Having trouble solving this

Answer:

I believe it's 4.5 seconds

Value of  [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.

What do you mean by algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are 3 main types of algebraic expressions which include:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression which is having only one term is known as a monomial.

Given expression:

a + 4/a = 4

We need to simplify the above expression and will find the value of a.

[tex]a+\frac{4}{a}=4[/tex]

⇒ [tex]\frac{a^2+4}{a}=4[/tex]

⇒ [tex]a^{2}+4=4a[/tex]

⇒ [tex]a^2-4a+4=0[/tex]

⇒ [tex]a^2-2a-2a+4=0[/tex]

⇒ a(a-2) -2(a-2) = 0

⇒ (a-2)(a-2) = 0

⇒ a = 2

Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]

[tex]2^5-\frac{1}{2^5}[/tex]

= 32 - 1/32

= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]

Therefore, value of  [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.

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The rate of change between (2,-1) and (-6,-5) is 1/2.

What is the rate of change?

The slope is the ratio of the rate of change between two points (also known as the "slope") to (the change in the x coordinate).

Let (x,y)=(2,-1), (m,n)=(-6,-5)

Rate of change=(n-y)/(m-x)=(-5-(-1))/(-6-2)=1/2.

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The remainder of the division problem given by the image at the end of the answer is as follows:

When a division does not result in an exact term, we have that the quotient is added to the remainder.

A long division problem is represented as follows:

q(x) + (r(x)/b(x))

In which the terms are listed as follows:

In this problem, the division is given as follows:

(x + 1)/x.

Separating the division into two terms, we have that:

(x + 1)/x = x/x + 1/x = 1 + 1/x.

Hence:

The division in this problem is:

(x + 1)/x.

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Answer: B. 1

Step-by-step explanation:

edge 2023

64 unique extensions are there with no repeated digits.

Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged.

For the 3-digit area code, the first digit can be any digit from 2 through 9, and each of the two digits that follow can be any digit from 0 through 9. That's a total of 8 × 10 × 10 = 800 different combinations.

Given:

A school district telephone system has three-digit extensions.

So,  first digit cannot be zero then we have possibility of total 8 digits.

and the last number is a nine.

unique extensions are there with no repeated digits

= 8 x 8 x 1

= 64

Hence, 64 unique extensions are there with no repeated digits.

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a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.

b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.

The link between variables is described by correlation. It can be characterized as strong or weak, as well as positively or negatively.

Given,

The two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a statistics course at a university.

a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.

b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.

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Answer:

y = -4x

b. y = -20.

Step-by-step explanation:

y = kx

-8 = 2k

k = -8/2

k = -4

y = -4x

y = kx

y = -4 × 5

y = -20

Answer:

John has 4 pair of jeans.

Hope this helps : )

Step-by-step explanation:

Together they 10, so if Janet has 6 more, we have to subtract.

10 - 6 = 4

Check:

6 + 4 = 10 ✔

A sample should be 47 to be taken if the desired margin of error is two minutes at a 95% level of confidence

Given information:

A medical facility wants to determine the average amount of time each patient spends with a staff member while creating patient appointment schedules. utilize a planned value of seven minutes for the population's standard deviation.

б=7, ME=2

95% Confidence (to the nearest whole number):

For 95% confidence interval z-critical value is z_{c}=1.96. So

n = (z * б /ME )² = (1.96* 7/ 2)= 47.05

The Requried sample size is 47

If the acceptable margin of error is two minutes at a 95% level of confidence, then a sample of 47 should be taken.

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The values of x and y are 3 and 4.

Given:

shows an equilateral triangle with the lengths of its sides given in terms of x and y.

A 4x cm B 3y cm C (x + y + 5) cm

In equilateral triangle all sides are equal:

4x = 3y = x+y+5

4x = 3y

4x - 3y = 0.                            ---------eq(1)

4x = x + y + 5

3x - y = 5.                              ----------eq(2)

solving eq 1  -  eq 2*3 we get,

4x - 3y - 9x + 3y = 0 - 15

-5x = -15

x = 3

4x - 3y = 0

4*3 - 3y = 0

12 = 3y

y = 12/3

y = 4

Therefore The values of x and y are 3 and 4.

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Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.

Cost of both the plans will be equal for 6 movies.

A linear function is defined as a function that has either one or two variables without exponents.

Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.

According to question,

A = 19 + 0.50x and

B = 13 + 1.5x

For costs being equal, we have,

A = B

19 + 0.50x = 13 + 1.5x

x = 6

Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x

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The principal square root of √64 is 8, √100 is 10,√169 is 13, √196 is 14 and √256 is 16.

According to the question,

We have the following information:

1. √64

2. √100

3. √169

4. √196

5. √256

Now, in order to find the principal square root of these numbers, we will express these numbers in the form of the product of numbers then we will find the square root.

1) [tex]\sqrt{64}[/tex]

We have the following expression:

[tex]\sqrt{2*2*2*2*2*2}[/tex]

2*2*2

8

2) [tex]\sqrt{100}[/tex]

[tex]\sqrt{2*2*5*5}[/tex]

2*5

10

3) [tex]\sqrt{169}[/tex]

[tex]\sqrt{13*13}[/tex]

13

4) [tex]\sqrt{196}[/tex]

[tex]\sqrt{2*2*7*7}[/tex]

2*7

14

5) [tex]\sqrt{256}[/tex]

[tex]\sqrt{2*2*8*8}[/tex]

2*8

16

Hence, the principal square root of √64 is 8, √100 is 10,√169 is 13, √196 is 14 and √256 is 16.

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Answer:

Step-by-step explanation:

x² + (x + 2)² = (x + 3)²

x² + x² + 4x + 4 = x² + 6x + 9

x² - 2x - 5 = 0

[tex]x_{1}[/tex] = [tex]\frac{-(-2)+\sqrt{4+20} }{2}[/tex] = 1 + √6 ≈ 1 + 2.45 = 3.45 units

[tex]x_{2}[/tex] = [tex]\frac{-(-2)-\sqrt{4+20} }{2}[/tex] = 1 - √6 < 0 can not be solution of the given problem.

x ≈ 3.4 units

x + 2 ≈ 5.4 units

x + 3 ≈ 6.4 units

Step-by-step explanation:

to create a vertical asymptote (a tangent of the curve in infinity) at x = n we define e.g.

f(x) = 1/(x - n)

the cost x gets to n, the much closer the function gets to 1/0 and infinity.

so, the part to get us the asymptote at x = -4 is

1/(x + 4)

the part to get us the asymptote at x = 2 is

1/(x - 2)

and the part that gives us a zero solution at x = 3 is

(x - 3)

because that is what the point (3, 0) is : when x = 3. then y = 0.

now we only need to multiply all 3 parts to combine them :

f(x) = 1/(x + 4) × 1/(x - 2) × (x - 3)

(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.

Let us pull out the critical elements

Population: Normally distributed with mean of 2870

population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180

As population sigma is known, we do not have apply any corrections

P(xbar < $2500) = ?    

Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.

Ztest = (2500-2870 )/ 180  or -370/180 = -2.055

As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma  being 95.44% to get a close estimate.   If the area between -2 and 2 sigma = .9544 then the area outside = .0456.  Half of this (the amount under the curve LESS THAN -2) would be .0228

Using a calculator or computer for an exact answer we find (using a TI-83/86):

nmcdf(-9E6,2500,2870,180) = .0199

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Answer:

I believe the answer is number 2, which is 20 degrees.

Step-by-step explanation:

When I plugged that number in for x for both of them I got the numbers 81 and 99. Added them together ad they made 180 degrees. Which makes them supplementary.

The type of software should Jace use will be "Entry level accounting system" as his company has 17 employees who work full time. The company has a number of very dedicated clients, and last year they generated $2 million in revenue.

Entry-level accounting includes typical accounting operations such as accounts payables and receivables, as well as basic financial reporting. These are, predictably, among the most affordable items; some sellers even provide an entry-level bundle for free for a brief time as a trial period. Entry-level accounting jobs are the initial level of accounting positions for people who are just starting out in their careers. Accounting Representative, Accounting Executive, Accounting Assistant, Accounting Associate, Entry-Level Accounting Clerk, Staff Accountant, and Bookkeeper are examples of entry-level occupations.

