Enter the number that makes the equation true. 17
0. 54 +
100
+
100
17
100

Answer:11

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

Answer:

16.2

Step-by-step explanation:

The x is 6.6.

2x+3 = DE

2(6.6)+3

13.2+3

16.2

Hope this helps!

Using a calculator, you should get

f(x) = 4*e^x

f(2) = 4*e^2 .... replacing every x with 2

f(2) = 29.5562243957433

This is an approximate value. Round this however you need to.

The value of f(2) = 29.5562243957433

For eveluate for f(x)  we put x = 2,

f(x) = 4*e^x

f(2) = 4*e^2 .... replacing every x with 2

f(2) = 29.5562243957433

Therefore, This is an approximate value f(2) = 29.5562243957433.

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Answer:

It is true that the product of a complex number and its conjugate is a real number.

Step-by-step explanation:

You're welcome.

Answer:

True

Step-by-step explanation:

....this is how you 'rationalize' denominators that have complex numbers in them

The radius of table can be 13 inches or 73 inches.

Let r inches be the table's radius.

Make the corner the starting point or origin.

the coordinates for the table's center are as follows: (r, r).

So  \((x-r)^{2} +(y-r)^{2}=r^{2}\)  is the equation for the table's diameter.

The distance between the mark at the table's edge and one wall is 18 inches and 25 inches, respectively. Consequently, this point's coordinates are (18, 25). It might alternatively be (25, 18), but our calculations would not be affected.

Given that the mark is on the edge, it satisfies the criteria established by the table's circumference equation.

\((18-r)^{2} +(25-r)^{2} =x^{2}\)

\(324-36r+r^{2} +625-50r+x^{2} =x^{2}\)

\(r^{2} -86r+949=0\)

(r−13)(r−73)=0

r=13 inches or r=73 inches

As a result, the table's radius can be either 13 inches or 73 inches.

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Answer:

14

Step-by-step explanation:

First, find out how many half-lives have passed. Divide the number of minutes by the length of a half-life. 34÷17=22 half-lives have passed. Now figure out how much praseodymium will be left after 2 half-lives have passed. Multiply the starting amount of praseodymium by 12 a total of 2 times. 56 x 1/2 x 1/2 = 14 That calculation could also be written with exponents:56x (1/2)^2=14 After 2 half-lives, the amount of praseodymium left will be 14 grams.

Assuming the half-life of a radioactive kind of praseodymium is 17 minutes.The amount that will be left after 34 minutes is 14g.

Since 34 minutes is exactly 2 half-lives of 17 minutes.

Hence, remaining amount will then be:
Remaining amount= (1/2)×(1/2) = (1/2)² of the initial amount

Final amount:

Final amount = (1/2)² (56g)

Final amount=0.25 (56g)

Final amount = 14 g

Inconclusion  the half-life of a radioactive kind of praseodymium is 17 minutes.The amount that will be left after 34 minutes is 14g.

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Answer:

Step-by-step explanation:

Answer:it will be 20 inches long at the end of 5 weeks

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

i got it wrong and it showed me the real answer

Answer:

2,2

Step-by-step explanation:

I don't really know how to explain it, but if you plot E and F on a coordinate plane it would make more sense.

*Note that the ratio 1:1 is not the same as the fraction 1/1, rather, 1:1 = 1/2 so point F is like a midpoint of segment EG

The coordinates of point G is (2,2)

The coordinate points are given as:

The ratio is given as:

\(m : n = 1 : 1\)

Given that the ratio is 1 : 1, it means that, point F is at the midpoint of line segment EG

So, we have:

\(F =0.5 \times (x_1 + x_2, y_1 + y_2)\)

This gives

\((1,3) =0.5 \times (0 + x, 4+ y)\)

\((1,3) =0.5 \times (x, 4+ y)\)

Multiply both sides by 2

\((2,6) =(x, 4+ y)\)

By comparison, we have:

\(x = 2\)

\(4 + y = 6\)

\(y =2\)

Hence, the coordinates of point G is (2,2)

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There is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.

Since, A total of 3 x 5 = 15 outcomes are possible given the presence of 3 characters and 5 defense mechanisms.

There are three scenarios if the character is a hobbit (hobbit with magic, hobbit with sword, and hobbit with shield), three scenarios where the tool is an umbrella (any character with an umbrella), and one scenario where neither.

As a result, there are the following number of possibilities where neither the character nor the tool is a hobbit:

15 - 3 - 1 = 11

One of these 11 outcomes is likely to occur at a rate of:

= 11/15

As a result, there is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.

