Identify the explicit formula for the sequence given by the following recursive formula:
(see picture below)

A) f(n) = 2 – 4(n – 1)
B) f(n) = –4 + 2(n – 1)
C) f(n) = 4 – 2(n – 1)
D) f(n) = –2 + 4(n – 1)

Answer:

The 4th term of the linear sequence = 3

Step-by-step explanation:

First term, a = -9

Common difference, d = -5 - (-9)

= -5 + 9

= 4

d = 4

The 4th term of the linear sequence = a + (n - 1)d

where,

n = 4

a + (n - 1)d

= -9 + (4 - 1)4

= -9 + (3)4

= -9 + 12

= 3

The 4th term of the linear sequence = 3

12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.

Para que un número sea divisible por 6 debe cumplir dos condiciones.

En este caso tenemos 12,480, que sabemos que es par.

La suma de sus digitos da:

1 + 2 + 4 + 8 + 0 = 15

15 es multiplo de 3.

Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.

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Answer:

Step-by-step explanation:

i donot knpw

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

The amount of money that each person would get for the three days of work is $92.

The first step is to add all the money earned on the three days together. Addition is the process of determining the sum of two or more values.

Total amount earned in the 3 days = amount earned on the first day + amount earned on the second day + amount earned on the third day

= $93 + $75 +$108  =$276

The next step is to divide the total amount of money earned in the three days by the total number of people that would share the money. Division is the process of determining the quotient of a number.

The amount of money gotten by each person = total earnings / total number of people

$276 / 3 = $92

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Answer:

False

Step-by-step explanation:

In the question, it is given a output of a single factor ANOVA analysis. It provided the measure of the effect of the amount of fertilizer on the pH of the soil samples.

pH may be defined as the content of alkalinity or acidity of a solution or the sample on a logarithmic scale. The pH value of 7 is considered to be neutral.

From the data sheet in the context, the p value of the ANOVA analysis is 0.8324. This value is very large value. So the results are not very statistically significant. As the p value is large, therefore, the answer is false.

Answer:

Each Candy Bar is 4 Dollars.

Step-by-step explanation:

The answer is 4 Dollars because first if you subtract 24 by 4 dollars you get 20 then if you divided 20 by 5 you get 4.

Answer:

-y+11

Step-by-step explanation:

Answer:-1y + 11

Step-by-step explanation:

7y + 5 - 8y + 6

-simplify

7y - 8y = -1y

5+6=11

= -1y + 11

Answer:

The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).

Step-by-step explanation:

Before building the confidence interval, we need to understand the Central Limit Theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles.

This means that:

\(p_S = \frac{82}{90} = 0.9111\)

\(s_S = \sqrt{\frac{0.9111*0.0888}{90}} = 0.045\)

Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles.

This means that:

\(p_N = \frac{86}{110} = 0.7818\)

\(s_N = \sqrt{\frac{0.7818*0.2182}{110}} = 0.0394\)

Distribution of the difference:

\(p = p_S - p_N = 0.9111 - 0.7818 = 0.1293\)

\(s = \sqrt{s_S^2+s_N^2} = \sqrt{0.045^2+0.0394^2} = 0.0598\)

Calculate a 99% confidence interval for the difference in the two proportions.

The confidence interval is:

\(p \pm zs\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower bound of the interval is:

\(p - zs = 0.1293 - 2.575*0.0598 = -0.0247\)

\(p + zs = 0.1293 + 2.575*0.0598 = 0.2833\)

The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).

Answer:

142.24$

Step-by-step explanation:

112 = 100% 9x112

/ 100100. = 10.08$

? = 9%

112 = 100% 18x112 /100 =. 20.16$

? = 18%

so.......

112$ + 20.16$ + 10.08$

= 142.24$

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

Answer:

Approximately 68% of students study between 22.9 and 25.7 hours.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 24.3 hours, standard deviation of 1.4 hours.

What percent of students study between 22.9 and 25.7 hours?

22.9 = 24.3 - 1.4

25.7 = 24.3 + 1.4

Within 1 standard deviation of the mean, so:

Approximately 68% of students study between 22.9 and 25.7 hours.

Answer:

The question is not complete

Blocking has reduced the estimate of experimental error from MS = 37.75 to MS = 2.65, a reduction of approximately 93%.

What is statistics ?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, summarize, and analyze data in order to make inferences and draw conclusions about populations based on samples. Statistics is widely used in fields such as science, medicine, business, engineering, social sciences, and many other areas where data are collected and analyzed. The goal of statistics is to provide insights and knowledge that can be used to make informed decisions and solve problems.

a. The sum of squares for the factor is 14.18

b. The number of degrees of freedom for the single factor in the experiment is DF = 1

c. The number of degrees of freedom for error is DF = 22

d. The mean square for error is MS = 37.75

e. The value of the test statistic is F = 0.376

f. If the significance level is 0.05, your conclusions are not to reject the null hypothesis. Yes

g. An upper bound on the P-value for the test statistic is p ≤ 0.05

h. A lower bound on the P-value for the test statistic is p > 0.01

i. Laura used 2 levels of the factor in this experiment

j. Laura replicated this experiment 12 times

k. Reconstructed ANOVA display:

Source DF SS MS F

Factor 1 14.18 14.18 15.97

Blocks 11 12.00 1.09 -

Error 12 31.75 2.65 -

Total 23 58.93 - -

Therefore, blocking has reduced the estimate of experimental error from MS = 37.75 to MS = 2.65, a reduction of approximately 93%.

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Answer:x-(2 7/8)=1/2

Step-by-step explanation:

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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Answer:

473 yd²

Step-by-step explanation:

bottom area = 11x11 = 121 yd²

each of the 4 sides = 11x16x0.5 = 88 yd²

4(88) + 121 = 473 yd²

The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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Answer:

22 cents per mile

Step-by-step explanation:

to get this answer, divide 17.60 by 4 to get the unit rate, or the rate when x=1.

The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

The number of days that this solution will probably last would be = 8 days.

To calculate the number of days the solution will last the following is taken into consideration.

The parameters given which are not in ml should be converted to ml as follows;

2 Oz of Lidocaine to ml = 2×29.6=59.2ml

½tsp of banana flavouring;

= 1/2×4.92

= 2.5ml

Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml

But 2×10 = 1 day

20ml = 1 day

161.7ml = X

Make X the subject of formula;

X = 161.7/20

= 8.1

= 8 days.

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Answer:

49

hope this helps!!

Answer:

Step-by-step explanation:

If you mean √200, you cannot write it as V200.

√200 = √(10²×2) = 10√2

Answer:

B.) 2/10

Step-by-step explanation:

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

Below

Step-by-step explanation:

3.15 can be read as  3 and 15 hundredths =   3   15/100  = 3  3/20

Answer:  63/20

Step-by-step explanation: