A recursive rule for an arithmetic sequence is a1=−7;an=an-1 Times (1/3)

Answer:

Four brothers and three sisters.

Step-by-step explanation:

Answer:

[tex]\frac{x^6}{3} +\frac{2x^3}{3} +5x+C[/tex]

which agrees with the second answer in your list

Step-by-step explanation:

[tex]\int {2x^5+2x^2+5} \, dx =\frac{2x^6}{6} +\frac{2x^3}{3} +5x+C=\frac{x^6}{3} +\frac{2x^3}{3} +5x+C[/tex]

Answer:

A

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, 0) , thus

y = a(x - 1)² + 0

To find a substitute the coordinates of the y- intercept (0, 1) into the equation

1 = a(- 1)² = a , thus

a = 1

y = (x - 1)² → A

Considering it's y-intercept and vertex, the equation of the parabola is given by:

[tex]y = (x - 1)^2[/tex]

The equation of a quadratic function, of vertex (h,k), is given by:

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

In which a is the leading coefficient.

In this problem, the vertex is (1,0), hence h = 1, k = 0 and:

[tex]y = a(x - 1)^2[/tex]

The y-intercept is of 1, hence, when x = 0, y = 1, so:

[tex]y = a(x - 1)^2[/tex]

[tex]1 = a(0 - 1)^2[/tex]

[tex]a = 1[/tex]

Hence, the equation is:

[tex]y = (x - 1)^2[/tex]

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

Answer:

- How does their confidence level compare to the confidence level of the interval stated above?

Provided all the other parameters involved in the determination of margin of error remains constant, the confidence level of the interval obtained by the second set of researchers (with a larger margin of error) is definitely greater than the confidence of the first stated interval.

- How will the margin of error of the 95% confidence interval constructed based on data from the new survey compare to the margin of error of the interval stated above?

Provided all the other parameters involved in the determination of margin of error remains constant, the margin of error of the confidence interval of data from the new survey will be less than the margin of error of the initially stated interval because the margin of error is inversely proportional to the sample size and the sample size of the new survey (2500) is more than the sample size of the old survey (1155).

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Since the sample sizes are so large, the critical value for this would be obtained from the z-distribution tables.

And critical value increases with higher confidence level.

Which directly translates to margin of error increasing with higher confidence level.

A) Hence, if all other parameters stay the same, the margin of error can only be larger if the confidence level of the second researchers is more than than the confidence level at which the initial research was carried out.

B) In the determination of the margin of error

Margin of Error = (Critical value) × (standard Error of the mean)

Standard error of the mean = σₓ = (σ/√n)

where σ = population standard deviation or sample standard deviation for a sample size that's very large

n = sample size

If the critical value stays the same (the tests in the two years being considered are performed at the same level) and the standard deviation too remain almost the same (the question asks us to assume that the population characteristics, with respect to how much time people spend relaxing after work, have not changed much within a year), the margin of error is obviously inversely proportional to the sample size.

Margin of error = (zσ/√n)

zσ = constant = k

Margin of error = (k/√n)

So, if the sample size increases, the new margin of error that will be obtained will be lesser.

Hope this Helps!!!

Answer:

7

Step-by-step explanation:

Rs 150- Rs 75=Rs 75 remaining

Rs 75/10= 7 as whole

Step-by-step explanation:

given,

total amnt =rs.150

cost of pen= rs.75

now,

left money =150_75

=rs.75

now,cost of 1 copy=10

then , no. of copies=75/10

=7.5

so he can buy 7 copies.

Answer:

9

Step-by-step explanation:

x² − 36 = 5x

x² − 5x − 36 = 0

(x − 9) (x + 4) = 0

x = 9 or -4

Answer:

5+8=13, and  13+8=21, 13+21=34

Step-by-step explanation:

fibonacci sequence...

1+1=2

1+2=3

2+3=5, etc...

sooo,

5+8=13, and  13+8=21, 13+21=34

The missing numbers in the pattern is 13 and 21.

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

The given sequence is 1, 1, 2, 3, 5, 8, __, __, 34, 55.

Here,

1+1=2

1+2=3

2+3=5

3+5=8

5+8=13

8+13=21

13+21=34

21+34=55

Therefore, the missing numbers in the pattern is 13 and 21.

Learn more about the pattern here:

https://brainly.com/question/23136125.

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Answer:

a. The plane's speed in mph is 560

b. At this rate, the plane can travel 5,600 miles in 10 hours.

Step-by-step explanation:

In order to find the planes speed in mph, some simple arithmetic must be done and you should divide 3,360 by 6.   Now that you have determined that 3,360/6 equals 560, you know that in order to figure out how many miles the plane can travel in 10 hours, all you must do is multiply 560 by 10 which equals 5,600.

Answer:

Step-by-step explanation:

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

a

 [tex]z = 6.25 \ cm/yr[/tex]

b

   [tex]k = -0.25 \ cm /yr[/tex]

Step-by-step explanation:

From the first image  the rate of  rate of change of the height from age 8 to 16  

  is  mathematically evaluated from the graph as  

             [tex]z = \frac{175 - 125}{16-8}[/tex]

            [tex]z = 6.25 \ cm/yr[/tex]

From the first image  the rate of  rate of change of the height from age 60 to 80.

  is  mathematically evaluated from the graph as

             [tex]k = \frac{175 - 170}{60-80}[/tex]

            [tex]k = -0.25 \ cm /yr[/tex]

Answer:

Step-by-step explanation:

For private Institutions,

n = 20

Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public Institutions,

n = 20

Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.

The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.

We would set up the hypothesis. The correct option is

-B. H0: μ1 = μ2 ; H1: μ1 > μ2

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

We would determine the probability value from the t test calculator. It becomes

p value = 0.000065

Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.

Answer:

Step-by-step explanation:

When the variation is inverse, the product of values is a constant:

  f·L = k = (400)(11) = 4400

  f = 4400/L

Then a 10-inch string will vibrate with a frequency of ...

  f = 4400/10 = 440 . . . cycles per second

Answer:

L= 4400/f

440 cycles per second

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

Even numbers on a 6-sided die are 2, 4, and 6.

3 numbers out of 6 are even.

3/6 = 1/2

0.5 = 50%

Answer:

Z = -2.054 and Z = 2.054

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Middle 96%

The normal distribution is symmetric, so:

From the: 50 - (96/2) = 2nd percentile

To the: 50 + (96/2) = 98th percentile

2nd percentile:

Z with a pvalue of 0.02. So Z = -2.054.

98th percentile:

Z with a pvalue of 0.98. So Z = 2.054.

Z = -2.054 and Z = 2.054

Answer:

Step-by-step explanation:

Ron needs to lose 35 kgs in order to be 105 kgs. 35000 grams equals 35 kgs. Divide 35000 by 500 and you get 70 weeks.

To double check it, 500 grams equals 0.5 kgs. 0.5*70=35. This equation represents weight lost per week*time=total weight loss.

The explaination might not be the best but I hope it helped you:)

Answer:

  62.3538

Step-by-step explanation:

There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.

Answer:

The probability that he requires 18 shots is 0.04785

Step-by-step explanation:

To answer this, we shall be using the negative binomial distribution

From the question;

P = 0.25 , r = 6

q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial

P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)

P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785

Answer:

a = 5

b = 1.3

c = 6.3

Step-by-step explanation:

To find the values of a, b and C respectively, let's find a first by recalling that the diagonals of a rhombus are perpendicular to each other.

Therefore, the angle given as (14a + 20) = 90°

Solve for a

14a + 20 = 90

14a = 90 - 20

14a = 70

a = 70/14

a = 5

==>To find b, also recall that all sides of a rhombus are equal.

Therefore 3b + 4 = 13b - 9

Solve for b

4 + 9 = 13b - 3b

13 = 10b

13/10 = b

b = 1.3

==>Find value of c

c = a + b

c = 5 + 1.3

c = 6.3

Answer:5.52 or -4. 52

Step-by-step explanation:

Answer:

y=x-1

Step-by-step explanation:

since the slope is just one up and one over and it's positive it would just be x

and since the intercept is just -1 it would be y=x-1

Answer:

Systematic sampling is used.

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

Every 14th CD.

So systematic sampling is used.

Answer:

Q1 is: 2.2 percent per minute

Q2 is: 35 minutes

Step-by-step explanation:

For the first question, take 89 percent, and subtract 23 from it, then divide by 30 minutes for the rate per minute.

For the second question take 23 percent, find out how much is left until 100 percent (77 percent) and use the rate from the last question (2.2 percent per minute), to find out how much time charging 77 percent takes. (You get 35 by using: 77 divided by 2.2)

Answer:

[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]

Step-by-step explanation:

hello,

first of all let's assume that r is different from 0 as this is not allowed to divide by 0

[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]

multiply by 13r it comes

[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]

now multiply by 15

[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]

hope this helps

Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....

Step-by-step explanation:

[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]

[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex]    =-104/15

simplify

[tex]r=-\frac{104}{15}[/tex]

MARK BRAINLIEST PLEASE

Answer:

150 Degrees

Step-by-step explanation:

The angle next to the 30 deg. is the same angle as x because the lines are parallel.

So we do 180 - 30 = 150

So x = 150

Answer:

B. 150

Step-by-step explanation:

Opposite angles are equal so 180-30=150. Points A X D and C add up to 180 degrees.

Hope this helps!!

Answer:

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Step-by-step explanation:

Data given

20 13 21 18 19 22 19 15 12 12 18 21

We can calculate the sample mean and deviation with the following formulas:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And we got:

[tex]\bar X = 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=3.61 represent the sample standard deviation

n=12 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=12-1=11[/tex]

Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]

Now we have everything in order to replace into formula (1):

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Answer: The value of the test statistic is z= 1.63 .

Step-by-step explanation:

Test statistic for proportion :

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

, where p =population proportion.

[tex]\hat{p}[/tex] = sample proportion

n= sample size.

Let p be the proportion of chips do not fail in the first 1000 hours of their use.

As per given, we have

[tex]p=0.41\\ n= 1600\\\hat{p}=0.43[/tex]

Then, required test statistic would be

[tex]z=\dfrac{0.43-0.41}{\sqrt{\dfrac{0.41(1-0.41)}{1600}}}\\\\=\dfrac{0.02}{\sqrt{0.0001511875}}\\\\\approx\dfrac{0.02}{0.0123}\approx1.63[/tex]

Hence, the value of the test statistic is z= 1.63 .

Answer:

x=2

Step-by-step explanation:

5(2x - 3) = 5

Divide by 5

5/5(2x - 3) = 5/5

2x-3 = 1

Add 3 to each side

2x-3 +3 = 1+3

2x = 4

Divide by 2

2x/2 = 4/2

x =2

Answer:

x = 2

Step-by-step explain:

5(2x-3) = 5

Divide both sides by 5

2x-3 = 1

Add 3 to both sides

2x = 4

Divide both sides by 2

x = 2

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: production cost of a major move

Its average is μ= 65 million dollars, and standard deviation σ= 18 million dollars.

a)

This variable has a normal distribution X~N(μ;σ²)

X~N(65;324)

b)

The distribution of the sample mean has the same shape as the distribution of the variable, but its variance is affected by the sample size:

[tex]\frac{}{X}[/tex]~N(μ;σ²/n) ⇒ [tex]\frac{}{X}[/tex]~N(65;8.3077)

σ²/n= 324/39= 8.30769≅ 8.3077

c)

You have to calculate the probability of a single movie costing between 69 and  66 million dollars, symbolically:

P(66≤X≤69)= (X≤69)-P(X≤66)

You have to use the standard normal distribution to calculate this probability, so first you have to calculate the Z values that correspond to each value of X using: Z= (X-μ)/σ  ~ N(0;1)

Z₁= (69-65)/18= 0.22

Z₂=(66-65)/18= 0.05

Now you look for the corresponding probability values using the standard normal table

P(Z≤0.22)= 0.58706

P(Z≤0.05)= 0.51994

P(66≤X≤69)= (X≤69)-P(X≤66)

P(Z≤0.22)-P(Z≤0.05)= 0.58706 - 0.51994= 0.06712

d)

Now you have to calculate the probability of the average production cost to be between 69 and 66 million. Since the probability is for the average value of the sample, you have to work using the distribution of the sample mean. The values od Z are to be calculated using the formula Z=  ([tex]\frac{}{X}[/tex]-μ)/(σ/√n)

σ/√n= 2.8823

P(66≤[tex]\frac{}{X}[/tex]≤69)= ([tex]\frac{}{X}[/tex]≤69)-P([tex]\frac{}{X}[/tex]≤66)

Z₁= (69-65)/2.8823= 1.387= 1.39

Z₂= (66-65)/2.8823= 0.346= 0.35

P(Z≤1.39)-P(Z≤0.35)= 0.91774 - 0.63683= 0.28091

e)

No

If the variable has an unknown or non-normal distribution, but the sample is large enough (normally a sample n≥30 is considered to be large) you can apply the central limit theorem and approximate the sampling distribution to normal.

I hope this helps!

Answer:

T = 24 so it would be 24x24=576 square units

Step-by-step explanation:

How did we calculate this triangle?

The calculation of the triangle progress in two phases. The first phase is such that we try to calculate all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase is the calculation of other characteristics of the triangle, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

Answer: NO, class limits and class marks are not meaningful to qualitative data.

Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.

Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.

Answer:

D(4,-3)

Step-by-step explanation:

Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)

Let the coordinate of the fourth vertex be D(x,y).

We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.

The diagonals are BD and AC

Midpoint of BD = Midpoint of AC

[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]

The coordinates of the fourth vertex is D(4,-3)

Answer:

(4,-3)

Step-by-step explanation: