Orville is thinking of a number. The product of the number and 39 is 156. Find Orville's number. 46​

The 14th term of the geometric sequence 10, 20, 40, ... is 81920.

"A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term."

The geometric sequence formulas include the formulas for finding its nth term and the sum of its n terms. We will see the geometric sequence formulas related to a geometric sequence with its first term 'a' and common ratio 'r' (i.e., the geometric sequence is of form \(a, ar, ar^{2},ar^{3} ,.............\)). Here are the geometric sequence formulas.

\(a_{n}=ar^{n-1}\)

Given geometric sequence

10, 20, 40, .........

From the given sequence

\(a_{1} = 10\), \(a_{2} = 20\), \(a_{3} = 40\)

Using the formula \(a_{n}=ar^{n-1}\)

⇒ \(a_{4} = 10(2)^{3} =80\)

⇒ \(a_{5} = 10(2)^{4} =160\)

⇒ \(a_{6} = 10(2)^{5} =320\)

⇒ \(a_{7} = 10(2)^{6} =640\)

⇒ \(a_{8} = 10(2)^{7} =1280\)

⇒ \(a_{9} = 10(2)^{8} =2560\)

.

.

.

⇒ \(a_{14} = 10(2)^{13} =81920\)

Hence, the 14th term of the geometric sequence 10, 20, 40, ... is 81920.

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Answer:

Vertical shrink by 2

Step-by-step explanation:

Multiplying by 2 stretches the function. It does not shrink it.

Answer: Vertical shrink by 2

Answer:

1/4, 3/5

Step-by-step explanation:

0.8/3.2=8/32=1/4

0.3/0.5=3/5

Answer:

B) Cluster Sampling.

Step-by-step explanation:

Cluster sampling refers to a methodology for probability sampling, in which researchers split the populace into several study groups or one can say clusters. And after this investigators pick random groups for collecting and analyzing data, using a systematic random or simple random sampling technique, depending on the research subject. As per the question, instead of 200 grids selected a cluster of 30 grids for the research and therefore it is a classic of cluster sampling.

The original cost of the tablet is $70.89 in the given algebraic equation.

A mathematical claim containing two equated algebraic expressions is known as an algebraic equation. When P and Q are polynomials, an algebraic equation has the general form P = 0 or P = Q. The term "multivariate equation" refers to an algebraic equation that has more than one variable.

Univariate equations are algebraic equations that only have one variable. Equations in algebra are balanced by definition. Due to this, the right and left sides of the equation will be equal.

Let the original cost be  x

then

15/100 = 24.99.x

x =  166.6

237.49 - 166.6

= $70.89

Thus, the original cost of the tablet is $70.89 in the given algebraic equations.

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Full question?

Lucas bought a tablet that was on sale at a 15% discount on your supra case for $24.99 which is been a total of $237.49. Write an equation to find the original cost of the tablet?

Answer:

-2 5/6

Step-by-step explanation:

First, you have to change the fraction 2/3 to have a common denominator with 1/6. 2/3 x 2/2 = 4/6.

Second, now your equation is -2 1/6 + ( -4/6 ).

Third, you have to add -2 1/6 and -4/6 which gets you -2 5/6

Hope this helps!

Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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Answer:

The answer is B.

Step-by-step explanation:

I just simplified each separately.

Answer:

b.) b < 7 or b > -1

Step-by-step explanation:

Answer:

8.5

Step-by-step explanation:

This is a simple similar triangles problem

Since 15/7.5 = 2, we know that the ratio between the triangles is 2

This means that 17/x = 2, which means x = 8.5

Answer:

Solve for b: b = 6 - a

Solve for a:  a = 6 - b

Step-by-step explanation:

There are two ways we can solve this, solve for a and solve for b.

Lets solve for b first

\(4-b=2-a\)

Add 4 on both sides

\(b=2-a+4\)

Simplify

\(b=6-a\)

Now lets solve for a

\(4-b=2-a\)

Flip the equation

\(2-a=4-b\)

Add 2 on both sides

\(a=4-b+2\)

Simplify

\(a=6-b\)

At the end of the first 3 seconds, there would be 6 customers in line at the book store.

Little's Law can be used to calculate the number of customers in line at the end of the first 3 seconds. According to Little's Law: the average number of customers in the system is equal to the arrival rate multiplied by the time spent in the system.

In this case, the arrival rate during the first 3 seconds is 29 customers per second, and the time spent in the system is 3 seconds. Therefore the average number of customers in the system is 87 (29 customers per second x 3 seconds).

