What is the metric system based on

Answer:

x = -1

Step-by-step explanation:

the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Why is it?

To find the distance from the first plant to the last plant, we need to add up the distances between each adjacent pair of plants. Since there are 8 plants, there are 7 pairs of adjacent plants, and each pair is separated by 1.5 feet.

So, the total distance from the first plant to the last plant is:

7 ×1.5 = 10.5 feet

Therefore, the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Distance refers to the measurement of the physical space between two points or objects. It is a scalar quantity that only considers the magnitude of the separation between two points and does not take into account the direction of the separation.

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Answer:

meter - yard

kilogram - 2 pounds

liter - quart

The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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The definition of limits and the squeeze theorem indicates that any positive value of δ corresponds with both ε = 0.6 and ε = 0.3, in the ε-δ definition

The squeeze theorem, also known as the sandwich or the pinching theorem, allows the finding of the limit of a function by squeezing the function between two other functions with known and equivalent limits.

The ε-δ definition of a limit states that there exists a δ > 0 for every ε > 0, such that where 0 < |x - c| < δ, then |f(x) - L| < ε, where;

c = The value which is approached by x

L = The limit of the function f(x) as x approaches c

The details indicates; \(\lim\limits_{x\to0}\frac{e^{2\cdot x}-1}{x} = 2\), therefore, c = 0, and L = 2

The values of δ that corresponds to ε = 0.6 and ε = 0.3 are required

Therefore, when 0 < |x - 0| < δ, then |\(\frac{e^{2\cdot x} - 1}{x}\)| - 2 < 0.6

|\(\frac{e^{2\cdot x} - 1}{x}\)| - 2 < 0.6

-0.6 < \(\frac{e^{2\cdot x} - 1}{x}\) - 2 < 0.6

1.4 < \(\frac{e^{2\cdot x} - 1}{x}\) < 2.6

The squeeze theorem can be used to find the value of δ as follows;

\(e^{2\cdot x\) > 1 for all x > 0, therefore;

\(\frac{e^{2\cdot x} - 1}{x}\) > (1 - 1)/x = 0

The upper bound for δ, is therefore;

\(\frac{e^{2\cdot x} - 1}{x}\) - 2 > -2

|\(\frac{e^{2\cdot x} - 1}{x}\) - 2| > |-2|

Whereby the required value is; |\(\frac{e^{2\cdot x} - 1}{x}\) - 2| < ε = 0.6, a value of δ can be chosen such that |-2| < ε = 0.6, which indicates that any positive value for δ will be adequate in the present case.

The value of δ  that corresponds to ε = 0.3 can found as follows;

|\(\frac{e^{2\cdot x} - 1}{x}\) - 2| < 0.3

-0.3 < \(\frac{e^{2\cdot x} - 1}{x}\) - 2 < 0.3

1.7 < \(\frac{e^{2\cdot x} - 1}{x}\) < 2.3

The squeeze theorem indicates;

\(\frac{e^{2\cdot x} - 1}{x}\) > (1 - 1)/x = 0

\(\frac{e^{2\cdot x} - 1}{x}\) > (1 - 1)/x - 2 = -2

|\(\frac{e^{2\cdot x} - 1}{x}\) > (1 - 1)/x - 2| = |-2|

The required inequality is; |\(\frac{e^{2\cdot x} - 1}{x}\) > (1 - 1)/x - 2| < ε = 0.3, therefore any value of the variable δ, such that |-2| < ε = 0.3 will be acceptable

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Answer:

$678.83

Step-by-step explanation:

Given :

Principal, P = $600

Rate = 3.09% = 0.0309

Period, t = 4 years

Compounding times per period, n = 12 (monthly)

The compound interest formula :

A = P(1 + r/n)^nt

A = 600(1 + 0.0309/12)^(12*4)

A = 600(1 + 0.002575)^48

A = 600(1.002575)^48

A = 600 * 1.1313834

A = 678.83004

Worth in 4 years = $678.83

Answer:

3/4

Step-by-step explanation:

divide each by 2

28/2 = 14

12/2 = 6

14/2 = 7

6/2 = 3

therefore 3/7

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.

To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:

lim(x→-1) [f(x) - f(-1)] / (x - (-1))

First, let's substitute the values into the expression:

lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)

Simplifying further:

lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)

lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)

lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)

Now, we can directly substitute x = -1 into the expression:

\((-1^2 + 2(-1) + 1) / (-1 + 1)\)

(1 - 2 + 1) / (0)

0 / 0

We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.

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Answer:

Step-by-step explanation:

let x be necromancers and y be wizards

if you know the amount of wizards and want to find the amount of necromancers. you just use y + 6

but if you know the amount of necromancers and want to find out the amount of wizards you just do x - 6

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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Answer:

70%

Step-by-step explanation:

As they are 10 pieces and only 7 are shaded me need to multiply 7x10 and it's 70

Answer:

Complementary angle

<y+61° =90°

<y = 90°- 61°

<y =29°

I Hope this helps.

Answer:

339, 340, 341

Step-by-step explanation:

To find the 3 consecutive numbers, divide the sum by 3 to get the average. 1020/3=340. So the middle number is 340. That means the numbers are 339, 340, and 341.

