I can use the arithmetic sequence formula to find the nth term.I can write an arithmetic sequence equation to represent an arithmetic sequence.I can graph an arithmetic sequence function.An arithmetic sequence is a sequence of numbers in which the difference between each term is constant.There is a formula we can use to work with arithmetic sequences (explicit):.Qr =, +(n-1)-110nth term1st termTerm NumberDifference between termsSequence: 0, 4, 8, 12, ...A. Is this an arithmetic sequence? Why or why not? (2 points)B. If so, use the Explicit Formula above to create an equation to find the nth term. (13 points)C. Find the 18th term. (5 points)

Answer:

Probability that the measure of a segment is greater than 3 = 0.6

Step-by-step explanation:

From the given attachment,

AB ≅ BC, AC ≅ CD and AD = 12

Therefore, AC ≅ CD = \(\frac{1}{2}(\text{AD})\)

                                  = 6 units

Since AC ≅ CD

AB + BC ≅ CD

2(AB) = 6

AB = 3 units

Now we have measurements of the segments as,

AB = BC = 3 units

AC = CD = 6 units

AD = 12 units

Total number of segments = 5

Length of segments more than 3 = 3

Probability to pick a segment measuring greater than 3,

= \(\frac{\text{Total number of segments measuring greater than 3}}{Total number of segments}\)

= \(\frac{3}{5}\)

= 0.6

Answer:

$48.30

Step-by-step explanation:

the other answer's start is correct.

30% discount of $20 is 30/100*20 = $6

so, a shirt costs now only $14.

but sales tax is always calculated from the actual sales price. not from the original list price.

so, we need to calculate 15% of $14 (and not $20) as sales tax.

=> 15/100*14 = $2.10

a shirt now costs incl. sales tax $14 + $2.10 = $16.10

three shirts cost 3 * $16.10 = $48.30

It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.

Answer:

−x+5

Step-by-step explanation:

Answer:

-x + 5

Step-by-step explanation:

-2x + x = -x

10 -5 = 5

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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Answer:

I'd say 4 because there is 32 miles in 8 hours there would be 4 moles per hour 32÷8=4

9514 1404 393

Answer:

Step-by-step explanation:

The area can be decomposed into a rectangle and a trapezoid.

The rectangle is 2' by 5', so has area ...

  A = LW

  A = (5 ft)(2 ft) = 10 ft²

The trapezoid has bases 8 ft and 5 ft, and height 4 ft, so its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(8 ft +5 ft)(4 ft) = 26 ft²

Then the total area of the figure is ...

  total area = 10 ft² +26 ft² = 36 ft²

__

The slant side of the trapezoid is the hypotenuse of a triangle with sides 3 and 4. The Pythagorean theorem tells us its length is ...

  c = √(a² +b²) = √(3² +4²) = √25 = 5

The perimeter of the figure is the sum of the side lengths. Working clockwise from the top, that sum is ...

  P = 5 + 4 + 2 + 2 + 5 + 2 + 5 + 5 = 30 . . . feet

The perimeter of the figure is 30 feet.

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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Answer:

x should be less than or equal to -5. in other words anything below -5

Step-by-step explanation:

Answer:

The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.

Step-by-step explanation:

The point estimate is the sample proportion.

Sample proportion:

103 out of 249, so:

\(p = \frac{103}{249} = 0.4137\)

The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.

Total number of people = 500

Let X denote the universal set.

Then n(X) = 500

Number of people who like tea = 285

Let T denote the number of people who like tea.

Then n(T) = 285

Number of people who like coffee = 195

Let C denote the number of people who like coffee.

Then n(C) = 195

Number of people who like lemon juice = 115

Let L denote the number of people who like lemon juice.

Then n(L) = 115.

We are given that the number of people who like tea and coffee is 45.

⇒ n(T ∩ C) = 45

We are also given that the number of people who like tea and juice is 70.

⇒ n(T ∩ L) = 70

Also, given that the number of people who like juice and coffee is 50.

⇒ n(L ∩ C) = 50

Given that 50 people do not like any drinks.

⇒ n(T U C U L)' = 50

n(T U C U L)' = n(X) - n(T U C U L)

⇒ 50 = 500 - n(T U C U L)

⇒ n(T U C U L) = 500 - 50 = 450

⇒ n(T U C U L) = 450

We have to find out how many people like all three drinks.

That is to find: n(T ∩ C ∩ L)

n(T U C U L) = n(T) + n(C) + n(L) - n(T ∩ C) - n(C ∩ L) - n(L ∩ T) + n(T ∩ C ∩ L)

⇒ 450 = 285 + 195 + 115 - 45 - 50 - 70 + n(T ∩ C ∩ L)

⇒ 450 = 595 - 165 + n(T ∩ C ∩ L)

⇒ 450 = 430 + n(T ∩ C ∩ L)

⇒ n(T ∩ C ∩ L) = 450 - 430

⇒ n(T ∩ C ∩ L) = 20

Therefore, the number of people who like all three drinks is 20.

