Find the first four terms of the recursive sequence defined by the following formula:
an = an-14 where a4 = 2 14

 ,  ,  , 2 14

​

Answer:

  A.  4

Step-by-step explanation:

The common ratio will be the ratio of any adjacent pair of y-values:

  32/8 = 128/32 = 512/128 = 2048/512 = 4

[tex]p+b=27\\p=4b-3\\\\4b-3+b=27\\5b=30\\b=6\\\\p+6=27\\p=21[/tex]

21

Final answer:

To determine the number of purple marbles, we can use a system of linear equations derived from the problem's conditions. Solving these gives us 21 purple marbles in the bag.

Explanation:

To solve the problem, let's denote the number of blue marbles as x and the number of purple marbles as y. According to the problem, the total number of marbles is 27, which is our first equation, x + y = 27. Additionally, the number of purple marbles is 3 less than 4 times the number of blue marbles, giving us a second equation, y = 4x - 3.

Now, we'll solve for x using substitution. We place the expression for y from the second equation into the first equation:

x + (4x - 3) = 27

5x - 3 = 27

5x = 30

x = 6

Since x is 6, we can find y by substituting back into the second equation:

y = 4(6) - 3

y = 24 - 3

y = 21

There are therefore 21 purple marbles in the bag.

Answer:

see explanation

Step-by-step explanation:

Find equivalent routes for the directed lines, that is

(a)

FE = FA + AB + BE = b + a - 3b = a - 2b

(b)

BC = BE + ED + DC = - 3b + a + 2b = a - b

(c)

FC = FA + AB + BE + ED + DC

     = b + a - 3b + a + 2b = 2a

Answer:

xy = 1.6

Step-by-step explanation:

The equation for inverse variation is

xy = k  where k is the constant of variation

8 * .2 = k

1.6 = k

xy = 1.6

For this case we can raise a rule of three:

[tex]\frac {3} {4}[/tex]cup of water ---------> [tex]\frac {1} {8}[/tex] pound of flour

x --------------------------------- > 1 pound of flour

Where:

x: Represents the amount of water that Tamie must use with 1 pound of flour.

[tex]x = \frac {1 * \frac {3} {4}} {\frac {1} {8}}\\x = \frac {\frac {3} {4}} {\frac {1} {8}}\\x = \frac {3 * 8} {4 * 1}\\x = \frac {24} {4}\\x = 6[/tex]

So, Tamie should use 6 cups of water

Answer:

6 cups of water

Answer:

see below

Step-by-step explanation:

Let r = number of rides

total amount of money spent has to be less than  or equal to 50

costs are admission and food and rides

rides cost 1.50 each

50≥ admission + food + rides

50 ≥ 15 +10 + 1.50r

Combine like terms

50 ≥25 + 1.50 r

Subtract 25 from each side

50-25 ≥25-25 + 1.50 r

25  ≥ 1.50 r

Divide by 1.5 on each side

25/1.5 ≥ 1.5r/1.5

50/3  ≥ r

Changing this to a mixed number

16 2/3  ≥r

We can only take a whole number of rides

r = 16

Beverly has not spent all of her 50 dollars since there was a fraction for the rides

cost =  15 +10 + 1.50r

        15+10 + 1.5*16

            25+24

           49

She has 1 dollar left

Answer:

  b.  42.875 units³

Step-by-step explanation:

The volume of a cuboid is the product of its edge dimensions (length×width×height):

  (3.5 units)(3.5 units)(3.5 units) = 3.5³ units³ = 42.875 units³

Answer: x = 20

Step-by-step explanation:

Multiply by 10 ( next LCF )

10 ( x / 2 + 2x / 5 ) = 18 * 10

5x + 4x = 180

9x = 180

x = 20

Answer:

[tex]\dfrac{x}{2} + \dfrac{2x}{5} = 18[/tex] has the unique solution x = 20.