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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Answer:

Filling the values we have;

Explanation:

Given the data on the given table, we want to fill them in a stem leaves plot.

The tens values would be in the stems while the unit values will be written in their corresponding leaves.

Filling the values we have;

The minimum amount of plastic wrap needed to completely wrap 8 containers is  794. 4 in². Option D

The area of each circular end is:

A = πr²

A = 3.14 × (2.75)²

A = 23.68in²

The area of the rectangular side is:

A = h * circumference

circumference = 5.5in * π

circumference = 17.27in

Using the given height of 3 inches, we get:

A = 3in * 17.27

A = 51.81in²

Therefore, the total surface area of each container is:

A = 2 * 23.68 + 51.81

A = 98.17in²

To wrap 8 containers, we need to multiply the surface area of each container by 8:

Total surface area = 8 × 98.17

Total surface area = 794. 4 in²

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Answer:

599000

Step-by-step explanation:

Refer to the images attached. Now I am guessing when it says "use geometry" was to graph it? I wasn't completely sure. I attached how I would normally evaluate that problem and a graph of the piecewise function. It has been a while since I have dealt with integrating piecewise function, please let me know what process you were supposed to use if you figure it out. Hope this helps you a bit, have a good one!

The result to the equation is x = 7.

To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step

Abate 4 from both sides of the equation

√( 2x- 5) = 1- 4

√( 2x- 5) = -3

Square both sides of the equation to exclude the square root

√( 2x- 5))² = (- 3)²

2x- 5 = 9

Add 5 to both sides of the equation

2x = 9 + 5

2x = 14

Divide both sides of the equation by 2

x = 14/2

x = 7

Thus, the result to the equation is x = 7.

Checking the extraneous result

Substituting x = 7 back into the original equation

√(2(7)-5)+4=1

√(14-5)+4=1

√9+4=1

3+4=1

7 = 1

This equation isn't true, which means that x = 7 is an extraneous result.

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9x +14

aisdlkjfhajlsdfhlakjsdhfla

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

it would be within the range of $0.77 <x< $0.78

hello

to solve this question, we need to find the volume of a sphere

the formula is given as

the minimum volume of the sphere is would be as a result in reduction of the radius of the sphere

we can use this radius to calculate the volume of the sphere

from the calculations above, the minimum volume of the sphere is 28.72cm^3 which corresponds to option C

Answer:

A = 9

B = 4 (If not included the minus)

Step-by-step explanation:

We are given the expression:

\( \displaystyle \large{4 \tan (x) \sin (x) + 5 \sec(x) }\)

We are going to rewrite the expression as Asec(x)-Bcos(x).

Let's recall the Identity of Trigonometric Function:

\( \displaystyle \large{ \tan(x) = \frac{ \sin(x) }{ \cos(x) } } \\ \displaystyle \large{ \sec(x) = \frac{1}{ \cos(x) } } \\ \displaystyle \large{ { \sin}^{2} x = 1 - { \cos}^{2} x}\)

We are going to use these identities to rewrite the expression. First, let's convert tan(x) to sin(x)/cos(x) and sec(x) to 1/cos(x).

\( \displaystyle \large{4 ( \frac{ \sin(x) }{ \cos(x) } )\sin (x) + 5( \frac{1}{ \cos(x) }) }\)

Simplify the expression — multiply sin(x) to sin(x)/cos(x).

\( \displaystyle \large{4 ( \frac{ { \sin}^{2} x}{ \cos(x) } )+ 5( \frac{1}{ \cos(x) }) }\)

Rewrite sin^2 of x as 1-cos^2(x).

\( \displaystyle \large{4 ( \frac{ 1 - { \cos}^{2} x}{ \cos(x) } )+ 5( \frac{1}{ \cos(x) }) }\)

Separate the fraction:

\( \displaystyle \large{4 ( \frac{1}{ \cos(x) } - \frac{ { \cos }^{2} x}{ \cos(x) } )+ 5( \frac{1}{ \cos(x) }) }\)

Rewrite 1/cos(x) as sec(x) again as we need it for rewrite.

\( \displaystyle \large{4 ( \sec(x) - \frac{ { \cos }^{2} x}{ \cos(x) } )+ 5\sec(x) }\)

Simplify cos^2 of x and cos(x).

\( \displaystyle \large{4 ( \sec(x) - \frac{ \cos(x) }{ 1} )+ 5\sec(x) } \\ \displaystyle \large{4 ( \sec(x) - \cos(x) )+ 5\sec(x) }\)

Expand 4 in sec(x)-cos(x).

\( \displaystyle \large{4 \sec(x) - 4 \cos(x) + 5\sec(x) }\)

Add 4sec(x) and 5sec(x).

\( \displaystyle \large{9 \sec(x) - 4 \cos(x) }\)

Hence, rewritten in form of Asec(x)-Bcos(x)

The value of A is 9 and B is 4 (If not included the sign).

Answer:

b

Step-by-step explanation:

Answer:

The logical answer is 246

Step-by-step explanation:  So, (X+1)+ (X+2) + (X+3)=738 then 3x+3=738 so x=245. 245 is the first number so then the answer is 245+246+247=738. And that leads to the conclusion that the middle number is 246.