Determine the common ratio and find the next three terms of the geometric sequence. 8, -20, 50, ...

Final answer:

To solve the equation 3w - 4z = 8 for w, add 4z to both sides and then divide by 3, resulting in the expression w = (4z + 8) / 3.

Explanation:

The student's equation, 3w - 4z = 8, involves algebraic manipulation to solve for the variable w. To isolate w, we rearrange the equation to get w by itself on one side of the equation:

Add 4z to both sides to get: 3w = 4z + 8

Divide both sides by 3 to solve for w: w = (4z + 8) / 3

Now we have w expressed in terms of z. This is the solution for w assuming you have a specific value for z you can substitute into this expression.

Final answer:

To find w, isolate it by adding 4z to both sides and then dividing by 3, resulting in w = (8 + 4z) / 3.

Explanation:

To solve for w in the equation 3w - 4z = 8, you would isolate w on one side of the equation. First, add 4z to both sides of the equation so that you have 3w = 8 + 4z. Then, divide both sides by 3 to get w by itself. The final equation representing w would be w = (8 + 4z) / 3. This doesn't directly correspond to the provided physics equations; however, we can apply a similar method of isolating the unknown in those as well.

Answer:

20.25π

Step-by-step explanation:

The circumference (C) of a circle is calculated using the formula

C = 2πr ← r is the radius

given C = 9π, then

2πr = 9π ( divide both sides by 2π )

r = [tex]\frac{9\pi }{2\pi }[/tex] ( cancel the π on numerator/denominator )

  = 4.5

The area (A) of a circle is calculated using the formula

A = πr² = π × 4.5² = 20.25π

ANSWER

The system has one solution.

EXPLANATION

The given system is

1st: 5x-3y=10

2nd: 10x+6y=20

Make y the subject in the first equation to get:

[tex]y = \frac{5}{3} x + \frac{10}{3} [/tex]

Solve for y in the second equationquation to get;

[tex]y = - \frac{5}{3} x + \frac{10}{3} [/tex]

The slope of the two equations are not the same.

The two lines will intersect at exactly one point.

.The system has one solution.

Answer:

One solution

Step-by-step explanation:

We are given the following system of equations and we are to tell if the system has one solution, infinite solution, many solutions or no solutions:

[tex]5x-3y=10[/tex] --- (1)

[tex]10x+6y=20[/tex] --- (2)

If we take the common out from (2), we get:

[tex]2(5x+3y) = 20 [/tex]

[tex]5x+3y = 10 [/tex] --- (3)

So adding the two equations (1) and (3) gives 10x=20 ⇒ x=2.

Therefore, this system of equations has one solution.

A Monte Carlo simulation can be used to answer questions about the type of lunch students will choose.

A simulation that could be used to answer questions about the type of lunch students will choose is a Monte Carlo simulation.

In this simulation, the probability of a student choosing a salad over a grilled chicken sandwich is represented by a random number generator.

Each time the simulation is run, a random number between 0 and 1 is generated, and if the number is less than or equal to 0.33, it is considered a salad choice. This process is repeated multiple times to generate a distribution of lunch choices.

By analyzing the distribution, you can estimate the likelihood of students choosing a salad over a grilled chicken sandwich.

Final answer:

A simulation to model the 33% chance of students choosing a salad over a grilled chicken sandwich could involve a random generator where the number 1 (out of 1 to 3) represents the choice of a salad, simulating the probability accurately.

Explanation:

To simulate the situation where there is a 33% chance that a student will choose a salad over a grilled chicken sandwich for lunch, you could use a simple random process to model this probability. You might simulate the choice by using a random number generator set to generate numbers from 1 to 3, where one of the numbers (say 1) represents choosing a salad, and the other two numbers (2 and 3) represent choosing a grilled chicken sandwich. Every time the number 1 comes up, it would count as a 'success', representing a student choosing a salad. You could run this simulation a large number of times to answer questions about the likelihood of various outcomes related to the students' lunch choices.

Answer:

The simple interest is 3.80% per year.

