what is the first term, common difference, and 16th term

The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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anwser

4

Step-by-step explanation:

17

Answer:

B. Domain is left to right so the left point is solid on 2 and the right is solid on 8. The solid point means it can also be equal to.

Answer:

B) {x : 2 \(\leq\) x \(\leq\) 8 }

Step-by-step explanation:

The function of the graph's x values are between 2 and 8, but the dots at the ends of the function are closed, hence the answer is

2 \(\leq\) x \(\leq\) 8

Answer:

Perpendicular

Step-by-step explanation:

2x-10y=14

-2x        -2x

-10y=14-2x

/-10      /-10

y=14+1/5

in order for them to be perpendicular the slope has to be the complete opposite to be more exact the number has to be flipped and so does the sign and since -5 was flipped to +1/5 it shows that they would be perpendicular

( sorry if this doesn't make sense, its hard to explain it virtually.)

This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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A = P(1 + r/n)^(nt) Where: A is the future value

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

For each scenario:

a) Quarterly compounding:

P = $10,000, r = 0.08 (8% as a decimal), n = 4 (quarterly compounding), t = 5 years

A = 10,000(1 + 0.08/4)^(4*5) ≈ $14,693.28

b) Monthly compounding:

P = $10,000, r = 0.08, n = 12 (monthly compounding), t = 5 years

A = 10,000(1 + 0.08/12)^(12*5) ≈ $14,804.84

c) Annual compounding:

P = $10,000, r = 0.08, n = 1 (annual compounding), t = 5 years

A = 10,000(1 + 0.08/1)^(1*5) = $14,693.28

Therefore, the future values of the investments are approximately $14,693.28 for both the quarterly and annual compounding scenarios, and approximately $14,804.84 for the monthly compounding scenario.

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The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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The correct answer is \(F \vee ( E \wedge M )\)

Given statement:

Either fortune favors the foolish, or love is eternal and life is meaningless.

Key:F= Fortune favors the foolish.

E = Love is eternal.

M = Life is meaningless.

Translation:    \(F \vee ( E \wedge M )\).

Therefore, the correct Translation is \(F \vee ( E \wedge M )\)

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The alternating series error bound is 0.05.

Firstly, let us recall what the alternating series means. An alternating series is a series whose terms are alternatively positive and negative. Mathematically, an alternating series is represented as:

s = a1 - a2 + a3 - a4 + a5 - ...

Where a1, a2, a3, ... are positive real numbers.

Now, let us suppose that the alternating series converges to a limit s. In that case, we know that the sequence of partial sums {Sn} converges to s as well. Mathematically, we can represent this as:

lim n→∞ Sn = s

In the question, we are given the values of the partial sum for four values of n. Let us suppose that these values are:

s2 = 2

s4 = 3.1

s6 = 3.45

s8 = 3.55

Therefore, we know that |a9| is less than or equal to |a8|. Mathematically, we can represent this as:

|a9| <= |a8|

Therefore, the alternating series error bound is given by:

|s - s8| <= |a9| <= |a8|

Now, to determine the error bound, we need to find the value of |a8|. To do this, we can use the fact that:

a8 = s9 - s8

From the values given in the table, we know that s9 = 3.6. Therefore,

|a8| = |s9 - s8| = |3.6 - 3.55| = 0.05

This means that if we use s8 to approximate the value of the series, the actual value of the series is within 0.05 of the approximation.

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Answer:

52⁰

Step-by-step explanation:

x⁰=52⁰ ( vertical opposite angles ) (V.O.A)

(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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The cost of the carpet is $526.75

What is the area of any shape?

The area of a shape is a measure of the size of the region occupied by the shape. The formula for finding the area of a shape depends on the specific shape being considered

Based on the information given:

The carpet costs $1.75 per square foot

Get the area of the carpet

Area = 24(7) + 7(15) + 0.5(28) + 0.5(28)

Area of the composite figure = 273 + 28

Area of the composite figure = 301 ft²

Cost of the carpet = 301 * 1.75

Cost of the carpet = $526.75

Hence, the cost of the carpet is $526.75

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Answer:  the Coat is $526.75

Answer: 3x+120

Step-by-step explanation:

(3x−1)=3x−1

=3x−1+90+31

Add the numbers: −1+90+31=120= 3x+120

I couldnt solve x because the problem isnt complete so i simplfied the equasion. Hope this helps :). I would really apreciate brainliest if not that alright.

Have a great day!

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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Answer:

A

7

B

14

Step-by-step explanation:

As

n

C

4

,

n

C

5

,

n

C

6

are in A.P., so

n

C

4

+

n

C

6

=

2

n

C

5

⇒

1

+

n

C

6

n

C

4

=

2

×

n

C

5

n

C

4

⇒

1

+

n

!

4

!

(

n

−

4

)

!

n

!

6

!

(

n

−

6

)

!

=

2

×

n

!

4

!

(

n

−

4

)

!

5

!

(

n

−

5

)

!

n

!

⇒

1

+

(

n

−

4

)

(

n

−

5

)

6

×

5

=

2

×

(

n

−

4

)

5

⇒

30

+

n

2

−

9

n

+

20

=

12

n

−

48

⇒

n

2

−

21

n

+

98

=

0

⇒

(

n

−

7

)

(

n

−

14

)

=

0

∴

n

=

7

,

14

Answer:

(4i+1)^2

4i^2 + 2(4i) + 1

16(-1) + 8i + 1

-15+8i

8i-15

(x+1) + (x-2)(x+3)

(x+1) + (x^2-2x+3x-6)

(x+1)+x^2+x-6

x+1+x^2+x-6

x^2+2x-5

Let me know if this helps!

Answer:

Step-by-step explanation:

if it's talking about between the numbers 75 to 97, then it's 22.

Answer:

second number = - 28

Step-by-step explanation:

let the first number be x and the second number y , then

x + y = - 18 , that is

10 + y = - 18 ( subtract 10 from both sides )

y = - 28 , that is

the second number is - 28

Answer:

Step-by-step explanation:

The equation that represents the situation is -28 + 10 = -18

The second number is -28.

The perimeter of a rectangle is calculated using the formula:

The question gives that the length and width of the rectangle are equal. This means that:

Therefore, the perimeter will be calculated to be:

The perimeter is given to be 32 m. Therefore, the length of the rectangle will be:

Using the formula for the area:

Therefore, the area will be:

The area is 64 square meters.

Answer:

-2

Step-by-step explanation:

-8 + |-6|

|-6| = 6

so you put 6 instead of |-6|

-8 + 6 which equals -2.

:D

The standard form of the polynomial 2m-3m²+4m⁵+21 is 4m⁵ - 3m² + 2m + 21.

The standard form of a polynomial is when the polynomial is written with the terms in descending order of degree, with each term having a coefficient and an exponent. To convert the given polynomial 2m-3m²+4m⁵+21 to standard form, we need to rearrange the terms in descending order of degree.

The degree of a term is the exponent of the variable in that term. For example, the degree of the term 4m⁵ is 5, and the degree of the term -3m² is 2.

So, we start by arranging the terms in descending order of degree:

4m⁵ - 3m² + 2m + 21

Next, we can simplify the coefficients of each term if possible. In this case, all of the coefficients are already simplified, so we leave them as they are.

In summary, to convert a polynomial to standard form, we arrange the terms in descending order of degree and simplify the coefficients of each term if possible. This makes it easier to compare and manipulate polynomials, and is often required when solving equations or finding roots of polynomials.

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The selling price of the DVD that has a cost of 15 dollars is 19 dollars and 50 cents.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

A store owner paid $15 for a DVD.

He marked up the price of the DVD by 30%.

The cost price is $15.

Then the selling price will be given as

Selling price = 15 × 1.3

Selling price = $19.50

The selling price is 19 dollars and 50 cents.

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There are at least two ways of doing that.

First one is just to find those roots: x² + 2x - 8 = x² + 2x + 1 - 9 = (x + 1)² - 3² = (x+1+3)(x+1-3) = (x+4)(x-2). α = 2; β = -4; α⁴+β⁴= 16 + 256 = 272.

The second way is a bit nore interesting, and you can easily evaluate this even if the roots are "bad" (irrational or complex, for example). What we should do now is to use Vieta's formulas: we know that α + β = -2 and αβ = -8. Now we can find that (α + β)² = (-2)² = 4 = α² + β² + 2αβ; since αβ = -8, 2αβ = -16. α² + β² - 16 = 4; α² + β² = 20; α²β² = (αβ)² = 64. (α² + β²)²= 20² = 400 = α⁴ + β⁴ + 2α²β²; 2α²β² = 128; α⁴ + β⁴ = 400 - 128 = 272. It lead us to the same answer.

Answer:

α⁴ + β⁴ = 272

Step-by-step explanation:

To find the value of α⁴ + β⁴, we can use Vieta's formulas, which relate the coefficients of a polynomial to its roots.

Vieta's formulas state that for a quadratic polynomial of the form ax² + bx + c, with roots α and β, the following relationships hold:

    \(\bullet \quad \textsf{Sum of the roots:} \quad \alpha + \beta=-\dfrac{b}{a}\)

    \(\bullet \quad \textsf{Product of the roots:} \quad \alpha \beta=\dfrac{c}{a}\)

For the polynomial f(x) = x² + 2x - 8, the coefficients are:

As f(x) has roots α and β, then according to Vieta's formulas:

\(\alpha + \beta = -\dfrac{2}{1}=-2\)

\(\alpha \beta=\dfrac{-8}{1}=-8\)

Using the identity a² + b² = (a + b)² - 2ab, we can rewrite α⁴ + β⁴ in terms of (α + β) and αβ:

\(\begin{aligned}\alpha^4 + \beta^4 &= (\alpha^2)^2 + (\beta^2)^2\\&=(\alpha^2+\beta^2)^2-2\alpha^2\beta^2\\&=((\alpha + \beta)^2 - 2\alpha \beta)^2-2(\alpha\beta)^2\end{aligned}\)

Substitute the values of (α + β) = -2 and αβ = -8:

\(\begin{aligned}\alpha^4 + \beta^4 &=((-2)^2 - 2(-8))^2-2(-8)^2\\&=(4+16)^2-2(64)\\&=(20)^2-128\\&=400-128\\&=272\end{aligned}\)

Therefore, α⁴ + β⁴ = 272.

\(\hrulefill\)

The other method we can use is to find the zeroes of the polynomial by factoring the quadratic:

\(\begin{aligned}f(x)&=x^2+2x-8&\\&=x^2+4x-2x-8\\&=x(x+4)-2(x+4)\\&=(x-2)(x+4)\end{aligned}\)

Set the factored quadratic to zero, and solve for x:

\(\begin{aligned}(x-2)(x+4)&=0\\\\x-2&=0 \implies x=2\\x+4&=0 \implies x=-4\end{aligned}\)

Therefore, the zeroes of the polynomial are 2 and -4.

If α and β are the zeroes, then α = 2 and β = -4. Therefore:

\(\begin{aligned}\alpha^4+\beta^4&=2^4+(-4)^4\\&=16+256\\& = 272\end{aligned}\)

Answer:

-7

Step-by-step explanation:

Since we have two points, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 20-6)/(-6- -4)

    = ( 20-6)/ ( -6+4)

    = 14/-2

    = -7

Answer:

-3(3 - 10x)

-9 - 10x*-3

-9 + 30x

The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.

In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.

The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.

By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.

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Answer:

6/11

Step-by-step explanation:

Since there are 3 possible outcomes for the game (win,lose and draw) and the total probability for the three outcomes must be equal to 1.

Then;

The probability that the game will be a draw Pd = 1 - (probability that they will lose Pl + probability that they will win Pw)

Pd = 1 - (Pl + Pw) ........1

Given;

Pl = 3/11

Pw = 2/11

Substituting the values into equation 1;

Pd = 1 - (2/11 + 3/11)

Pd = 6/11

The probability that the game will be a draw Pd = 6/11

The equation in slope-intercept form to model the cooking time in minutes, y, for x patties is y = (3/2)x + 1.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given,  On a box of chicken patties state that one patty should be cooked for 2.5 minutes in the microwave.

If more than one patty is cooked, an additional 1.5 minutes should be added per patty.

So,  The equation in slope-intercept form to model the cooking time in

minutes, y, for x patties.

If we write this as y = 1.5x + 2.5 and put x = 0 , y = 2.5 which is not satisfying the given statement.

∴ y  = 1.5x + (2.5 - 1.5). (the additional patty cooking time).

y = 1.5x + 1.

y = (3/2)x + 1.

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Answer:

b

Step-by-step explanation:

4(45)+3(5)=195

the graph increases when the values ​​in y are increasing

we must mention the part of x where the function increases

so

Increassing:

because the graph is increasing from a very small number to the number 1

the graph decreases when the values ​​in and are less and less

we must mention the part of x where the function decreasing

so

Decreasing:

because the graph starts to decrease from the number 1 to a very large number

the range is the part of y that the graph uses, from the lowest point to the highest

Range:

because the smallest number is a very small number and the largest number that takes in y is 2