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The number of students in the class after the changes here are 35.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The question tells us that 7 more juniors have joined this class, while 2 seniors have dropped the class. Then the ratio would be 5 : 2 from the question.

This would give us the ratios as

From here we would have to cross multiply

2(3x + 7) = 5(2x - 2)

6x + 14 = 10x - 10

6x - 10x = -10 - 14

- 4x = -24

x = 6

Put the value of x in both equations

3x + 7 = 3 x 6 + 7

= 25

2x - 2 = 2 x 6 - 2 = 10

25 + 10 = 35

The number of students that are in the class is given as 25

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Answer:

After 1 yr P1 = .946 Po

After 2 yrs P = .946 P1 = .946^2 Po

After n yrs P = .946^n Po

.45  = .946^n       What is n needed to drop P to .45 P

log .45 = n log .946

n = log .45 / log .946 = -.347 /-.0241 = 14.4 years

The number of books each boy had based on the 3:1 ratio of the books remaining is 34 books

A ratio is a quantitative expression of the relationship between two values that indicates the relative proportion of each amount.

The initial number of books Ben had = The initial number of books Charlie has

The number of books Ben gave away = 16 books

The number of books Charlie gave away = 28 books

The ratio of the number of books Ben and Charlie had left is 3:1

Let x represent the number of books each of them initially have. Representing the numbers as a ratio gives;

The number of books Ben had left = x - 16

The number of books Charlie had left = x - 28

[tex]\dfrac{x - 16}{(x - 16) + (x - 28)} = \dfrac{3}{3+1}[/tex]

Which gives; [tex]\dfrac{x - 16}{(2\cdot x - 44) } = \dfrac{3}{4}[/tex]

4 × (x - 16) = 3 × (2·x - 44)

6·x - 4·x = 3×44 - 4×16 = 68

2·x = 68

x = 68 ÷ 2 = 34

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The magnitude of earthquake on seismograph will be 3 .

What is seismograph?

A seismograph is a device that measures and records crucial data concerning earthquakes. Electromagnetic sensors in seismographs convert ground vibrations into electrical voltages. Seismograms are records that a seismograph generates and displays .

Main Body:

formula given : M = ㏒₁₀T           where T =1000

substituting the value of T in the formula

M = ㏒₁₀ 1000

M = ㏒₁₀10³

M = 3㏒₁₀           (㏒₁₀Xᵃ = a㏒₁₀)

M = 3                  (㏒₁₀10 =1)

Therefore the magnitude of the earthquake is 3.

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Answer: 3 cups of sugar will be required for 18 cups of flour.

Step-by-step explanation:

1 cup of sugar - 6 cups of flour

2 cups of sugar - 12 cups of flour

3 cups of sugar - 18 cups of flour

I hope this make sense.

The value of the account in the year 2009 will be $682.

The acount's balance, in t years after 1999, can be modeled by the following equation.

In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.

In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.

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-x/y is equivalent to x/-y according to the division rule a/b*d/c=a/b*c/d.

In division, a number is divided, which is an easy operation. In mathematics, division is the division of a sum into equal parts. A group of 20 people, for instance, could be divided into four groups of 5, five groups of 4, and so on. Division's opposite is multiplication. If 3 groups of 4 add up to 12, then 4 are in each group when 12 is divided into 3 equal groups.

According to the division rule a/b/c/d=a/b*d/c, 

=1/(y/-x)

=1*-x/y

=-x/y

-x/y is equivalent to x/-y according to the division rule a/b÷c/d=a/b*d/c.

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The pack of hot dogs that the shopper should buy that would be cheaper is six - pack of hot dogs

If the shopper decided to buy the six-pack of hot dogs for $2.10, their total cost to be able to get 48 hot dogs would be:

= Cost per six pack of hot dogs x ( Number of hot dogs needed / Number of hot dogs in pack)
=2.10 x (48 / 6)

= 2.10 x 8

= $16.80

The cost if the shopper wants the eight pack is:

= 3.12 x (48 / 8)

= $18.72

The shopper should pick the six - pack of hot dogs because it is cheaper.

The rest of the question is:

Which option would be cheaper to the shopper?

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