Step-by-step explanation:

We are presented with a simple interest problem and the following information has been availed;

Accumulated amount = 5503.51

Time = 19 years

Principal = 3196

The first step is to determine the total interest earned over the entire time period;

Interest = Amount - Principal

             = 5503.51 - 3196

             = 2307.51

The simple interest formula states the total interest earned is equal to the product of the principal, the interest rate and the time;

[tex]I=\frac{P*R*T}{100}[/tex]

Making R the subject of the formula yields;

[tex]R=\frac{100*I}{P*T}[/tex]

Substituting the values we have and simplifying;

[tex]R=\frac{100*2307.51}{3196*19}=3.80[/tex]

The simple interest is thus 3.80% per year.

The next term would be -27

Lets pretend that all the negative signs went away, that way you have the data:

2, 5, 9, 14, 20

^^^In my opinion it just makes it easier because I don't like negative numbers. Keep in mind that the negatives are still there but I just made them "Invisible"

The pic below is how I found the pattern. If you can't tell by the picture from 2 to 5 it increases by 3. From 5 to 9 it increases by 4. From 9 to 14 it increases by 5. From 14 to 20 it increases by 6.

This means the pattern is to increase the number 1 more then the amount the previous number was increased (keep in mind this is the pattern for the positive version and therefore the original pattern would be decreasing (since the bigger a number that is negative is, the farther away it gets from zero, therefor getting smaller.) For the original version the rule would be: it would decrease the number 1 more then the amount the previous number was decreased) <<<Hope that makes sense

That means that 20 will be increased by 7 ( 6+ 1 = 7). Which equals 27. Make the negative sign visible again and your answer is -27.

Let me know if this made sense and if it was helpful!

Answer:

r = 6

Step-by-step explanation:

Given that p varies directly as r, then the equation relating them is

p = kr ← k is the constant of variation

To find k use the condition p = 4, r = 2

k = [tex]\frac{p}{r}[/tex] = [tex]\frac{4}{2}[/tex] = 2

p = 2r ← equation of variation

When p = 12

12 = 2r ( divide both sides by 2 )

hence r = 6

To solve any questions relating to ages, I find it easier to make a table, like in the picture below.

See picture for answer and clear diagram.

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Notes/Explanations + answer in written form

Let's say that Halley's age now is:              x

That means that her age in 18 years is:      x + 18

It also means that her age 2 years ago is:   x - 2

In the question, we are told that when Halley is 18 years older that her current age, she will be 5 times the age she was when she was 2 years younger than her current age

That means:

Halley's current age + 18 years = 5 times (Halley's current age - 2 years)

So we get this equation (which we solve to get the answer) :

x + 18 = 5 * (x -2)                       ( expand the brackets)

x + 18 = 5x - 10                           (subtract x from both sides)

18 = 4x - 10                                 (add 10 to both sides)

28 = 4x                                       (now divide both sides by 4)

7 = x

Therefore, Halley's current age is 7 years

If [tex]A^C[/tex] has occurred, then [tex]A[/tex] cannot occur, so the probability is 0.

This follow directly from the definition of conditional probability:

[tex]P(A\mid A^C)=\dfrac{P(A\cap A^C)}{P(A^C)}[/tex]

but [tex]A[/tex] and [tex]A^C[/tex] are disjoint, so the probability of their intersection is 0.

Answer:

B.

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

there are 4 numbers that are less than 5.

1,2,3,4 make a fraction 1/4

which equals 0.25

sorry if this wasn't a good explanation..

Answer:

4/6 = 0.67

Step-by-step explanation:

someone please answer

Answer:

A

Step-by-step explanation:

I did the same test

Answer:

225 feet.

Step-by-step explanation:

15 X 15

it it c becauee I had already learned this

If we have two functions [tex]f \ and \ g[/tex] such that [tex]f(g(x))=x[/tex] for every [tex]x[/tex] in the domain of [tex]g[/tex], and [tex]g(f(x))=x[/tex] for every for every [tex]x[/tex]in  the domain of  [tex]f[/tex]. If we prove this, then [tex]g[/tex] is the invers function of [tex]f[/tex] and denoted by [tex]f^{-1}[/tex]

1. We need to prove whether [tex]f(g(x))=x[/tex]. So:

[tex]f(x)=\frac{4}{5}x+1 \\ \\ g(x)=\frac{5x-5}{4} \\ \\ So: \\ \\ f(g(x))=\frac{4}{5}\left(\frac{5x-5}{4})+1 \therefore f(g(x))=\frac{4}{5}\left(\frac{5x-5}{4})+1[/tex]

[tex]\therefore f(g(x))=x-1+1 \\ \\ \boxed{f(g(x))=x}[/tex]

2. We need to prove whether [tex]g(f(x))=x[/tex]. So:

[tex]g(f(x))=\frac{5(\frac{4x}{5}+1)-5}{4} \\ \\ \\ g(f(x))=\frac{4x+5-5}{4} \\ \\ \\ g(f(x))=\frac{4x}{4} \\ \\ \\ g(f(x))=x[/tex]

Since [tex]f(g(x))=g(f(x))=x[/tex], then:

[tex]f(x) \ and \ g(x)[/tex] are inverses to each other.

