Find an explicit rule for the nth term of the sequence.

-3, -15, -75, -375, ...

Answer:

2.4

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer: the answer is 7

Step-by-step explanation:

The side of the larger square is represented by x and the side of the smaller square is represented by y. We are given that the shaded region is 2/27 of the area of the larger square and 3/8 of the area of the smaller square. The side of the larger square is 3/2 times larger than the side of the smaller square.

Let's assume the side of the larger square is represented by x and the side of the smaller square is represented by y. We are given that the shaded region is 2/27 of the area of the larger square and 3/8 of the area of the smaller square.

To find the ratio between the sides of the two squares, we can set up the following equation:

(2/27) * x^2 = (3/8) * y^2

We can simplify this equation by multiplying both sides by the reciprocal of (3/8):

(2/27) * x^2 * (8/3) = y^2

Simplifying further, we have:

(16/81) * x^2 = y^2

Taking the square root of both sides, we get:

(4/9) * x = y

Now, we can see that the side of the larger square (x) is (4/9) times larger than the side of the smaller square (y). In other words, the side of the larger square is 3/2 times larger than the side of the smaller square.

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Answer:

1.33

because you have to divide

6 cm from what im seeing

Answer: 7 cm

Step-by-step explanation:

The power-reducing identity sin^2(x) = 1/2 - 1/2cos(2x) to rewrite sin3(x) as sin(x)sin^2(x). Substituting sin^2(x) with 1/2 - 1/2cos(2x), we get sin3(x) = sin(x)(1/2 - 1/2cos(2x)).  we can write sin3(x) as 1/2sin(x) - 1/2sin(x)cos(2x), which contains only first powers of sine and cosine.

To rewrite sin3(x) in terms containing only first powers of sine and cosine, we can use the power-reducing identity for sine:  sin^2(x) = 1/2 - 1/2cos(2x)
Using this identity, we can rewrite sin3(x) as:
sin3(x) = sin(x)sin^2(x)
= sin(x)(1/2 - 1/2cos(2x))
= 1/2sin(x) - 1/2sin(x)cos(2x)

A power-reducing identity to rewrite sin3(x) in terms containing only first powers of sine and cosine .

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Answer:

In a 45 - 45 - 90 triangle, the legs are equal and the ratio of sides from shortest to longest is 1 : 1 : √2 where 1 are the legs and √2 is the hypotenuse. In this case the leg is 10 / √2 = 5√2.

Answer:

sin=24/=x

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

it will be 5 /3

sec theta will be hypotanus/ Adjacent

Answer:

50,000

Step-by-step explanation:

1st car had $1,750 tax

2nd car has $3,500 tax

1750(2) = 3500

so your tax doubled so the price must be doubled.

The car is $50,000

Algebraically using direct variation:

t = kp    where t=tax, p = purchase price, 

             and k is constant of variation

1750 = 25000k

k = 1750/25000

k = 0.07

Your equation is:  t = 0.07p

3500 = 0.07p

p = 3500/0.07

p = $50,000

Answer:

\(-16\pi\)

Step-by-step explanation:

\(\displaystyle \iint_Rf(x,y)\,dA\\\\=\iint_Df(r\cos\theta,r\sin\theta)\,r\,dr\,d\theta\\\\=\iint_D3\sqrt{r^2\cos^2\theta+r^2\sin^2\theta}\,r\,dr\,d\theta\\\\=\iint_D3r^2\,dr\,d\theta\\\\=\int^\pi_{3\pi}\int^2_03r^2\,dr\,d\theta\\\\=\int^\pi_{3\pi}8\,d\theta\\\\=8\pi-8(3\pi)\\\\=8\pi-24\pi\\\\=-16\pi\)

Inequalities help us to compare two unequal expressions. The correct option is D.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The complete question is:

Which ordered pair makes both inequalities true?

y > –2x + 3

y < x – 2

(0,0)

(0,–1)

(1,1)

(3,0)

For the given inequalities, the graph can be drawn as shown below. Now, if we plot the points on the graph, then the point that will satisfy both the inequalities is (3,0).

Hence, the correct option is D.

