Find secα, if sinα=−2/3 and 3π/2 <α<2π . Also the α=alpha symbol

Answer:

y = |x + 2| + 1

Step-by-step explanation:

Parent Graph: f(x) = a|bx + c| + k

a is vertical stretch/shrink

b is horizontal stretch/shrink

c is horizontal movement left/right

k is vertical movement up/down

Since we are given an equation and we want to move it 1 unit up (vertical movement up), we only manipulate k:

y = |x + 2| + k

k = 1

y = |x + 2| + 1

Answer:

y = |x+2| + 1

Step-by-step explanation:

The equation will be y = |x+2| + 1.

By translating the graph one unit up, the equation will simply change by adding +1 to the graph, outside of the absolute value part.

Answer: You will need 8 cup scales

Step-by-step explanation:

kg=1000 grams

2000/250=8

Answer:

2

Step-by-step explanation:

The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.

Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.

Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).

Slope = rise/run

Slope = 2/1

Slope = 2

Hope that helps.

Answer:

slope=2

Step-by-step explanation:

take two points from graph (0,0) and (1,2)

m=y2-y1/x2-x1

m=2-0/1-0

m=2

Answer: a. $40,800 b. 36

Step-by-step explanation:

Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].

[tex]\sigma= \$14,900[/tex]

a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.

Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]

= 40,800

hence, the point estimate of the mean salary for all college graduates in this town = $40,800

b.  Since  lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.

Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]

Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.

z-value for 99% confidence level  = 2.576

So,

[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]

The sample size used for the analysis =36

Answer:

Hey there!

We can write: -2+9=7.

Let me know if this helps :)

Answer:

[tex]\large \boxed{{-2+9=7}}[/tex]

Step-by-step explanation:

-2 is also 0-2

The arrow goes from 0 to -2.

-2 + 9 = 7

The arrow goes from -2 to 7.

Answer:

[tex]\frac{}{d}[/tex] = −0.26

[tex]s_{d}[/tex] = 0.4219

Step-by-step explanation:

Given:

Sample1:  98.1  98.8  97.3  97.5  97.9

Sample2: 98.7  99.4  97.7  97.1  98.0

Sample 1           Sample 2              Difference d

98.1                        98.7                       -0.6  

98.8                       99.4                       -0.6

97.3                        97.7                       -0.4

97.5                        97.1                         0.4

97.9                        98.0                       -0.1

To find:

Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]

d overbar ( [tex]\frac{}{d}[/tex])  is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5

[tex]\frac{}{d}[/tex] = ∑d/n

 = (−0.6 −0.6 −0.4 +0.4 −0.1) / 5

 = −1.3 / 5

[tex]\frac{}{d}[/tex] = −0.26

s Subscript d is the sample standard deviation of the difference which is calculated as following:

[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1

[tex]s_{d}[/tex] =

√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]

    =  √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −  

                                                                     (−0.26))² + (−0.1 − (−0.26))² / 5−1

=  [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]

= [tex]\sqrt{\frac{0.712}{4} }[/tex]

= [tex]\sqrt{0.178}[/tex]

= 0.4219

[tex]s_{d}[/tex] = 0.4219

Subscript d ​represent

μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.

Answer:

  28) -1

  29) 9

  30) x^2+4x+7

  31) x-2

Step-by-step explanation:

Given:

  f(x) = x + 2

  g(x) = x^2 +3

Find:

  28) f(-3)

  29) f(g(2))

  30) g(f(x))

  31) f-1(x)

Solution:

Put the function argument values into the expression and do the arithmetic.

28) f(-3) = (-3) +2 = -1

__

29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9

__

30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7

__

31) The meaning of y = f^-1(x) is x = f(y).

  x = f(y) = y+2

  y = x -2

  f^-1(x) = x -2

Answer:

c + 11 = 43

Step-by-step explanation:

C = Carlos age

11 = The number added

43 = The number added plus carlos' age

c +11 = 43

c = 43 - 11

c = 32

Carlos' age is 32 years.

Answer:

C+11=43

Step-by-step explanation:

C= Carlos age

11= added number

43= Carlos age +added number

C+11=43

C=43-11

C=32

Age of Carlos 32.  :)

The given quadrilateral (call it Q) is a trapezoid with "base" lengths of 6 and 12, and "height" 2, so its area is (6 + 12)/2*2 = 18. This means the joint density is

[tex]f_{X,Y}(x,y)=\begin{cases}\frac1{18}&\text{for }(x,y)\in Q\\0&\text{otherwise}\end{cases}[/tex]

where Q is the set of points

[tex]Q=\{(x,y)\mid0\le x\le 2\land0\le y\le12-3x\}[/tex]

(y = 12 - 3x is the equation of the line through the points (0, 12) and (2, 6))

Recall the definition of expectation:

[tex]E[g(X,Y)]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty g(x,y)f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy[/tex]

(a) Using the definition above, we have

[tex]E[X]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty xf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac x{18}\,\mathrm dy\,\mathrm dx=\frac89[/tex]

(b) Likewise,

[tex]E[Y]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\ifnty yf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac y{18}\,\mathrm dy\,\mathrm dx=\frac{14}3[/tex]

Answer:

32

Step-by-step explanation:

Everyone added together = 68

Four years ago, they were 68 -16 = 52

But the question told 54 years.

So there was a girl who was 2 years.

Girl = 2

Boy = 2 +3 = 5

Husband = 3 +w

Wife =w

3 +w +w + 5 + 2 = 68

10 + 2w = 68

2w = 58

w = 29

Wife = 29

Husband = 29 +3 =32

Husband = 32 years

Answer:

[tex]\large \boxed{\sf \bf \ \ 32 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."

If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?

It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.

The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68

2 W + 10 = 68

2 W = 68 - 10 = 58 so W = 29

and then the husband's age is 29 + 3 = 32.

And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

$6284.4≤μ≤$6313.6

Step-by-step explanation:

Using the formula for calculating confidence interval as shown:

CI = xbar ± Z×S/√n

xbar is the average premium

Z is the z-score at 95% confidence

S is the standard deviation

n is the sample size

Given parameters

xbar = $6600

Z score at 95% CI = 1.96

S = $800

n = 25

Substituting this parameters in the formula we have;

CI = 6600±1.96×800/√25

CI = 6600±(1.96×800/5)

CI = 6600±(1.96×160)

CI = 6600±313.6

CI = (6600-313.6, 6600+313.6)

CI = (6284.4, 6913.6)

Hence the 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance is $6284.4≤μ≤$6313.6

Answer:

15.7% of students made above an 89.

Step-by-step explanation:

If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%

Answer:

432 mm³

Step-by-step explanation:

Volume of a Rectangular Prism: V = lwh

Step 1: Define variables

l = 8

w = 6

h = 9

Step 2: Plug into formula

V = 8(6)(9)

Step 3: Evaluate

V = 48(9)

V = 432

And we have our answer!

Answer:

number of successes

                 [tex]k = 235[/tex]

number of failure

                 [tex]y = 265[/tex]

The   criteria are met    

A

    The sample proportion is  [tex]\r p = 0.47[/tex]

B

    [tex]E =4.4 \%[/tex]

C

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from  the true population proportion will not  more than 4.4%

Ci  

   [tex]r = 0.514 = 51.4 \%[/tex]

 [tex]v = 0.426 = 42.6 \%[/tex]

D

   This 95% confidence interval  mean that the the chance of the true    population proportion of those that are happy to be exist within the upper   and the lower limit  is  95%

E

  Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

F

 Yes our result would support the claim because

            [tex]\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 500[/tex]

     The sample proportion is  [tex]\r p = 0.47[/tex]

Generally the number of successes is mathematical represented as

             [tex]k = n * \r p[/tex]

substituting values

             [tex]k = 500 * 0.47[/tex]

            [tex]k = 235[/tex]

Generally the number of failure  is mathematical represented as

           [tex]y = n * (1 -\r p )[/tex]

substituting values

           [tex]y = 500 * (1 - 0.47 )[/tex]

           [tex]y = 265[/tex]

for approximate normality for a confidence interval  criteria to be satisfied

          [tex]np > 5 \ and \ n(1- p ) \ >5[/tex]

Given that the above is true for this survey then we can say that the criteria are met

  Given that the confidence level is  95%  then the level of confidence is mathematically evaluated 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 value is

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

Generally the margin of error is mathematically represented as  

                [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }[/tex]

substituting values

                 [tex]E = 1.96 * \sqrt{ \frac{0.47 (1- 0.47}{500} }[/tex]

                 [tex]E = 0.044[/tex]

=>               [tex]E =4.4 \%[/tex]

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from  the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

          [tex]\r p - E < p < \r p + E[/tex]

substituting values

        [tex]0.47 - 0.044 < p < 0.47 + 0.044[/tex]

         [tex]0.426 < p < 0.514[/tex]

The upper limit of the 95% confidence interval is  [tex]r = 0.514 = 51.4 \%[/tex]

The lower limit of the   95% confidence interval is  [tex]v = 0.426 = 42.6 \%[/tex]

This 95% confidence interval  mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit  is  95%

Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

            [tex]\frac{1}{3 } < \frac{1}{2} (50\%)[/tex]

Answer: A) (-2, 4), (6,8)

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).

Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor [tex]\dfrac23[/tex] about the origin.

Let A' and B' b the endpoints of the dilated line segment.

Then, [tex]A'(\dfrac{2}{3}(-3), \dfrac23(6))=A'(-2,4)[/tex]

[tex]B'(\dfrac{2}{3}(9), \dfrac23(12))=B'(6,8)[/tex]

Hence, the correct option is A) (-2, 4), (6,8)

Answer:

4x

Step-by-step explanation:

Given:

√x • 4√x

Required:

Simplify in rational exponent form

SOLUTION:

Recall => [tex] \sqrt{a} = a^{\frac{1}{2}} [/tex]

Thus,

[tex] \sqrt{x}*4\sqrt{x} [/tex] can be expressed in exponent form as [tex] x^{\frac{1}{2}}*4x^{\frac{1}{2} [/tex]

When multiplying 2 bases having exponents together, their exponents should be added together, while you multiply the bases. I.e. [tex]x^m*x^n = x^{m+n }[/tex]

[tex] = x*4^{\frac{1}{2}+\frac{1}{2} [/tex]

[tex] = 4x^{1} = 4x [/tex]

The answer is 4x

Answer:

ii. 75 steps

iii. 75 steps

iv. 106 steps, and [tex]315^{0}[/tex]

Step-by-step explanation:

Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.

ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;

bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]

To determine distance AB,

[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex]   +  [tex]/25/^{2}[/tex]

          = 25000 + 625

          = 3125

AB = [tex]\sqrt{3125}[/tex]

     = 55.90

AB ≅ 56 steps

Thus, AC = 50 steps + 56 steps

               = 106 steps

From ΔACD,

Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]

⇒ x = 106 × Sin [tex]45^{0}[/tex]

      = 74.9533

     ≅ 75 steps

Musah's distance west from centre to final point is 75 steps

iii. From the secon attachment, Musah's distance north, y, can be determined by;

Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]

⇒ y = 106 × Cos [tex]45^{0}[/tex]

      = 74.9533

      ≅ 75 steps

Musah's distance north from centre to final point is 75 steps.

iv. Musah's distance from centre to final point is AC = AB + BC

                                     = 50 steps + 56 steps

                                     = 106 steps

From ΔACD,

Tan θ = [tex]\frac{75}{75}[/tex]

          = 1.0

θ = [tex]Tan^{-1}[/tex]  1.0

 = [tex]45^{0}[/tex]

Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]

                                                           =  [tex]315^{0}[/tex]

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

Answer:

Jargon that they both understand will be used.

Step-by-step explanation:

Jargon that they both understand will be used.

Jargon is a literary term that is defined as the use of specific phrases and words in a particular situation, profession, or trade. The use of jargon becomes important in prose or verse or some technical pieces of writing, when the writer plans to convey something only to the readers who are aware of these terms. Some of such examples are:

Due diligence: This is a business term, which refers to the research that should be done before making an important business decision.

AWOL: Short for "absent without leave," AWOL is military jargon used to describe a person whose whereabouts is unknown.

Answer:

Step-by-step explanation:

The approximate learning percentage can be estimated by using a doubling method.

If we breakdown the repetitions into three consecutive parts, we have:

1 - 2

2 - 4

3 - 6

then

1 - 2        →         46P = 39

P =39/46

P = 0.8478

P = 84.8%

2 - 4        →       39P = 33

P = 33/39

P = 0.84615

P = 84.6%

3  -  6    →       35P = 30

P = 30/35

P = 0.8571

P = 85.7%

The average value of P = (84.8 + 84.6 + 85.7)/3 = 85.03%

[tex]\simeq[/tex] 85%

From the tables of Learning Curves coefficient

The values are likened against times derived from 85% table factors at T[tex]_1[/tex] = 46

Unit                 1                2           3                    4                5            6

Date                46            39         35                33                32          30

Computed       -              39.1       35.56          33.26        31.56       30.22

b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)

The average completion time = [tex]\mathtt{\dfrac{T_1 \times \ Total \ time\ factor}{n}}[/tex]

At the total time factor 30, from the learning curves table , n(30) = 17.091

Thus:

The average completion time = [tex]\mathtt{\dfrac{46 \times \ 17.091}{30}}[/tex]

The average completion time = [tex]\mathtt{\dfrac{786.186}{30}}[/tex]

The average completion time = [tex]\mathtt{26.2062}[/tex]

Answer:

f(x)= 3x-5

f(2) = 3(2)-5 = 6-5= 1

f(-1)= 3(-1)-5= -3-5= -8

Hope this helps

if u have question let me know in comments ^°^

Answer:

Step-by-step explanation:

Given vector the following vector equations OA = 13x+7y , OB = 5x+12y and CO = -15x+12y, the following expression is true about vector OA, OB and OC;

OA+OB = CO (CO is the resultant since its is moving in the opposite direction compare to OA and OB)

Also BO+OA = BA and AO+OC = AC

If OB = 5x+12y, then BO = -(5x+12y)

BO = -5x-12y (BO = -OB)

Since BO+OA = BA

BA = -5x-12y + 13x+7y

BA = -5x+13x-12y+7y

BA = 8x-5y

Similarly AO+OC = AC

Since AO = -OA and OC = -CO

-OA-CO  = AC

AC = -(13x+7y)-(-15x+12y)

AC = -13x-7y+15x-12y

AC = -13x+15x-7y-12y

AC = 2x-19y

Answer:

0.0321

Step-by-step explanation:

This can be found by binomial probability distribution as the  probability of success is constant. There are a given number of trials. the successive tosses are independent.

Here n= 5

The probability of getting a four in a roll of a die = 1/6

The probability of not getting a four in a roll of a die = 5/6

The probability of getting exactly three 4s in five throws is given by

5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321

Answer:

13.75 dollars

Step-by-step explanation:

n=4

3n+7/n =3(4) + 7/4

=12 + 1.75

=$13.75

Answer: A) 4.75

Step-by-step explanation:

Answer:  19.2222

Step-by-step explanation:

given data;

no of tornadoes = 2,1,0 because it’s fewer than 3.

period = 14 years

probability of a tornado in a calendar year = 0.12

solution:

probability of exactly 2 tornadoes

= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )

= 0.0144 * 0.2451 * 1092

= 3.8541

probability of exac one tornado

= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )

= 0.12 * 0.2157 * 182

= 12.7109

probability of exactly 0 tornado

= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )

= 1 * 0.1898 * 14

= 2.6572

probability if fewer than 3 tornadoes

= 3.8541 + 12.7109 +2.6572

= 19.2222

Answer:

[tex]\theta[/tex] =2mπ + π/3 for m ∈ Z.

Step-by-step explanation:

Given the equation [tex]2sin\theta - \sqrt{3} = 0[/tex], we are to find all the values of [tex]\theta[/tex] that satisfies the equation.

[tex]2sin\theta - \sqrt{3} = 0\\\\2sin\theta = \sqrt{3} \\\\sin\theta = \sqrt{3}/2 \\\\\theta = sin{-1} \sqrt{3}/2 \\\\\theta = 60^0[/tex]

General solution for sin[tex]\theta[/tex] is [tex]\theta[/tex] = nπ + (-1)ⁿ ∝, where n ∈ Z.

If n is an even number say 2m, then [tex]\theta[/tex] = (2m)π + ∝ where ∝ = 60° = π/3

Hence, the general solution to the equation will be [tex]\theta[/tex] = 2mπ + π/3 for m ∈ Z.

Answer: 247.92 euros

Step-by-step explanation:

Given:  Varia is required pay $3,500 (in US dollars) per year to the university.

So, [tex]$3500\div 12 \approx\$291.67[/tex]

i.e. She will pay $ 291.67 per month.

Recent currency value: 1 US dollar = 0.85 euro

∴ $291.67 = ( 0.85 ×291.67) euros

= 247.92 euros  [Round to the nearest cent]

∴ She can expect 247.92 euros to pay per month to the university.

Answer:

[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]

[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]

Step-by-step explanation:

Part 1: Writing a ratio as a fraction

A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,

Therefore, 8:18 as a fraction is 8/18.

Part 2: Fraction in simplest form

To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.

8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.

Instead, if both numbers are even, divide by 2.

8/2 = 4

18/2 = 9

Check to see if the new numerator and denominator can reduce any further.

4/9 = 4/9

The fraction in simplest form is 4/9.

Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]

$h=10$, $r=\frac 42$

So the volume is $\pi\cdot(2)^2\cdot10=125.66$

hence you can fill up to 125.66 cubic Inches of milkshake

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