Answer:

Step-by-step explanation:

Ratio is a relationship between two numbers indicating how many times the first number contains the the second.

Proportion is a part or share or number considered in comparative relation to whole.

So Ratio and Proportion wouldn't go under the same category.

I hope this would help you!!

Answer:

A) Quadratic

Step-by-step explanation: It has the U shape of a parabola which a quadratic equation has.

Answer:

The correct option is A.

Step-by-step explanation:

In a scatter plot the best fit curve in known as regression curve. Types of regression curves are

1. Linear regression line : If the best fit of a data is a straight line, then it is known as linear regression line.

2. Quadratic regression : If the best fit of a data is a U-shape curve, then it is known as quadratic regression.

3. Exponential regression : If the best fit of a data is an exponential curve, then it is known as exponential regression.

From the given graph it is clear that scatter data forms a U-shaped curve. Since the best fit of a data is a U-shape curve, therefore the quadratic regression model is best for the data.

Thus, option A is correct.

Answer:A

Step-by-step explanation:

80+141+74+4+3+1=303

Answer:A) 303

Step-by-step explanation:

Answer:

[tex]a_{14}=-7[/tex]

Step-by-step explanation:

The given sequence is:

6, 5, 4, 3, 2, . . .

The first term of the sequence is:

[tex]a_1=6[/tex]

The common difference is

d=5-6=-1

The nth term of the sequence:

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_n=6-1(n-1)[/tex]

[tex]a_n=6-n+1[/tex]

[tex]a_n=7-n[/tex]

When n=14

[tex]a_{14}=7-14=-7[/tex]

Answer:

12x

Step-by-step explanation:

add the numbers and then put the variable in front of it

Answer:

3*x

Step-by-step explanation:

Note that 3*x + 9 = 3*x if you choose to put the expression 3*x on the right side of the expression.

To solve this equation, you subtract 3 * x on both sides of the equation, obtaining:

3*x+9-3*x=3*x-3*x

9=0

You get 9 = 0. This expression cannot be true regardless of the value taken by x. You can tell then that in this case the equation has no solution.

Answer:

23 miles

Step-by-step explanation:

Substitute into the formula d = 3 s + 5

We know s = 6 so

d = 3 s + 5

d = ( 3 × 6 ) + 5

d = ( 18 ) + 5

d = 23

Hope this helps :)

Have a great day !

5INGH

Answer:

23 miles

Step-by-step explanation:

Substitute the numbers into d=3s+5.

d=(3×6)+ 5 (d=18+5)

18+5=23

I would say 45 degrees

The whole square is 360 degrees because each corner is a 90 degree angle

Which means each triangle section would be 90 degrees but angle 2 is cut in half, so half of 90 is 45

Hope this helps :)

Answer:

9pi

Step-by-step explanation:

I think it’s D. Because A) and B) are not true and im pretty sure that C) is also false

Answer:

its d

Step-by-step explanation:

Answer:

The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.

Step-by-step explanation:

I assume an x is missing, and the function is h(x) = -3x^2 + 30x + 225

You want to know the number of days in which the function value is zero.

-3x^2 + 30x + 225 = 0

Divide both sides by -3.

x^2 - 10x - 75 = 0

(x - 15)(x + 5) = 0

x - 15 = 0 or x + 5 = 0

x = 15 or x = -5

We discard the negative solution.

Answer: The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.

Answer:

h(x) = -3 (x + 5) (x - 15)

Step-by-step explanation:

h(x) = -3x^2 + 30 + 225

      = -3(x^2 - 10x - 75)

      = -3(x + 5)(x - 15)

      x = -5    x = 15

Answer:

d.  4, 8, 16, 32

Step-by-step explanation:

We'll use the formula  f(x) = 2x  for each iteration.  The output of the first iteration will be come the input of the second iteration, and so on.