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The solution to the equation is x = -2, -1.46, -1, x = 5.46

From the question, we have the following parameters that can be used in our computation:

0 = x^{5}+x^{4}-20x^{3}-68x^{2}-80x-32

Express properly

So, we have

x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0

Next, we plot the graph of x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0 to determine the solution graphically

See attachment for graph

From the graph, we have

x = -2, -1.46, -1, x = 5.46

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Answer:

230

Step-by-step explanation:

230 answer

Answer:  W= -4/3=-1.33333

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

w*(-3)-(-3+7)=0

Pull out like factors :  -3w - 4  =   -1 • (3w + 4)

Solve  :    -3w-4 = 0  

Add  4  to both sides of the equation :  

                     -3w = 4

Multiply both sides of the equation by (-1) :  3w = -4

w = -4/3 = -1.333

Answer:

20

Step-by-step explanation:

16 1/4 ÷ 3.25

16×4=64+1=65

65/3.25=20

Answer:

The answer is 5.

Step-by-step explanation:

you do this by converting the decimal 3.25 into a fraction. This would equal   3 1/4 (simplified) now since that both fractions have the same denominator we can solve by dividing the fractions.  

To find this answer, we need to understand how to get the Volume.

We get the volume by the formula: L x W x H

L = Length

W = Width

H = Height

So, we can see that there are 3 units required to know for getting the volume, if that's true, then, to do the inverse operation of finding the volume. That can be done by using thie formula:

\(V=a^3\)

a= edge

Solving for a

a=V⅓=216⅓=6

now, let's look at how to find whether our answer is right or wrong

6x6=36

36x6=216

So hence, our answer is right!

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The length of a betta fish tank that has a shape of a cube and volume of 216 cubic inches is 6 inches.

A cube has all its sides equal to each other. Therefore,

volume of cube = L³

where

Therefore,

L = >

volume = 216 cubic inches

volume of cube = L³

216 = L³

cube root both sides

∛216 = ∛L³

L = ∛216

L = 6 inches

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Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

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c. The result is the same because the formula is not dependent on the symbols.

The sample correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, x and y. The formula for r is:
r = [ Σ(xy) - n(¯x)(¯y) ] / [ √(Σ(x²) - n(¯x)²) * √(Σ(y²) - n(¯y)²) ]
If we exchange the symbols x and y, the formula remains the same because it calculates the correlation based on the product of deviations, which is symmetric in nature. Exchanging x and y will not alter the correlation value, as the formula itself is not dependent on the specific symbols used. In the computation formula for the sample correlation coefficient, the symbols x and y represent the two variables being analyzed. The formula calculates the correlation between these two variables based on their individual data points.

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We take a look at the reduction in the area of the bacteria.

In the first hour, its arae is 20cm2. Following that, it reduces 1.25x, to 16. Then another 1.25x, from 16 to 12.8. And another 1.25x, from 12.8 to 10.24.

So, every hour, the bacteria's area reduces by 1.25x
Therefore, in the 5th hour (prediction probably if this is all a coincidence), the bacteria's area will be : 10.24 : 1.25 = 8.192 cm2.

Answer:

17) b. commutative property

18) NOT SURE d. associative property

19) NOT SURE d. associative property

20) a. commutative property

The percent of students in grade 8 those who like to join dance club is equal to 25%.

Total number of students in grade 8 = 20

Total number of students of grade 8  join in dance club = 5

Percent of students of grade 8 prefer to join dance club

= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100

Substitute the value in the formula we get,

⇒ Percent of students of grade 8 prefer to join dance club

= ( 5 ) / ( 20 ) × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 0.25 × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 25%

Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.  

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The above question is incomplete, the complete question is:

What percent of students in grade 8 prefer to join a dance club?

                      Dance club      Hiking club     Total

Grade 7               15                       15                 30

Grade 8               5                        15                  20

Total                    20                     30                    50

A statement in the form p→q has three related implications that are called converse, inverse, and contrapositive.

A statement in the form p→q has three related implications.

Statement: If p then q (p→q)

Converse: If q then p (q→p)

Inverse: If not p then not q (-p → -q)

Contrapositive: If not q then not p (-q → -p)

For the given implications, its converse, inverse, and contrapositive can be written as.

Given statement:

(a)  If a quadrilateral is a parallelogram, then its opposite sides are congruent then its converse, inverse, and contrapositive are:

Converse: If a quadrilateral has opposite sides that are congruent then it's a parallelogram.