Step-by-step explanation:

The equation has the equivalences

[tex]\displaystyle\frac{x}{2} + \frac{2x}{5} = 18 \Leftrightarrow x\left( \frac{1}{2} + \frac{2}{5} \right) = 18 \Leftrightarrow x \left( \frac{9}{10} \right) = 18 \Leftrightarrow x = 18 \cdot \frac{10}{9} = 20.[/tex]

Answer:

x = ⅓ acos(y/7) + π/18, [-7, 7/2]

Step-by-step explanation:

y = 7 cos(3x − π/6)

Solving for x:

y/7 = cos(3x − π/6)

acos(y/7) = 3x − π/6

acos(y/7) + π/6 = 3x

x = ⅓ acos(y/7) + π/18

The domain of x is the same as the range of y.

When x = π/6:

y = 7 cos(3π/6 − π/6)

y = 7 cos(π/3)

y = 7/2

When x = 7π/18:

y = 7 cos(21π/18 − π/6)

y = 7 cos(π)

y = -7

So the domain of x as a function of y is [-7, 7/2].

Hello There!

The volume for a cylinder is Pi*r^2*h

We are going to leave our Answer in terms of pi so first we need to square our radius which we know is 5

Our radius is 25 because we squared 5. Next, we need to multiply 25 by our height which is 11.

25 multiplied by 11 is 275 so our Answer would be 275[tex]\pi[/tex]

Answer:

D is the contrapositive.

Step-by-step explanation:

Contrapositive of if A then B is if not B then not A

Answer:

Option D is correct here.

Step-by-step explanation:

A conditional statement is in the form of if p then q.

A contrapositive statement is when we interchange the hypothesis and conclusion of the sentence and negate both of them. It is in the form of - if not q then not p.

Given statement here is - A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.

This is a true statement. It is the definition of converse statement.

Its contrapositive will be : A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement.

So, here option D is the contrapositive that is also true.

Answer:

[tex]8\ years[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=?\ years\\ P=\$100\\A=\$150\\ r=0.05[/tex]  

substitute in the formula above  

[tex]150=100(e)^{0.05*t}[/tex]  

[tex]1.5=(e)^{0.05*t}[/tex]  

Applying ln both sides

[tex]ln(1.5)=(0.05t)ln(e)[/tex]  

[tex]ln(1.5)=(0.05t)[/tex]  

[tex]t=ln(1.5)/(0.05)[/tex]  

[tex]t=8\ years[/tex]  

Answer:

If you need all the answers for that assignment:

Step-by-step explanation:

1. Consider 8^x-4 = 8^10

Because the (blank a) are equal , the (blank b) must also be equal.

Answer: Bases, Exponents

The solution to the equation is 14

2.What equation is equivalent to 9^(x-3)=729?

Answer 3^x - 3 = 3^6  

Solve: 9x - 3 = 729

Answer: x = 6

3. To solve 5(2^x+4)=15, first divide each side by

Answer: 5

Solve 5(2^x+4) = 15. Round to the nearest thousandth.

Answer: -2.415

4. Which of the following is the solution of 5e^2x- 4 = 11?

Answer: x=In3/2

5. Select all of the potential solution(s) of the equation 2log5x = log54.

Answer: 2,-2

What is the solution to 2log5x = log54?

Answer: 2

6. Which equation is equivalent to log5x3 - logx2 = 2?

Answer: 10^log5^3/x^2=10^2

Solve: log5x3 - logx2 = 2

Answer: 20

7. What is the solution to ln (x2 - 16) = 0?

Answer: x=+-(17)

8. Solve: ln 2x + ln 2 = 0

Answer: ¼

Solve: e^ 2x+5 = 4

Answer: x=(In4) - 5/2

9. Consider the equation log(3x - 1) = log2(8). Explain why 3x - 1 is not equal to Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Answer: The bases are not the same, so you cannot set 3x - 1 equal to 8.You can evaluate the logarithm on the right side of the equation to get .You can use the definition of a logarithm to write 3x - 1 = 1000.

10. An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e^0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

Answer: 8

For this case we convert the mixed numbers to fractions:

Dwight:[tex]1 \frac {1} {3} = \frac {3 * 1 + 1} {3} = \frac {4} {3} = 1.33[/tex]

Mike:[tex]3 \frac {1} {5} = \frac {5 * 3 + 1} {5} = \frac {16} {5} = 3.2[/tex]

It is observed, that in fact, Mike takes more time to travel the road.

We subtract to know how much more time it takes Mike:

[tex]\frac {16} {5} - \frac {4} {3} = \frac {48-20} {15} = \frac {28} {15}[/tex]

So, Mike takes [tex]\frac {28} {15}[/tex] hours more than Dwight to walk the road.

Answer:

Mike takes[tex]\frac {28} {15}[/tex]hours longer than Dwight to walk the road.

It takes Mike 2.4 times as long to walk the trail as it takes Dwight to run it.

To determine how many times as long it takes Mike to walk the trail as it takes Dwight to run it, we first need to convert the mixed numbers into improper fractions.

Dwight takes: 1 ÷ 1÷3 hours. Converting to an improper fraction:
1 ÷ 1÷3 = 4÷3 hours

Mike takes: 3 ÷ 1÷5 hours. Converting to an improper fraction:
3 ÷ 1÷5 = 16÷5 hours

Next, we find the ratio of the time it takes Mike to walk the trail to the time it takes Dwight to run the trail:

Ratio = (Time taken by Mike) \ (Time taken by Dwight)
= (16÷5) ÷ (4÷3)
= (16÷5) * (3÷4)
= (16 * 3) ÷ (5 * 4)
= 48÷20
= 2.4

It takes Mike 2.4 times longer to walk the trail than it does for Dwight to run it.

Answer: The wavelength increases

Step-by-step explanation:

As frequency increases, wavelength decreases. Frequency and wavelength are inversely proportional. This basically means that when the wavelength is increased, the frequency decreases and vice versa.

Hope that this helps! Have a great day!

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &3 \end{cases} \\\\\\ A=6500e^{0.06\cdot 3}\implies A=6500e^{0.18}\implies A\approx 7781.91[/tex]

Question 1:

For this case we have that the function [tex]f (x) = \frac {5x} {x ^ 2-25}[/tex] is undefined or discontinuous where the denominator equals 0.

[tex]x ^ 2-25 = 0\\x ^ 2 = 25\\x = \pm \sqrt {25}\\x_ {1} = + 5\\x_ {2} = - 5[/tex]

Thus, the function is undefined or discontinuous at +5 and -5.

To find the zeros of the function we match the function to zero and clear "x":

[tex]\frac {5x} {x ^ 2-25} = 0[/tex]

Factoring the denominator, taking into account that the roots are -5 and +5:

[tex]\frac {5x} {(x + 5) (x-5)} = 0[/tex]

We multiply by[tex](x + 5) (x-5)[/tex]on both sides of the equation:

[tex]5x = 0\\x = 0[/tex]

ANswer:

Discontinuity: + 5, -5

Zero: x = 0

Question 2:

For this case we propose a system of equations:

x: Be the variable that represents the yellow fish

y: Be the variable that represents the green fish

[tex]x = y-6\\x = 0.4 (x + y)[/tex]

We manipulate the second equation:

[tex]x = 0.4x + 0.4y\\x-0.4x = 0.4y\\0.6x = 0.4y\\y = \frac {0.6} {0.4} x\\y = 1.5x[/tex]

We substitute in the first equation:

[tex]x = y-6\\x = 1.5x-6\\x-1.5x = -6\\-0.5x = -6\\x = \frac {-6} {- 0.5}\\x = 12[/tex]

So, we have 12 yellow fish in the aquarium.

[tex]y = 1.5 * 12\\y = 18[/tex]

So, we have 18 green fish.

Answer:

12 yellow fish

18 green fish

Answer:

[tex]7x^3-2x^2-5[/tex]

Step-by-step explanation:

We need to add the two terms.

[tex](6x^3+3x^2-2)+(x^3-5x^2-3)[/tex]

Solving,

Combine the like terms and adding those terms

[tex](6x^3+3x^2-2)+(x^3-5x^2-3)\\=6x^3+3x^2-2+x^3-5x^2-3\\=6x^3+x^3+3x^2-5x^2-2-3\\=7x^3-2x^2-5[/tex]

So, the answer is:

[tex]7x^3-2x^2-5[/tex]

Answer:

x=5

Knowing that the length of the rectangle is 9, we can simply multiply this by 2 since there are two sides that will equal the same. This gets us 18. If we subtract that from 28, we get 10. There are four sides in a rectangle, meaning we have two sides left. This leaves us to divide 10 by two to get a final answer of the width of the retangle being 5 centimeters.

The value of x, which represents the width of the rectangle, can be found by inserting the given length and perimeter into the perimeter formula of a rectangle, P = 2L + 2W. Then, solve for W to get the value of x.

The first step to solve this problem is to understand the formula for the perimeter of a rectangle. This formula is P = 2L + 2W, where P is the perimeter, L is the length and W is the width. We know that the length (L) is 9 cm and the perimeter (P) is 28 cm based on the problem given. We are looking to find the value for x which represents the width (W).

Let's substitute the given values into the formula:
28 = 2(9) + 2W.

This simplifies to:
28 = 18 + 2W.

Now, let's solve for W by subtracting 18 from both sides of the equation:
10 = 2W.

To isolate W, divide both sides of the equation by 2:
W = 5
So, the value of x, which represents the width of the rectangle, is 5 cm.

https://brainly.com/question/32610670

#SPJ2

Answer:

x³ - 6x² + 18x - 10

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= x³ - 2x² + 12x - 6 - (4x² - 6x + 4)

= x³ - 2x² + 12x - 6 - 4x² + 6x - 4 ← collect like terms

= x³ - 6x² + 18x - 10

Answer:

1/5 or 20%

Step-by-step explanation:

Since the customer ordered a cold drink, that reduces our sampling population to 25 (8 + 12 = 5).

Out of those 25 people, 5 ordered a large size.

So, the probability that someone who has ordered a cold drink ordered a large one is 5 out of 25...

P = 5 / 25 = 1/5 or 20%

[tex]\text{Hey there!}[/tex]

[tex]\text{Question reads: What was the sensitive, well-insulated tool Willard F.}[/tex] [tex]\text{ Libby used to date artifacts with known ages?}[/tex]

[tex]\bf{Choices\downarrow}\\\bf{A) X-ray\ machine}\\\bf{B) Richter\ Scale}\\\bf{C)Geinger-Muller\ tubes}\\\bf{D)Petri\ dish}[/tex]

[tex]\boxed{\boxed{\bf{Answer: C. Geiger-Muller\ tubes}}}\checkmark[/tex]

[tex]\text{Your explanation}\downarrow[/tex]

[tex]\text{The people of the University of Berkeley were succeeding to make a(n)}[/tex] [tex]\text{energy to make the interest for the atomic energy force.}[/tex][tex]\text{. Some people thought this was delicate to handle.}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

C. Geiger-Müller tubes

Step-by-step explanation:

Geiger-Müller tubes was the sensitive, well-insulated tool Willard F. Libby used to date artifacts with known ages.

Answer:

  100 lbs

Step-by-step explanation:

Let x represent the number pounds of $60 coffee that should be used to create the mix. The total cost of the mix will be ...

  60x + 90·50 = 70(x+50)

  60x +4500 = 70x +3500 . . . . simplify

  1000 = 10x . . . . . . . . . . . . . . . . subtract 3500+60x

  100 = x . . . . . . . . . . . . . . . . . . . divide by 10

The merchant should use 100 pounds of the $60 coffee.

_____

The cost of the mix parts and the total mix is figured from ...

  (dollars/lb)×(lbs) = dollars

Answer:

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

Step-by-step explanation:

Find the volume of the large cone and the volume of the small cone. The subtract the small volume from the large volume.

Large cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(9 in.)^2(15 in.)

V = 405pi in.^3

Small cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(3 in.)^2(5 in.)

