Preeti and Shikha have bookshelves of the same size. Preeti’s shelf is 56 full of books and Shikha’s shelf is 35 full. Whose bookshelf is more full and by how much?

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]

Cheers.

Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

The composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.

In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.

Solving a composite function means finding the composition of two functions.

The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].

The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:

s(t)= q[p(t)]

4t -21= 4[p(t)]³ – 1

Solving:

4t -21 +1= 4[p(t)]³

4t -20 = 4[p(t)]³

(4t -20)÷ 4 = [p(t)]³

4t÷4 -20÷ 4 = [p(t)]³

t -5 = [p(t)]³

[tex]\sqrt[3]{t-5}=p(t)[/tex]

Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

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Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.

Answer:

see details in graph and below

Step-by-step explanation:

There are many ways to generate the function.

We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.

1. f(x) has a local minimum at x = -3, and

2. a local maximum at x = 3

Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.

Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.

f'(x) = -x^2+9

will satisfy the above conditions.

Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.

Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0  so ok.

f(x) can then be obtained by integrating f'(x) :

f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3

A graph of f(x) is attached, and is found to satisfy all three conditions.

A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

Given that:

The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]

The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:

[tex]x = -3[/tex] or [tex]x = 3[/tex]

Equate both equations to 0

[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]

Multiply both equations to give y'

[tex]y' = (3 - x) \times (x + 3)[/tex]

Open bracket

[tex]y' = 3x + 9 - x^2 - 3x[/tex]

Collect like terms

[tex]y' = 3x - 3x+ 9 - x^2[/tex]

[tex]y' = 9 - x^2[/tex]

Integrate y'

[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]

[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]

[tex]y = 9x - \frac{x^3}{3} + c[/tex]

Express as a function

[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(-5) < 0[/tex] implies that:

[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]

[tex]-45 - \frac{-125}{3} + c < 0[/tex]

[tex]-45 + \frac{125}{3} + c < 0[/tex]

Take LCM

[tex]\frac{-135 + 125}{3} + c < 0[/tex]

[tex]-\frac{10}{3} + c < 0[/tex]

Collect like terms

[tex]c < \frac{10}{3}[/tex]

[tex]c <3.33[/tex]

We can then assume the value of c to be

[tex]c=3[/tex] or any other value less than 3.33

Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

See attachment for the function of f(x)

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Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

Answer:

Lori will pay $12 more if she makes monthly payments

Step-by-step explanation:

to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72

subtracting the amount she would pay as a down payment

$72 - $60 is $12

Lori will pay $12 more if she makes monthly payments

Answer: 8

Step-by-step explanation:

Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]

Number of sets of seven marbles include at least one yellow one but no green ones = 8

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

x= 5.5

Step-by-step explanation:

(segment piece) x (segment piece) =    (segment piece) x (segment piece)

x*4 = 11*2

4x = 22

Divide each side by 4

4x/4 = 22/4

x =5.5

Answer:

The question is incomplete, below is a possible match for the complete question:

You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.

(a) If you contribute $200 every month to your 401k, what will your company contribute each month?

The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)

(b) If you contribute $830 every month to your 401k, what will your company contribute each month?

The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)

(c) What is the maximum amount of money the company will contribute to your 401k each year?

The maximum amount that the company will contribute each year is $

(Type an integer or a decimal rounded to two decimal places as needed.)

Answer:

a.) The company will contribute $100

b.) The company will contribute $415

c.) maximum amount the company will be willing to contribute = $6,800 per year

Step-by-step explanation:

First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:

Annual salary = $85,000

Monthly salary = $7083.3333

maximum amount = 8% = 8/100 = 0.08 of salary

maximum amount = 0.08 × 7083.3333 = $566.67

a.) If you contribute $200 every month.

Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:

Company matches 50 cents for every dollar you deposit

1 dollar deposited = 50 cents from company

but 1 cent = $0.01

∴ 50 cents = 0.01 × 50 = $0.5

$1 deposited = $0.5 from company

∴ $200 deposited = 0.5 × 200 = $100 contributed by company

Therefore, if you contribute $200 every month, your company will contribute $100 each month.

from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.

b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:

half of $830 = 830 ÷ 2 = $415

Therefore, if you contribute $830 per month, your company will contribute $415 per month.

c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year

= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]

Therefore, the company will be willing to contribute $6,800 per year.

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

James town is 5 meters higher than Takoradi​ .

Step-by-step explanation:

Given:

Height of James town = 2 meters below sea level

Height of Takoradi town = 7 meters below sea level

To find:

How much higher is James town that Takoradi = ?

Solution:

As we can see the standard of height is how much the town is below the sea level.

So, the height of town having lesser value will be at a higher level.

Value of Height of James town is lesser than that of Takoradi town.

Therefore, James town is at a higher level.

Difference of height = 7 meters - 2 meters = 5 meters

So, the answer is:

James town is 5 meters higher than Takoradi.

Answer:

Step-by-step explanation:

12x - 9 = 8x + 7

4x - 9 = 7

4x = 16

x = 4

solution is C

The solution is Option C.

The value of x is given from the equation x = 4

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as CD

Let the second line be represented as XY

Now , CD is the perpendicular bisector of XY

So , the point F is the midpoint of the line segment XY

The measure of line segment XF = 12x - 9

The measure of line segment FY = 8x + 7

From the perpendicular bisector theorem ,

The measure of line segment XF = The measure of line segment FY

Substituting the values in the equation , we get

12x - 9 = 8x + 7

Subtracting 8x on both sides of the equation , we get

4x - 9 = 7

Adding 9 on both sides of the equation , we get

4x = 16

Divide by 4 on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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Answer:

sine and tangent

will be positive.

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Negative Integers are :

Answer:

(1, -9)  yes

(7,3)  no

(-9,4)  no

(0, -9) yes

Step-by-step explanation:

The y value must be -9

The x value can be any value to satisfy   the equation y = -9

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is  [tex]49.85 < \mu < 54.15[/tex]

This means that there is 95% chance that the true population mean is within this interval

Step-by-step explanation:

From the question we are told that

    The  sample size is n = 30  

    The sample mean is  [tex]\= x = 52[/tex]

    The population standard deviation is  [tex]\sigma = 6[/tex]

Given that the confidence level is 95% then the level of confidence is evaluate as

             [tex]\alpha = 100 - 95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is

                 [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

            [tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]

           [tex]E = 2.147[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]52 - 2.147 < \mu < 52 + 2.147[/tex]

         [tex]49.85 < \mu < 54.15[/tex]

Answer:

1,2 and 6

Step-by-step explanation:

pie symbol

2/3

0.333333....

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]

Given: Mean = 191  and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

Answer:

5x+4f-1(x)=3 this is short answer

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

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

Answer:

The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.

Answer:

Step-by-step explanation:

Initial population of wolf = 850 wolves

If the wolves increases by 7% each year, yearly increment will be 7% of 850

=  7/100 * 850

= 7*8.5

= 59.5 wolves.

This shows that the wolves increases by 59.5 each year.

After 7 years, increment will be equivalent  to 59.5 * 7 = 416.5

The wolf population after 7 years = Initial population + Increment after 7 years

= 850 + 416.5

= 1266.5

≈ 1267 wolves

Hence the population of the wolves after 7 years is approximately 1,267 wolves

Answer:

7

Step-by-step explanation:

it's simply 13 - 6

7 it the answer, that was easy

Answer:

6 lockers have both students' stickers

Step-by-step explanation:

There are 130 lockers in the hallway

Janine goes down a hallway in the school and puts a sticker on every fourth locker.

Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.

Thor goes down the same hallway, putting one of his stickers on every fifth locker

Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.

Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120

Therefore,

6 lockers have both students' stickers