The first term of a linear sequence is 3 and the 8th term is 31. find the common difference​

Answer:

Step-by-step explanation:

1. (4x5) is 20

2. (4x 2) is 8

3. 20 plus 8 is 28

4. 28= 4x (5+n)

5. isolate n by dividing 4 on both sides= 28/4= 4+n

6. subtract 4 on both sides to get 7-4=n

7. n=3

Answer: $26.99

Step-by-step explanation:

53.98/2=26.99

Therefore , the solution of the given problem of median comes out to be

confidence interval = [ 51.708 , 64.558 ].

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

(48, 51, 65, 71, 61, 45, 48, 72, 74, 66, 43, 47, 70, 66, 45) sample data; sample mean, x = 58.133; sample size, n = 15; standard deviation, s = 11.6;

Standard deviation equals sd/√(n)

where, n = sample size and sd = standard deviation

Margin of error is equal to t alpha/2 and the standard error is (11.6/√( (15)) = 2.995. (standard error)

where ta/2 is the t-table level of significance, alpha is 0.05 from the standard normal table, the two-tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145, and the margin of error is 2.145 * 2.995, which equals 6.425. The confidence interval for this margin of error is [58.133 6.425] = [51.708, 64.558].

being that,

sample data: (48 , 51 , 65 , 71 , 61 , 45 , 48 , 72 , 74 , 66 , 43 , 47 , 70 , 66 , 45 )

sample mean, x =58.133

standard deviation, s =11.6

sample size, n =15

level of significance, alpha = 0.05

from standard normal table, two tailed  value of |t alpha/2| with n-1 = 14 d.f is 2.145

we use CI = x ± t a/2 * (sd/ √((n))

where,

x    = mean

sd   = standard deviation

a    = 1 - (confidence level/100)

ta/2 = t-table value

CI   = confidence interval

confidence interval = [ 58.133 ± t a/2 ( 11.6/ sqrt ( 15) ]

= [ 58.133-(2.145 * 2.995) , 58.133+(2.145 * 2.995) ]

=  [ 51.708 , 64.558 ]

Therefore , the solution of the given problem of median comes out to be

confidence interval = [ 51.708 , 64.558 ].

To know more about median , visit

brainly.com/question/28060453

#SPJ1

Using the values for x and y and substituting these values in the expression of equations provided, The answer is 23 and 1728.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.

x=3 and y=4

[tex]x^2 + 2(x+y)\\=3^2 + 2* (3+4)\\=9+2*7\\=9+14\\=23[/tex]

[tex](xy)^3\\=(3*4)^3\\=12^3\\=1728[/tex]

To learn more about equations visit:

brainly.com/question/29657983

#SPJ1

Reason:

There are 6 sides to the number cube. It gives 6*6*6 = 216 ways to roll three such dice. Only one of those ways has the sequence "1,1,1" that we're after. Therefore, the probability is 1/216.

It roughly approximates to 0.0046296; which is about a 0.46% chance of happening.

This all assumes that each side is equally likely. The answer will be different if the die is loaded in some fashion.

Answer:

x=18

Step-by-step explanation:

brainliest?

By altering schedules without giving adequate notice, terminating employees without giving adequate notice, and making false claims about its products, company x is not adhering to best practises.

These include bar codes, ISBNs, ASCII codes, postal codes, and bank account numbers; many of these contemporary codes use a checking mechanism, also known as a check digit. The ISBN system, now used uniformly on all new books, is one illustration of this.

Adopting sensible company procedures and policies with reference to apparently contentious issues is referred to as practicing business ethics. Corporate governance, market manipulation, bribery, racism, social duty, and fiduciary responsibilities are a few of the topics that come up in an ethical discussion.

To know more about business ethics visit:

https://brainly.com/question/14971689

#SPJ1

Answer:

The first one is right...

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

top triangels 3 x4 = 12

Side triangels 1 x 5 = 5

the squer   4x 5 = 20

20 +5 +12= 37

Answer:

Step-by-step explanation:

20 inches i think

4

- + 2 = x = 10

5

this is how i see it..... 4 5ths plus 2 equals 10

Answer:

She needs a sample size of 25.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.68}{2} = 0.16[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.16 = 0.84[/tex], so Z = 0.995.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population SD is 2 grams.

This means that [tex]\sigma = 2[/tex]

What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?

She needs a sample size of n.

n is found when M = 0.4. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.4 = 0.995\frac{2}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = \frac{0.995*2}{0.4}[/tex]

[tex](\sqrt{n})^2 = (\frac{0.995*2}{0.4})^2[/tex]

[tex]n = 24.8[/tex]

Rounding up:

She needs a sample size of 25.

Answer:

m = number of minutes calls

Plan A : 30 + 0.15 m

Plan B: 16 + 0.20 m

For what amount of calling do the two plans cost the same?

30 + 0.15m = 16 + 0.20m

0.05m = 14

m = 280

280 minutes of calling, the two plans cost the same

What is the cost when the two plans cost the same?

Plan A: 30 + 0.15 m = 30 + 0.15 (280)  = 72

Plan B: 16 + 0.20 m = 16 + 0.20 (280) = 72

It's cost $72 when the two plans cost the same

Answer:

[tex]20\ln(5)-16\approx16.18876[/tex]

Step-by-step explanation:

[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]

Answer:

Yes

Step-by-step explanation:

If a right triangle, then the Pythagorean theorem will show an equality of the sum of the squares of the two shorter legs equal to the square of the longest leg.

does 39² + 80² = 89² ?