However since the bookstore can only serve 27 customers per second, the maximum number of customers that can be served during the first three seconds is 81 (27 customers per second x 3 seconds). This means that there are 6 customers who remain in line at the end of the first 3 seconds.

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Answer:

10 x squared minus 4 y + 2 x squared minus y

Step-by-step explanation:

9x^2-2y+3x^2-3y

Collect like terms

9x^2+3x^2-2y-3y

=12x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

Collect like terms

10x^2+2x^2-4y-y

=12x^2-5y

9x^2-2y+3x^2-3y is equivalent to

10x^2-4y+2x^2-y

Check all the options

6 x squared minus y + 6 x squared minus 5 y

6x^2-y+6x2-5y

12x^2-6y

6 x squared minus y + 3 x squared minus 4 y

6x^2-y+3x^2-4y

9x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

12x^2-5y

11 x squared + 2 y + x squared minus 3 y

11x^2+2y+x^2-3y

12x^2-y

Answer:

C.) 12x squared- 2y- 3y

Step-by-step explanation:

i'm not 100 percent on this but it is the only logical answer, i will comment if i am right or not :) good luck luvs

The speed of the faster airplane is 651 miles per hour.

Let's denote the speed of the slower airplane as x miles per hour. According to the problem, the speed of the faster airplane is 80 miles per hour more than the speed of the slower airplane.

Thus, the speed of the faster airplane can be represented as x + 80 miles per hour.When two objects move towards each other, their relative speed is equal to the sum of their individual speeds.

In this case, the relative speed of the two airplanes is x + (x + 80) = 2x + 80 miles per hour. Since the two airplanes start 3003 miles apart, we can write the following equation:3003 = 5(2x + 80).

Simplifying and solving for x, we get:x = 571 miles per hourTherefore, the speed of the faster airplane is x + 80 = 571 + 80 = 651 miles per hour.

This question requires us to determine the speed of the faster airplane, given that two airplanes fly towards each other from opposite directions.

The problem tells us that the two airplanes fly at a constant speed, but their speeds differ by 80 miles per hour. After 5 hours, the planes pass each other.

The question is asking for the speed of the faster plane. We can solve this problem using the formula speed = distance ÷ time. However, since the two planes are moving towards each other, we must add their speeds to find their relative speed.

The relative speed of the two airplanes can be represented as x + (x + 80) = 2x + 80 miles per hour, where x is the speed of the slower airplane.

The distance between the two planes is given as 3003 miles. Using the formula distance = speed × time, we get the following equation:3003 = 5(2x + 80).

Simplifying and solving for x, we get:x = 571 miles per hourTherefore, the speed of the faster airplane is x + 80 = 571 + 80 = 651 miles per hour. Hence, we can conclude that the speed of the faster plane is 651 miles per hour.

Thus, the speed of the faster airplane is 651 miles per hour.

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Answer: The length of the hypotenuse is  25

Step-by-step explanation:

Hi, to answer this question we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (the longest side) and a and b are the other legs of the triangle (vertical and horizontal leg)

Replacing with the values given:  

c^2 = 7^2 + 24^2  

c^2 = 49+576

c^2 = 625

c = √625

c = 25  

Feel free to ask for more if needed or if you did not understand something.  

Answer:

163

Step-by-step explanation:

\(2*(7^{2}) +9(7)+2\)

\(2*(49)+9(7)+2\)

\(98+63+2\)

\(=163\)

The lateral surface area of the prism is 384 square units.

The surface area of the right square prism has 6 sides the base and top are the same and the other side or usually called lateral also has the same size. The equation of lateral surface area can be written as

LA = 4S

LA = 4( l x h )

where LA is the lateral surface area of a prism, S is the side area, l is the base length of the prism and h is the height of the prism.

From the question above, we know that :

height = 12

length = 8

By substituting the parameter, we can determine the lateral surface area

A = 4( l x h )

A = 4( 8 x 12)

A = 384

Hence, the lateral surface area of the prism is 384 square units.

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Answer:

350 milliliters

Step-by-step explanation:

350 is 70% of 500 and is the answer

Answer:

The volume of this rectangular prism is 96 cubic centimeters

Step-by-step explanation:

The volume of a rectangular prism = Length × width × height

= 8 × 6 × 2

= 96 cubic centimeters

The account balance three years from now will be $13,666.10. So, the correct option is D) $13,666.10.

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4. (a) The maximum rate of change of f(x, y) = sin(xy) at point P(1, 0) is 1 and it occurs in the direction of the positive y-axis.

(b) The maximum rate of change of f(x, y, z) = P(8, 1.3) is -∇f(x) and it occurs in the direction opposite to the gradient vector ∇f.

4. (a) To find the maximum rate of change at point P(1, 0) for f(x, y) = sin(xy), we first calculate the partial derivatives with respect to x and y: ∂f/∂x = ycos(xy) and ∂f/∂y = xcos(xy). Evaluating these partial derivatives at P(1, 0), we get ∂f/∂x = 0 and ∂f/∂y = 1. The maximum rate of change is given by √((∂f/∂x)^2 + (∂f/∂y)^2), which equals 1. The direction of maximum rate of change is in the positive y-axis direction.

(b) To show that the function f decreases most rapidly at x in the direction opposite to the gradient ∇f(x), we consider the directional derivative in the direction of −∇f(x). The directional derivative is given by the dot product of the gradient ∇f(x) and the unit vector in the opposite direction −∇f(x)/|∇f(x)|. The maximum rate of decrease is equal to the magnitude of the negative gradient vector −|∇f(x)|.

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Answer:

The x intercept is 4 (by substituting y as zero we get x intercept)

And the y intercept is 8 (by substituting x as zero we get y intercept)

Take (4, 0) and take (8, 0) to graph the line

You're welcome!

Answer:

x = 4 y = 8 graph (4,0) and (8,0)

Answer:

(for your second question) 23.69

Step-by-step explanation:

Answer:

\(x^2+2x+1\)

Step-by-step explanation:

When given the following expression,

\((x+1)(x+1)\)

One must multiply every term in one of the parenthesis by every term in the other, thus, the resulting expression formed,

\((x)(x)+(1)(x)+(1)(x)+(1)(1)\)

After distributing, simplify the expression, perform the multiplication and combine like terms,

\(x^2 + 2x + 1\)

Answer:d

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

8×19= 152  

1 : 4.5  

152×4.5=684  

The minimum possible value of f ( 7 ) − f ( 3 ) f(7)-f(3) is −4 and the maximum possible value is 4.

Given that 2 ≤ f ' ( x ) ≤ 4 2≤f′(x)≤4 for all values of x, we can make use of the Mean Value Theorem to determine the minimum and maximum possible values of f ( 7 ) − f ( 3 ) f(7)-f(3).

According to the Mean Value Theorem, there exists a c ∈ ( 3 , 7 ) c\in(3,7) such that:

f ( 7 ) − f ( 3 ) = f ′ ( c ) ( 7 − 3 ) = 4 c − 12 4c-12

Since f'(x) is between 2 and 4 for all values of x, we know that 8 ≤ 4c ≤ 16 8\leq4c\leq16. Therefore, 2 ≤ c ≤ 4 2\leq c\leq 4.

To find the maximum value of f ( 7 ) − f ( 3 ) f(7)-f(3), we need to maximize 4c-12 when c is between 2 and 4. This occurs when c = 4, so the maximum value of f ( 7 ) − f ( 3 ) f(7)-f(3) is:

f ( 7 ) − f ( 3 ) ≤ 4 ( 4 ) − 12 = 4

To find the minimum value of f ( 7 ) − f ( 3 ) f(7)-f(3), we need to minimize 4c-12 when c is between 2 and 4. This occurs when c = 2, so the minimum value of f ( 7 ) − f ( 3 ) f(7)-f(3) is:

f ( 7 ) − f ( 3 ) ≥ 4 ( 2 ) − 12 = −4

Therefore, the minimum possible value of f ( 7 ) − f ( 3 ) f(7)-f(3) is −4 and the maximum possible value is 4.

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The straw would extend approximately 4.9 cm past the edge of the glass.

Answer:

Step-by-step explanation:

Let's assume the initial number of men at the exhibition is 10x, and the initial number of women is 3x.

After 110 men left, the number of men remaining is 10x - 110.

The total number of people remaining is (10x - 110) + (3x) = 13x - 110.

According to the given information, the number of men remaining (10x - 110) is 5/12 of the total number of people remaining (13x - 110). We can write this as an equation:

10x - 110 = (5/12)(13x - 110)

To solve this equation, we can start by simplifying both sides:

10x - 110 = (65/12)x - (55/6)

To get rid of the fractions, we can multiply both sides of the equation by 12:

12(10x - 110) = 65x - 110(2)

120x - 1320 = 65x - 220

Next, we can bring the x terms to one side and the constant terms to the other side:

120x - 65x = 1320 - 220

55x = 1100

Dividing both sides by 55, we find:

x = 20

Now, we can substitute the value of x back into the initial expressions to find the number of men and women:

Number of men = 10x = 10(20) = 200

Number of women = 3x = 3(20) = 60

Therefore, there were 60 women at the exhibition

Hope this answer your question

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The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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