 0.

The x-coordinate is the week, and the y coordinate is the amount paid. Because the weeks are incrementing by 1, x2-x1=1.

After that, to complete the rule, you need to find the y-intercept. If the amount paid is 200 on week 1, and the amount paid increases by 50 each week.

Another way to think about it is by plugging your points into the incomplete rule. Let b represent the y-intercept. Plug in the values for week 1 and solve for b.

The calculations to convince your friend that both your rules work are:

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

(x1,y1)=(1,200)

(x2,y2)=(2,250)

m=(250-200)/(2-1)

=50/1 =50

y=50x+b

200=50(1)+b

200=50+b

b=200-50

b=150

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1) Let's make a sketch to better understand this:

Suppose Shaq was on 40 feet after the snack he slipped 20 feet and then 6 feet.

After the snack, He traveled 20 +4 = 24 feet

From the initial point, He went 24 feet down.

The time it will take for the coin to hit the ground is 5 seconds for the given function.

Displacement and distance are terms used to describe how an object or person moves, but they have different meanings.

No matter where anything starts or ends, distance describes how much ground it has travelled. It is a scalar quantity with units like metres, kilometers, miles, etc. for measurement.

On the other hand, displacement describes a change in an object's or a person's location from their original position to their end position, including direction. Since it has both magnitude (the distance) and direction, it is a vector quantity. Displacement can be positive or negative depending on the direction of movement and is measured in units like metres, kilometers, miles, etc.

The given equation is  y=-5t² +125.

When the coin hits the ground the value of y = 0 thus,

y = -5t² + 125

0 = -5t² + 125

5t² = 125

t² = 25

t = ±5

Hence, the time it will take for the coin to hit the ground is 5 seconds.

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Answer:

Option B is correct. the required domain of the function will be expressed as[-5, 3) U (3, ∞)

Step-by-step explanation:

Answer:

= 34

Step-by-step explanation:

(32)-5+7

32 - 5 + 7

= 32 + 2

= 34.

Answer:

18√8 = 3√2 * 3√2

Step-by-step explanation:

I factored the square root of 8 into the square root of 2 times the square root of 2, because I believe that the square root of 8 was supposed to be factored based upon the hint provided.

This resulted in the expression 3√2 * 3√2, which is equivalent to 3*3*sqrt(2) * sqrt(2).