V = 15pi in.^3

Difference in volumes:

volume of part = 405pi in.^3 - 15pi in.^3 = 390pi in.^3

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

Answer:

The correct answer is option B.  -18

Step-by-step explanation:

It is given an expression : 3 × (50 – 62) ÷ 2

To find the answer we have to use BODMAS principle

BODMAS means that the order of operations

B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and  

S - Subtraction

To find the correct option

Step 1: Do the bracket first

3 × (50 – 62) ÷ 2 =  3 × (-12) ÷ 2

(Multiplication and division are in the order of appearance)

Step 2: Multiplication  

3 × (-12) ÷ 2 = -36  ÷ 2  

Step 3 : Division

-36 ÷ 2 = -18

The correct option is option B.  -18

Answer:

=-18

Step-by-step explanation:

3×(50-62)÷2

Using PEMDAS,  we first evaluate the parentheses. 50-62=-12

The new expression becomes

3×⁻12÷2

We now perform the multiplication in the order in which they occur.

3×-12=-36 and -36÷2= -18

=-18

Answer:

[tex]\large\boxed{b.\ 15.3}[/tex]

Step-by-step explanation:

[tex]-\dfrac{x}{17}=-0.9\qquad\text{multiply both sides by (-17)}\\\\(-17\!\!\!\!\!\diagup^1)\left(-\dfrac{x}{17\!\!\!\!\!\diagup_1}\right)=(-17)(-0.9)\qquad{/(-)(-)=(+)/}\\\\x=15.3[/tex]

Answer:

d

Step-by-step explanation:

Answer:

Option d

Step-by-step explanation:

Consider the parent function y =sinx which has amplitude 1 and period 2pi.

Compare this with out graph passing through 3 points given as

(0.5,5) (1.5,-15) and (0,5)

Since maximum value is 5 and min value is -15 amplitude = 1/2 (20) = 10

Also period =2 instead of 2pi.

Hence pi must be coefficient for x

Also the curve does not pass through origin but passes through (0,-5)

So vertical shift of 5 units down.

Hence the curve equation is

[tex]y=10sin \pi x -5[/tex]

Answer:

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where h, k an r are real numbers that can be added at the end.

First, to get to the general form of a circle, you have to expand the binomials. Meaning,

[tex](x-h)^2=x^2-2xh+h^2[/tex] and

[tex](y-k)^2=y^2-2yk+k^2[/tex].

After you do this, then the h^2, k^2, and r^2 terms can be added together to give you one number. Then put everything else in descending order, like this:

[tex]x^2+y^2-(2h)x-(2y)k+(h^2k^2r^2)=0[/tex]

It's very hard to describe when there are no values assigned to the h, k, and r in the equation.

Basic idea:

Expand the binomials and add like terms, setting the whole thing equal to 0.

ANSWER

(0,2)

EXPLANATION

The mapping point A has coordinate (0,2).

We want to find the coordinates of this point after a rotation of -90° about the origin.

In other words, we want to find the image of this point after a rotation of 90° anticlockwise.

The rule is

[tex](x,y) \to( - y,x)[/tex]

This implies that

[tex](2,0) \to(0,2)[/tex]

Answer:

3 (cos 93 + i sin 93)

Step-by-step explanation:

We are to find the cube roots of the following:

27 (cos 279° + i sin 279°)

[tex](cosx + i sin x) = cos (nx)) + i sin (nx)[/tex]

[tex]27 \times (cos 279+i sin 279)\frac{1}{3} =27\frac{1}{3} \times (cos 279+i sin 279)\frac{1}{3}[/tex]

Simplifying this to get:

[tex]3\times (cos279+i sin279)\frac{1}{3}[/tex]

[tex]3\times(cos 279+i sin 279)13=3(cos \frac{279}{3} +i sin \frac{279}{3})[/tex]

We know that [tex]\frac{279}{3}=3[/tex]

So, cube root = [tex]3(cos 93 + i sin 93)[/tex]

Answer:

Probability of selecting someone who doesn't watch ABC 16/45 or 35.56%

Step-by-step explanation:

There are a total of 45 people in the survey.  Of those 45, the number that doesn't watch ABC is 12 + 4 = 16.  So the probability is 16/45.