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Answer:

14\(\frac{2}{3}\)

Step-by-step explanation:

20 + 3.75x = 75  Subtract 20 from both sides

20 - 20 + 3.75x = 75 - 20

3.75x = 55  Divide both sides by 3.75

\(\frac{3.75x}{3.75}\) = \(\frac{55}{3.75}\)

x = 14\(\frac{2}{3}\)

Answer:

69

Step-by-step explanation:

trust me

Answer:

1. 67.2

2.13.34

3. 175.5

Step-by-step explanation:

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[Content Deleted]

Answer: 38

Step-by-step explanation:

4*8 =32

32/2=16

16*3=48

48-10=38

Answer:

x + 8 = 34

Step-by-step explanation:

Hope it helps.

Algebraic expressions

x = a certain number

added = addition

the result = addition result

the equation: 8 + x = 34

The solution set of 6 ㏑ e = e ^ ㏑ 2x is 3

What is relation between Exponents and logarithms ?

Exponents and logarithms are inverse functions, you can use exponents to "undo" logarithms and use logarithms to "undo" logarithms. Exponents specify the number of times you must multiply a value, while logarithms specify which exponent to apply to obtain a certain value.

The given expression is,

6 ㏑ e = e ^ ㏑ 2x

we know, ㏑ (e) = 1 and e ^ ㏑(x)  = x

Put these values,

6 * 1 = 2x

Now, find x

6 = 2x

x = 3

Hence, the solution set of 6 ㏑ (e) = e ^ ㏑ (2x)  is 3

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\(c(g) = 7g + 52 \\ c(0) = 52\)

\(g(x) = x {}^{2} - 7x + 12 \\ g(x) = 0 \\ x = 3 \: \: \: \: \: \: \: \: x = 4\)

Let's see

#1

So

x intercepts

True

#2

Option C

#3

Option D

#4

I solved it in your another question , Can't add that answer here due to copyright restrictions

Answer: 126 milligrams

Step-by-step Easy to answer but all your doing is converting your mg's and 35% into decimals. and you will get your answer

Answer:

B, D, and E

Step-by-step explanation:

You'll have to distribute each and put them into a full equation again.

A. -3x + 24

B. -3x - 24

C. -3x + 24

D. -3x - 8/3

E. -3x - 24

F. -3x + 24

I bolded the ones that did not equal -3x + 24

so your answer is B, D, and E

Answer:

The amount driven would be 275, and the cost for both plans will be 77.75$

Step-by-step explanation:

make both equations

y=0.09x+53

y=0.13x+42

set them equal to each other and solve for x to get the distance

take that number and put it in one equation and solve for y to get the price of the plan for that value

Answer:

\( \sf \: a = 5\)

Step-by-step explanation:

Now we have to,

→ find the required value of a.

The equation is,

→ 2 + a = 7

Then the value of a will be,

→ 2 + a = 7

→ a + 2 = 7

→ a = 7 - 2

→ [ a = 5 ]

Hence, the value of a is 5.

Answer:

29.4 cm^2

Step-by-step explanation:

We can use a proportion to find the height:

120 : 100 = x : 7

x = (120 *7)/100 = 8.4 cm

Area = (base * height)/2 = (7 * 8.4)/2 = 29.4 cm^2

Answer:

29.4cm²

Step-by-step explanation:

First we are going to find 120% of 7.

7 × \(\frac{120}{100}\) = 8.4 cm

Therefore, 8.4 cm is the height.

Area =  \(\frac{1}{2}\) Base × Height

= \(\frac{1}{2}\) × 7 × 8.4 = 29.4cm²

If the can's combined lips measure 38 inches and the adhesive overlaps by around 12 inches, the label's surface area will be 50 square inches.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

Given data;

Height of can,\(\rm H=5 \frac{3}{8} \ inch\)

Height of label,

\(\rm h=5\frac{3}{8} -\frac{3}{8} \\\\ h= 5 \ inch\)

Diameter,\(\rm d= 3 \ inch\)

The area of the label is;

A = ( overlap area  + circumfereence ) h

\(\rm A = [\frac{1}{2} + 2 \pi \times \frac{3}{2} ] \\\\ A =[ \frac{1+6\pi}{2} ] \times 5 \\\\ A = 49.6 \ inch^2\)

Hence, the label's surface area will be 50 square inches.

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The terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

In this question,

The function is f(x) = \(\frac{sin(x)}{1-x}\)

The general form of Maclaurin series is

\(\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......\)

To find the Maclaurin series, let us split the terms as

\(f(x)=sin(x)(\frac{1}{1-x} )\) ------- (1)

Now, consider f(x) =  sin(x)

Then, the derivatives of f(x) with respect to x, we get

f'(x) = cos(x), f'(0) = 1

f''(x) = -sin(x), f'(0) = 0

f'''(x) = -cos(x), f'(0) = -1

\(f^{iv}(x)\) = cos(x), f'(0) = 0

Maclaurin series for sin(x) becomes,

\(f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....\)

⇒ \(f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....\)

Now, consider \(f(x) = (1-x)^{-1}\)

Then, the derivatives of f(x) with respect to x, we get

\(f'(x) = (1-x)^{-2}, f'(0) = 1\)

\(f''(x) = 2(1-x)^{-3}, f''(0) = 2\)

\(f'''(x) = 6(1-x)^{-4}, f'''(0) = 6\)

\(f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24\)

Maclaurin series for (1-x)^-1 becomes,

\(f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....\)

⇒ \(f(x)=1+x+x^{2} +x^{3} +......\)

Thus the Maclaurin series for \(f(x)=sin(x)(\frac{1}{1-x} )\) is

⇒ \(f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)\)

⇒ \(f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....\)

⇒ \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\)

Hence we can conclude that the terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

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Answer:

yes.

Step-by-step explanation:

The general solution of the given recurrence equation is Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n.

The given recurrence equation is

Qn-1 + 5Qn-2 + 3Qn-3 = 3

Let's find the characteristic equation of the given recurrence equation:

By assuming Qn = rn,

the characteristic equation can be derived as:

r3 - r2 - 5r - 3 = 0

So, the characteristic polynomial is

(r + 1)(r - 3)2

Let α = -1 and β = 3 (repeated roots)

Now, the solution of the given recurrence equation is:

Qn = Arn + Bnαn + Cnβn

As α = -1 and β = 3 are the roots of the characteristic equation, substitute these values in the above equation.

We have

A(-1)n + Bn(-1)n + Cn(3)n ... (1)

As we are going to find the general solution of Qn, the constants A, B, and C need to be determined.

Let's solve for A, B, and C by considering the first few terms of the given recurrence equation.

Suppose n = 3 in the recurrence equation Qn-1 + 5Qn-2 + 3Qn-3 = 3, we have

Q2 + 5Q1 + 3Q0 = 3 ... (2)

Now, substitute n = 2 in the general solution (1), we have

Q2 = A(-1)2 + B2(-1)2 + C23 ... (3)

Now, substitute n = 1 in the general solution (1), we have

Q1 = A(-1)1 + B1(-1)1 + C31 ... (4)

Now, substitute n = 0 in the general solution (1), we have

Q0 = A(-1)0 + B0(-1)0 + C30 ... (5)

Now, let's solve for A, B, and C using equations (2), (3), (4), and (5).

Q2 + 5Q1 + 3Q0 = 3:

2A + 5B + 3C = 3A(-1)2 + B2(-1)2 + C23:

A - B + 9C = 3A(-1)1 + B1(-1)1 + C31:

-A - B + 3C = 1A(-1)0 + B0(-1)0 + C30:

A + B + C = 1

On solving the above equations,

we get A = -1/4, B = 1/4, and C = 1/2

So, the general solution of the given recurrence equation is  

Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n

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The potential rational zeros for the polynomial function \(F(x) = 3x^4 - 9x^3 + x^2 - x + 1\) are: A. -1, 1, -3/1, 3/1, -9/1, 9/1.

To find the potential rational zeros of a polynomial function, we can use the Rational Root Theorem. According to the theorem, if a rational number p/q is a zero of a polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient.

In the given polynomial function \(F(x) = 3x^4 - 9x^3 + x^2 - x + 1,\) the leading coefficient is 3, and the constant term is 1. Therefore, the potential rational zeros can be obtained by taking the factors of 1 (the constant term) divided by the factors of 3 (the leading coefficient).

The factors of 1 are ±1, and the factors of 3 are ±1, ±3, and ±9. Combining these factors, we get the potential rational zeros as: -1, 1, -3/1, 3/1, -9/1, and 9/1.

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Answer:

12

Step-by-step explanation:

Sum means addition. 3 + 3 + 6 = 12

Answer:

12

Step-by-step explanation:

i hope this is what you meant