Also, we need to find how many people like only one drink.

That is to find the sum: S = n(T only) + n(C only) + n(L only)

n(T only) = n(T) - n(T ∩ C) - n(L ∩ T) + n(T ∩ C ∩ L)

⇒ n(T only) = 285 - 45 - 70 + 20

⇒ n(T only) = 285 - 115 + 20

⇒ n(T only) = 170 + 20

⇒ n(T only) = 190

n(C only) = n(C) - n(T ∩ C) - n(L ∩ C) + n(T ∩ C ∩ L)

⇒ n(C only) = 195 - 45 - 50 + 20

⇒ n(C only) = 195 - 95 + 20

⇒ n(C only) = 120

n(L only) = n(L) - n(L ∩ C) - n(T ∩ L) + n(T ∩ C ∩ L)

⇒ n(L only) = 115 - 50 - 70 + 20

⇒ n(L only) = 115 - 120 + 20

⇒ n(L only) = 135 - 120

⇒ n(L only) = 15

Therefore, S = n(T only) + n(C only) + n(L only)

⇒ S = 190 + 120 + 15

⇒ S = 325

Therefore the number of people who like only one drink is 325.

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is is 169.47058823 yes this the anser

Thank you for asking this question. Here is your answer:

We will consider the price of the truck to be $x

And the amount of tax in the percentage would be 13%

13/100

= $ 0.13x (this is the actual amount of the tax)

Now we will calculate the total price of the truck =

$x + $ 0.13x

= $ x(1 + 0.13)

If there is any confusion please leave a comment below.

Answer:

(a) Null Hypothesis, \(H_0\) : \(\mu\) = 24  

    Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 24  

(b) The​ P-value is 0.004.

(c) Reject Upper H 0 because the​ P-value is less than the alpha = 0.01 level of significance.

(d) There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Step-by-step explanation:

We are given that a simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x overbar = 18.3 and the sample standard deviation is found to be s = 6.3.

Let \(\mu\) = population mean

(a) Null Hypothesis, \(H_0\) : \(\mu\) = 24      {means that the population mean is 24}

Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 24     {means that the population mean is different from 24}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean = 18.3

            s = sample standard deviation = 6.3

            n = sample size = 15

So, the test statistics =  \(\frac{18.3-24}{\frac{6.3}{\sqrt{15} } }\)  ~ \(t_1_4\)

                                    =  -3.504

The value of t-test statistics is -3.504.

(b) Now, the P-value of the test statistics is given by;

               P-value = P( \(t_1_4\) < -3.504) = 0.002 or 0.2%

For the two-tailed test, the P-value is calculated as = \(2 \times 0.002\) = 0.004 or 0.4%.

(c) Since the p-value of the test statistics is less than the level of significance as 0.002 < 0.01, so we will reject our null hypothesis.

(d) This means that we have sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Using proportions, it is found that the total amount budgeted for entertainment is of $720.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching the problem on the internet, it is found that the day trip amount is 10% of the budget for entertainment, hence:

0.1x = 72

x = 72/0.1

x = 720.

Hence the total amount budgeted for entertainment is of $720.

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

- 30 is the answer

Step-by-step explanation:

5 multiply 6 - 60​

5 × 6 - 60

= 30 - 60

= - 30

They are the congruency rule of triangles that means either all 3 sides of triangle should be congruent or two angle and one side should be congruent or one angle and two side should be congruent.

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle.

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Note that the characteristic solutions to this ODE are \(e^{-2x/5}\) and \(e^{2x}\), so we can safely assume a particular solution of the form

\(y_p=(ax+b)e^{3x}\)

with derivatives

\({y_p}'=ae^{3x}+3(ax+b)e^{3x}=(3ax+a+3b)e^{3x}\)

\({y_p}''=3ae^{3x}+3(3ax+a+3b)e^{3x}=(9ax+6a+9b)e^{3x}\)

Substitute these expressions into the ODE and solve for a and b. Notice that each term on either side contains a factor of \(e^{3x}\), which we can cancel.

\(-\dfrac54(9ax+6a+9b)+2(3ax+a+3b)+(ax+b)=3x\)

\(-\dfrac{17a}4x-\left(\dfrac{11a}2+\dfrac{17b}4\right)=3x\)

\(\implies\begin{cases}-\frac{17a}4=3\\\frac{11a}2+\frac{17b}4=0\end{cases}\)

\(\implies a=-\dfrac{12}{17}\text{ and }b=\dfrac{264}{289}\)

So the particular solution is

\(y_p=\left(-\dfrac{12x}{17}+\dfrac{264}{289}\right)e^{3x}=\boxed{\dfrac{12}{289}(22-17x)e^{3x}}\)

Answer:

There are 4 significant figures in the number 4105

Hope this helps!

Mark me brainliest if I'm right :)

Answer:

4 significiant figures

Step-by-step explanation:

please mark this answer as brainliest

Answer: 8:10, 8 to 10, 8/10

Step-by-step explanation:

Answer:

Shen has $15, Brian has $45, and Melissa has $25

Step-by-step explanation:

Let x represent how much money Shen has.

Since Brian has 3 times what Shen has, his amount can be represented by 3x.

Since Shen has $10 less than Melissa, Melissa's amount can be represented by x + 10.

Create an equation to represent the situation, and solve for x:

x + 3x + x + 10 = 85

5x + 10 = 85

5x = 75

x = 15

So, Shen has $15 in their wallet.

Find how much Brian has by multiplying this by 3:

15(3) = $45

Find how much Melissa has by adding 10 to this:

15 + 10 = $25

Shen has $15, Brian has $45, and Melissa has $25.

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

384x² - 486xy²

Step-by-step explanation:

I think this is the answer all I did us first i solved the brackets then I multiplied them by 6x

The number of chapters Junita could have read are 6 chapters.

The number of pages in those chapters are 8.

Since all the chapters are the same length, the number of chapters read must be a factor of 48. The factor of a number is the number that divides a number equally without leaving any remainder. For example, a factor of 20 is 10.

Factors of 48 that are greater than 5 but less 10 = 6 and 8

Number of pages if 6 chapters are read = 48 / 6 = 8 pages

Number of pages if 8 chapters are read = 48 / 8 = 6 pages

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Given that:

the number of 1-inch thick books = x

the number of 2-inch thick books= y

Total number of stacked books = 9

The height of the stacked books = 14 inches

First equation:

Since the total number of stacked books is 9, the addition of the 1-inch thick books and 2-inch thick books must equal 9.

That is,

Second equation

The height of the stack of books is 14

The height of the 1-inch books =

The height of the 2-inch books =

Since the total height of the stacked books is 14, the addition of the height of the 1-inch and 2-inch books must be 14.

That is,

Therefore, the system of equations that can be used to determine x and y is

Option H is correct

\(\huge\text{Hey there!}\)

\(\mathsf{25x^2=49}\)

\(\textsf{DIVIDE by 25 to BOTH SIDES}\)

\(\mathsf{\dfrac{25x^2}{25}=\dfrac{49}{25}}\)

\(\textsf{Cancel out: }\mathsf{\dfrac{25}{25}}\textsf{ because it gives you 1}\)

\(\textsf{Keep: }\mathsf{\dfrac{49}{25}}\textsf{ because it helps us solve for x}\)

\(\textsf{New equation: }\mathsf{x^2 = \dfrac{49}{25}}\)

\(\textsf{TAKE the SQUARE ROOT}\)

\(\mathsf{x\pm \sqrt{\dfrac{49}{25}}}\)

\(\mathsf{\sqrt{\dfrac{49}{25}}= 1.4}\)

\(\mathsf{- \sqrt{\dfrac{49}{25}}= -1.4}\)

\(\boxed{\boxed{\large\text{Answer: \huge \bf x = 1.4 or x = -1.4}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

$12

Step-by-step explanation:

Let's assume that buns cost x and cakes y dollars

Now, let's write two equations according to the given information and put them in a system:

\(5x + 7y = 52\)

\( \frac{y}{x} = 3\)

From the 2nd equation: y = 3x

Replace y in the 1st equation:

\(5x + 7 \times 3x = 52\)

\(5x + 21x = 52\)

\(26x = 52\)

\(x = 2\)

We found the price of one bun

Since we know that one cake costs thrice as much as a bun, we can find the price of one bun:

y = 3 × 2 = 6

Now multiply this number by 2 and we'll get the answer

2 × 6 = $12

Cost Of 2 Cakes = $12

━━━━━━━━━━━━━━━━━━━━━━

Let ::

Cost Of Bun = $x

Cost Of Cake = $3x

ㅤ

Then ::

Cost Of 5 Buns = $5x

Cost Of 7 Cakes = $(7 × 3x) = $21x

ㅤ

Atq ::

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{5x + 21x = 52}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{26x = 52}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{x = \cancel{\dfrac{52}{26}}}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; :\longmapsto{\underline{\boxed{\orange{\frak{x = 2}}}}} \; \pmb{\bigstar} \\ \\ \end{gathered}\)

ㅤ

➔ Cost Of Bun = $2

➔ Cost Of Cake = $(3 × 2) = $6

ㅤ

Now ::

\(\begin{gathered} \\ \; \; \sf{Cost \; Of \; 2 \; Cakes:-} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{\${(6 \times 2)}}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; :\longmapsto{\underline{\boxed{\frak{ \: \: \$ \: {12} \: \: }}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}\)

\(\bf{\pmb{\underline{\rule{170pt}{5pt}}}}\)