Inverse:  If a quadrilateral is not a parallelogram then its opposite sides are not congruent.

Contrapositive: If a quadrilateral has opposite sides that are not congruent then it's not a parallelogram.

(b) If two lines do not intersect, then they are parallel:

Converse: If the two lines do not intersect in the same plane, then they are parallel.

Contrapositive: If the two lines intersect in the same plane, then they are not parallel.

(c) If the sky does not look blue, then it is not nighttime:

Converse: If it is not nighttime, then the sky looks blue.

Inverse:  If the sky does not look blue then it is nighttime.

Contrapositive:  If it is nighttime then the sky does not look blue.

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Grant should pay approximately $211.96 today for the annual membership, considering an interest rate of 10% and the option to pay in 12 monthly installments of $55 each.

To determine how much Grant should pay today for the annual membership, we need to calculate the present value of the 12 monthly payments of $55 each, considering an interest rate of 10%.

The present value (PV) can be calculated using the formula:

PV = C * (1 - (1 + r)^(-n)) / r

Where:

C = the monthly payment amount ($55)

r = the monthly interest rate (10% / 12 = 0.00833)

n = the number of payments (12)

Plugging in the values into the formula, we can calculate the present value:

PV = 55 * (1 - (1 + 0.00833)^(-12)) / 0.00833

PV ≈ 55 * (1 - 0.6806) / 0.00833

PV ≈ 55 * 0.3194 / 0.00833

PV ≈ 211.96

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First, let's find how many cups the bird feeder uses 24 times.

24 x 6 = (20 x 6) + (4 x 6) = 120 + 24 = 148 cups.

Now, let's divide 148 by 32.

148 ÷ 32 = 4.625 bags of seed.

I hope this helped!

Answer:

18 bc there a 9 angles and below is is another angle so u do 9 + 9 or 9(2) and u will get 18

P(X)= R(X) - C(X)

Substituing the functions on the P(X) functions:

P(X)=25x-(1500+10x)

P(X)=25x-1500-10x

Solving:

P(x)=15x-1500, The answer would be the third option!

Answer: A 550g box for $10.89

Step-by-step explanation:

Represent each option as grams per dollar

225g / $5.77 = 38.99g / $1.00

550g / $10.89 = 50.51g / $1.00

725g / $16.89 = 42.92g / $1.00

The second option gives the most grams per dollar

Answer:

A) 12

Step-by-step explanation:

Notice that \(\int\limits^5_1 {f(x)} \, dx=-\int\limits^1_5 {f(x)} \, dx\) by the exchange-of-limits property of integrals, so  \(-\int\limits^1_5 {f(x)} \, dx=-1\)

We also know that \(\int\limits^1_{-1} {f(x)} \, dx+\int\limits^5_1 {f(x)} \, dx=\int\limits^5_{-1} {f(x)} \, dx\) by the additivity property of integrals, which means that:

\(\int\limits^1_{-1} {f(x)} \, dx+\int\limits^5_1 {f(x)} \, dx=\int\limits^5_{-1} {f(x)} \, dx\\\\\int\limits^1_{-1} {f(x)} \, dx-\int\limits^1_5 {f(x)} \, dx=\int\limits^5_{-1} {f(x)} \, dx\\\\5-1=\int\limits^5_{-1} {f(x)} \, dx\\\\4=\int\limits^5_{-1} {f(x)} \, dx\)

Therefore, \(3\int\limits^5_{-1} {f(x)} \, dx=3(4)=12\)

Answer:

The probability is 0.97682

Step-by-step explanation:

We start by finding the z-values of the runner times given.

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 13 seconds and SD = 0.3 seconds

So for 12.4 seconds, we have;

z = (12.4-13)/0.3 = -0.6/0.3 = -2

For 14 seconds, we have;

z = (14-13)/0.3= 1/0.3 = 3.33

So the probability we want to calculate is;

P(-2<z<3.33)

We can find this using the standard normal distribution table

Mathematically;

P(-2<z<3.33) = P(z<3.33) - P(z < -2)

Using the standard normal distribution table, the value of this is;

P(-2<z<3.33) = 0.97682