1521 + 6400 = 7921, yes

it is a right triangle

Answer:

A

Step-by-step explanation:

Volume of the solid = base x width x height = 36 x 36 x 24 = 31 104 in^3

Volume of one prism = total volume / 12 = 31 104 / 12 = 2592 in^3

Answer:

Their monthly house payment is of $2,184.65.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

A family buys a new home for $212,500 and pays a 20% down payment ($42,500).

This means that the loan is of 212,500 - 42,500 = $170,000, that is, [tex]P = 170,000[/tex]

Value of the loan in 15 years:

15 years means that [tex]t = 15[/tex]

5.75% interest means that [tex]r = 0.0575[/tex]

Compounded yearly, so [tex]n = 1[/tex]

Then

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(15) = 170000(1 + \frac{0.0575}{1})^{15}[/tex]

[tex]A(15) = 393237[/tex]

Monthly payment:

Total of $393,237 in 15*12 months. So

[tex]M = \frac{393237}{15*12} = 2184.65[/tex]

Their monthly house payment is of $2,184.65.

Answer: hello your question is incomplete attached below is the complete question

answer :  

a) 85.0

b) 27.4

c)  (82.26,   87.74 )

Step-by-step explanation:

Given data :

95% confidence interval

x ( mean ) = 85

s = 8.8

n ( sample size ) = 42

using t-distribution

a) calculate the point estimate

The point estimate = 85.0  given that a sample mean is the same as a point estimate of the sample population

b) calculate the Margin of error

df = 42 - 1 = 41

∝ = 0.05

critical value ( T ∝/2 , 41 ) = 2.02

hence ; margin of error  ( E )

=    2.74 ( using margin of error calculator )

c) The 95% confidence interval

 = 85 ± 2.74

(82.26,   87.74 )

A rational function is the algebraic expression y = 2 / x. (Correct choice: A)

Rational functions are algebraic expressions, whose form is described below:

R(x) = P(x) / Q(x)

Where:

Please notice that Q(x) must be a polynomial whose grade is greater than zero.

Polynomials are algebraic expressions of the form:

P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.

Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.

To learn more on rational functions: https://brainly.com/question/8177326

#SPJ1

Answer:

x<-35

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

26+20

The ladder is 26ft long, there is still 20ft to go, so 20+26

Answer:

2cot²(x)

Step-by-step explanation:

The simplified expression for cot²x/1+cot²x,  cos²x.

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

Given, A trigonometric function [tex]\frac{cot^2x}{1 + cot^2x}[/tex],

Now, Using different trig identities we have,

[tex]= \frac{cot^2x}{cosec^2x}[/tex]

[tex]= \frac{\frac{cos^2x}{sin^2x}}{\frac{1}{sin^2x}}[/tex]

[tex]= {\frac{cos^2x}{sin^2x}}\times\frac{sin^2x}{1}[/tex].

= cos²x.

learn more about trig identities here :

https://brainly.com/question/19549073

#SPJ7

Answer:

y - 1 = 3/2 (x + 10)

Step-by-step explanation:

Point-slope form of the equation of a line is a fill-in-the-blank shortcut to write an equation. If you know a point and the slope of a line you can fill in that info and voila! you have the equation.

Here is Point-slope equation:

y - Y = m(x - X)

Because the point given (-10,1) is in the form (X,Y), fill in -10 for X and 1 for Y.

The slope given is 3/2, fill that in for m.

y - Y = m(x - X)

y - 1 = 3/2 (x - -10)

y - 1 = 3/2 (x + 10)

The equation is

y - 1 = 3/2 (x + 10)

Answer:

J

Step-by-step explanation:

mode = 56

mean = 37.4

median = 35

Answer:

x=77

Step-by-step explanation:A triangle is always 180 degreesin total so u would take 26 away from 180 witch is 154 then devide it as the angles that are left are corresponding angles. Then you dwvide 154 by 2 witch is 77. X=77

Rewriting the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42 is 7(5 + 6).

The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.

The common factor to both 35 and 42 is 7. This will be:

35 + 42 = 7(5 + 6)

Learn more about factor on:

brainly.com/question/25829061

#SPJ1.

Complete question

How do i rewrite the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42

Answer:

1. 1/2, 0.5, 50%

2.1/4, 0.25, 25%

Step-by-step explanation:

1) 1/2 (Fraction), 0.50 (Decimal), and 50%

Explanation: 50 squares are shaded out of the 100 squares. 50 is the numerator and 100 is the denominator, then you just simplify it to get your answer. For the decimal, you just have to divide 50 by 100, and for the percentage, every time the denominator is 100, the numerator will always be the percentage of that fraction.

2) 1/4 (Fraction), 0.25 (Decimal), and 25%

Explanation: 25 squares are shaded out of the 100 squares. 25 is the numerator and 100 is the denominator, then you just simplify it to get your answer. For the decimal, you just have to divide 25 by 100, and for the percentage, every time the denominator is 100, the numerator will always be the percentage of that fraction.

Answer:

1

Step-by-step explanation:

if you put the line of symmetry anywhere else but down vertically it would not work .

Answer:

4.9375 lbs

Step-by-step explanation: