a box with a square base has length plus girth of 108 in. What is the length of the box if its volume is 2200 in^3?

Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is  less than 0.4

The square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.

For the square root of √0.09

√0.09 = 0.3

Similarly for the square root of √0.16

√0.16 = 0.4

Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.

Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is  less than 0.4

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The probability that the project will be completed before the graduation time is 0.6873.

It should be noted that probability simply means the likelihood of the occurence of an event.

From the table attached, it can be seen that the probability that the project will be completed before the graduation time is 0.6873.

Also, the probability that the project will be completed before the end of week 15 will be 0.3983.

Lastly, the probability that the project will be completed before the end of week 13 will be 0.0203.

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Answer:

300 tarts

Step-by-step explanation:

we must solve this equation by going backwards

3/4 of something (as 1/4 was given away) is 150

150 / 3/4 is what you must do

or

150 * 4/3

that is

200

3/5 was sold so 2/5 was left

2/5 of something is 200

200 / 2/5

200 * 5/2

that is

500

3/5 of that was sold

so

500 * 3/5 is 300

300 tarts were sold

Step-by-step explanation:

I assume this means exactly one wrong number in the 10 attempts.

the probability to get a wrong number is 0.15 (15%).

therefore, the probability to get a correct number is

1 - 0.15 = 0.85

in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :

0.15×0.85⁹ = 0.034742542...

this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.

how many different constellations can we have that way ?

10.

because the wrong number could be given at any of the 10 attempts.

so, the probability to get exactly 1 wrong answer is

10×0.15×0.85⁹ = 0.34742542... ≈ 35%

now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.

the probability to get all 10 numbers correctly is

0.85¹⁰ = 0.196874404... ≈ 20%

and therefore, the probability to get at least 1 number wrong is

1 - 0.196874404... = 0.803125596... ≈ 80%

FYI :

this would be, of course, also the result of we did it the complex way :

the sum of the probabilities of

exactly 1 number wrong

exactly 2 numbers wrong

...

exactly 9 numbers wrong

all 10 numbers wrong

and for each of the cases of n wrong numbers the probability is

(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)

this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.

and again, all this summed up (1 <= n <= 10) is the same as

0.803125596...

The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Now, Let q = probability of giving out wrong number = 15 % = 0.15

And, p = probability of not giving out wrong number = 1 - q

= 1 - 0.15 = 0.75

Hence, For a binomial probability,

P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.

With n = 10 and x = 1, the probability of getting a number wrong

P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹

          = 10(0.15)(0.75)⁹

           = 1.5(0.0751)

           = 0.1126

           = 11.26 %

b. At most one wrong is P(x ≤ 1) = P(0) + P(1)

= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹

= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹

= 0.0563 + 0.01126

= 0.06756

= 6.756 %

≅ 6.76 %

Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

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The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

Sum of vectors in x direction, ∑X = 5 - 1 = 4

Sum of the vectors in y direction, ∑Y = 6 + 14 = 20

Resultant vector = √(∑X² + ∑Y²)

Resultant vector = √(4² + 20²) = 20.4 units

θ = arc tan (ΣY/ΣX)

θ = arc tan (20/4)

θ = arc tan (5)

θ = 78.7⁰

θ ≈ 79⁰

Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

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Answer:

The linear function for the given pts. will be

[tex]y = \frac{ - 22}{3}x + 15[/tex]

Step-by-step explanation:

Hello!

[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]

The graph of the translated function can be seen in the image below.

For a given function f(x), we define a vertical translation of N units as:

g(x) = f(x) + N

Where if N is positive, the translation is upwards. If N is negative, the translation is downwards.

In this case, we have:

y = f(x) - 2

Then we just need to translate the given graph 2 units below, we will get the graph you can see below.

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Using continuous compounding, it is found that the value of r is of r = 7.7%.

The amount of money after t years in continuous compounding is:

[tex]P(t) = P(0)e^{rt}[/tex]

In which:

The doubling time of 9 years means that P(9) = 2P(0), which is used to find r, hence:

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]2P(0) = P(0)e^{9r}[/tex]

[tex]e^{9r} = 2[/tex]

[tex]\ln{e^{9r}} = \ln{2}[/tex]

[tex]9r = \ln{2}[/tex]

[tex]r = \frac{\ln{2}}{9}[/tex]

r = 0.077.

r = 7.7%.

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Answer:

Rounded to the nearest tenth would be 75.5 degrees

Step-by-step explanation:

The surface area of the balloon is 249 in².

A balloon has the shape of a sphere. The distance round the sphere is equal to the circumference of the sphere.

Circumference of the sphere = 2πr

Where:

Radius - circumference / 2π

28 / ( 2 x 22/7) = 4.45 inches

Surface area of a sphere = 4πr²

4 x 22/7 x 4.45² = 249 in²

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Using the normal distribution, the probability is given as follows:

P(x≤81) = 0.0158.

Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

For this problem, the proportion and the sample size are given by:

p = 0.000412, n = 250178

Hence the mean and the standard deviation for the approximation are given by:

The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:

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

[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]

Z = -2.13

Z = -2.13 has a p-value of 0.0158.

Hence:

P(x≤81) = 0.0158.

Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.

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Answer:

  $152,419.36

Step-by-step explanation:

The future value of an ordinary annuity is given by the formula ...

  FV = P((1 +r/12)^(12t) -1)/(r/12)

where P is the monthly payment, r is the annual interest rate, and t is the number of years.

For P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...

  FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36

The value of Jolene's retirement account when she turns 60 will be $152,419.36.

Answer: [tex]y=\frac{1}{2}x+3[/tex]

Step-by-step explanation:

We can solve this by using the point-slope form, which can help get the equation of a line given the slope of the line and a point on the line. Slope-intercept form is the form [tex]y=mx+b[/tex], and we can convert from point-slope form to this with simple algebra.

The point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope of the line, and [tex](x_1,y_1)[/tex] is the point.

We know that the line is parallel to [tex]y=\frac{1}{2}x+2[/tex], which means it will have the same slope. The slope of this line is [tex]\frac{1}{2}[/tex], so the slope of any line parallel to it will also be [tex]\frac{1}{2}[/tex].

[tex]y-5=\frac{1}{2}(x-4)\\y-5=\frac{1}{2}x-2\\y=\frac{1}{2}x+3[/tex]

If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.

Given sample size be 300 and about 5% of the population has a particular genetic mutation.

We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.

Sample size=300

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation=[tex]\sqrt{np(1-p)}[/tex]

Use the known values in the above formula.

Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]

=[tex]\sqrt{14.25}[/tex]

=3.77

Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.

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Answer:

110 [%].

Step-by-step explanation:

if the initial area is 24 m² and final area 50.4 m², then the required percentage can be calculated as:

[tex]\frac{50.4}{24}*100-100=110[/tex] ,  

where 50.4/24*100 - the final percentage.

P.S. It means, the final value of the paint is 3*2.1=6.3 [liters].

Considering the given function, it is found that:

Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.

The function is:

d = 5t².

Hence:

Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.

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Answer:

x = 4

Step-by-step explanation:

Hello!

We can solve for x by expanding the parentheses and isolating x.

The value of x is 4.

Answer:

y = (constant variable x time) + independent variable

y = 60x + 30    ← Health Club B

y = 27x + 50    ← Health Club A

Step-by-step explanation:

I can't see the question at the bottom due to the covering but if you comment I can edit this and give a proper answer. Otherwise this is all I can give you.

The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:

Beginning inventory of finished goods $11,850

Cost of goods manufactured                485,310

Ending inventory of finished goods      (12,670)

Cost of Goods Sold                           $484,490

The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.

The cost of goods sold budget is based on the cost of goods manufactured budget.

Direct materials:                            Enamel        Paint     Porcelain      Total    

Total direct materials purchases

budgeted for September            $35,870    $7,530    $139,890  $183,290

Estimated inventory, September 1   1,730        4,150          6,920      12,800 Desired inventory, September 30 (2,980)      (2,710)         (7,150)    (12,840)

Materials used in production                                                          $183,250

Direct labor cost:           Kiln Department    Decorating Department   Total

Total direct labor cost

budgeted for September    $51,550                   $149,500        $201,050

Finished goods inventories:             Dish       Bowl     Figurine             Total

Estimated inventory, September 1  $5,810   $3,310     $2,730        $11,850

Desired inventory, September 30    3,720    4,590       4,360         12,670

Work in process inventories:

Estimated inventory, September 1      $3,540

Direct materials used in production $183,250

Direct labor costs                              $201,050

Total factory overhead costs             $99,450

Desired inventory, September 30       (1,980)

Cost of goods manufactured           $485,310

Indirect factory wages $80,400

Depreciation of plant and equipment 10,550

Power and light 5,110

Indirect materials 3,390

Total 99,450

Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.

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The preparation of a bank reconciliation statement for Mathers Co. for July is as follows:

At July 31

Cash balance per bank statement as at July 31, $21,110

Deposit in transit                                                     3,260

Outstanding checks                                              (4,060)

Balance as per adjusted cash balance             $20,310

A bank reconciliation statement is a summary of banking and business cash transactions so that their balances can agree.

Bank reconciliations help the company to reconcile its bank account as per bank statements with its internal financial records.

The steps for preparing a bank reconciliation include:

Cash balance per Cash Account at July 31 $20,010

Cash balance per bank statement at July 31, $21,110

Checks outstanding, $4,060

Deposit in transit $3,260

Transposed payment $360 ($840 - $480)

Bank service charges $60

Cash balance per Cash Account as at July 31 $20,010

Transposed payment                                               360

Bank service charges                                               (60)

Adjusted cash balance per cash account       $20,310

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Step-by-step explanation:

Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))

a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The function has a minimum and grows in the + y direction.

d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.

In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:

4 · x² - 7 · x - 15 = 0

4 · [x² - (7 / 4) · x - (15 / 4)] = 0

x² - (7 / 4) · x - (15 / 4) = 0

x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64

x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64

(x - 7 / 8)² = 289 / 64

x - 7 / 8 = ± 17 / 8

x = 7 / 8 ± 17 / 8

Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.

d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.

First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.

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Answer:

C. 8√3

Step-by-step explanation:

* = multiply or times

To find √192 in its simplest form we need to divide it by a square number like 64.

192/64 = 3

√192 = √64 * √3 = 8√3

The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.

It should be noted that inequalities are simply used to compare two expressions that are unequal.

It can be seen that the solution set that's illustrated is:

x² + y² <= 16

-1/4x² + 2 <= y

Therefore, the inequality system that has the solution set shown will be option C.

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Answer:

Step-by-step explanation:

Let r(y)=x.

[tex]x=\frac{2}{3}(4y-5)\\\\\frac{3}[2}x=4y-5\\\\\frac{3}{2}x+5=4y\\\\y=\frac{3}{8}x+\frac{5}{4}\\\\r^{-1}(x)=\frac{3}{8}x+\frac{5}{4}[/tex]

Answer:

$144

Step-by-step explanation:

24*6 = 144

Answer:

x = − 6

Step-by-step explanation:

I have my work