So, we start with x0 = 2 and we plug that into the base equation:

x0 = 2 ==> f(x) = 2(2) = 4

x1 = 4 ==> f(x) = 2(4) = 8

x2 = 8 ==> f(x) = 2(2) = 16

x3 = 16 ==> f(x) = 2(2) = 32

x4 = 32 ==> f(x) = 2(2) = 64

Answer:

Step-by-step explanation:

Height:  h(t)= -0.2t^2+2t  =  2t(-0.1t + 1)

-0.2t^2+2t  is  a quadratic expression with a = -0.2 and b = 2.

The ball reaches its max height at t = -b/(2a).

Here, t = -2 / (2·[-0.2] ), or  t = 2/0.4 = 5 (sec)

The ball reaches its max height at at 5 sec.

The max ht. of the ball is h(5) = -0.2(5 sec)^2 + 2(5 sec) = (-5 + 10) sec, or 5 ft.

To determine after how many sec the ball reaches the ground, we set h(t) = 0 and solve for t:  

h(t)= -0.2t^2+2t = 0 = 2t(-0.1t + 1).  Thus, t = 0 sec or t = 10 sec

The ball reaches the ground again after 10 sec.

Answer:

[tex]x=\frac{32}{3}, y=\frac{2}{3}[/tex]

Step-by-step explanation:

We can multiply the second equation by 2 to eliminate.

[tex]2(y-x)=2(-10) \\ \\ 2y-2x=-20[/tex]

Let's eliminate.

[tex]2x-5y=18 \\ -2x+2y=-20 \\ -3y=-2 \\ y=\frac{2}{3}[/tex]

Now we can substitute back into the equation to find the value of [tex]x[/tex].

[tex]\frac{2}{3}-x=-10 \\ \\ \frac{2}{3}-x=-\frac{30}{3} \\ \\ -x=-\frac{32}{3} \\ \\ x=\frac{32}{3}[/tex]

Radius, r = 939 ft

Then:

Diameter, d = 1878 ft

Circumference, C = 5899.9110034416 ft

Area, A = 2770008.2161158 ft^2

AREA = 2770 if you're shortening.

For this case we assume that the moon is spherical. For definition, the surface area of a sphere is given by:

[tex]S = 4 \pi*r ^ 2[/tex]

Where:

A: It is the radius of the sphere

We have that the radius is 939 leagues.

by definition, 1 league is equivalent to 4.82803 kilometers.

ENtonces 939 leagues represent 4533.52 km.

Substituting:[tex]S = 4 \pi * (4533.52) ^ 2\\S = 20552803.5904 * 4 * \pi\\S = 258,274,147.081[/tex]

It has a surface area of 258,274,147 km

ANswer:

258,274.147 km

[tex]\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-3}x\stackrel{\stackrel{c}{\downarrow }}{-7}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-7)}}{2(1)}\implies x=\cfrac{3\pm\sqrt{9+28}}{2}\implies x=\cfrac{3\pm\sqrt{37}}{2}[/tex]

Answer:

A.  x = the quantity of 3 plus or minus the square root of 37 all over 2

Step-by-step explanation:

Answer:

Scale 1 35 ft by 25 ft and Scale 2 56 ft by 40 ft

Step-by-step explanation:

step 1

Find the actual dimensions of a patio with the scale 1

The scale 1 is equal to

1 cm/5 ft

Length=7 cm=7*5=35 ft

Width=5 cm=5*5=25 ft

therefore

The dimensions are 35 ft by 25 ft

step 2

Find the actual dimensions of a patio with the scale 2

The scale 2 is equal to

1 cm/8 ft

Length=7 cm=7*8=56 ft

Width=5 cm=5*8=40 ft

therefore

The dimensions are 56 ft by 40 ft

Answer:

C

Step-by-step explanation:

If Scale 1 is 1 cm:5 ft, multiply 5 and 7 by 5 to get the correct dimensions. 7×5=35 and 5×5=25. If Scale 2 is 1 cm: 8 ft, multiply 5 and 7 by 8 to get the correct dimensions. 7×8=56 and 5×8=40. The answer is: Scale 1: 35 ft by 25 ft; Scale 2: 56 ft by 40 ft.

Hope this helps!