How many cubic inches of a milkshake can you fit up to the brim of this cup without letting it overflow? The
cup is 10 inches tall, and the rim of the cup is 4 inches across. (Hint: the radius is half of the diameter.)

Answers

Answer 1

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

.


Related Questions

Matrix A is said to be involutory if A2 = I. Prove that a square matrix A is both orthogonal and involutory if and only if A is symmetric.

Answers

Answer:

4 · 1/4 (I-0) = (A-0)∧2

see details in the graph

Step-by-step explanation:

Matrix A is expressed in the form A∧2=I

To proof that Matrix A is both orthogonal and involutory, if and only if A is symmetric is shown by re-expressing that

A∧2=I in the standard form

4 · 1/4 (I-0) = (A-0)∧2

Re-expressing

A∧2 = I as a graphical element plotted on the graph

X∧2=I

The orthogonality is shown in the graphical plot displayed in the picture. Orthogonality expresses the mutually independent form of two vectors expressed in their perpendicularity.

The temperature dropped 15 degrees in an hour. If the starting temperature was 10 degrees, What was the final temperature?​

Answers

Answer:

Step-by-step explanation:

15-10=5 degrees

A box of colored crayons contains 11 distinct colors. In how many ways can 2 colors be chosen, assuming that the order of the colors chosen doesn’t matter? (If necessary consult a list of formulas.)

Answers

Answer:

55

Step-by-step explanation:

The first crayon is chosen out of 11,so there are 11 choices

11

The second crayon is chosen out of 10 crayons left so there are 10 choices

10

11*10 = 110

But we do not care about the order, so we divide by 2 since there are 2 places

110/2 =55

Answer:

55

Step-by-step explanation:

Equation is a = n * (n-1)

11 * 10 = 110

Order doesn't matter, and two colors, so divide by 2.

110/2 = 55

Simply this question and get marked branlist

Answers

Answer:

72/n^5r

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

13)

● 2d^3 × c^6 × 8d^5 × c^2

Isolate the similar terms

● (2×8)× (d^3 × d^5)×(c^6×c^2)

● 16 × d^(3+5) × c^(6+2)

● 16 × d^8 × c^8

● 16 × (dc)^8

● 16(dc)^8

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 8n×r^(-4) ×9×n^(-6)×r^3

Isolate the similar terms

● (8×9)× (r^(-4)×r^3) × (n×n^(-6))

● 72 × r^(-4+3) × n^(1-6)

● 72 × r^-1 × n^(-5)

● 72 ×(1/r) × (1/n^5)

● 72/(r×n^5)

Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?

Answers

Answer:

The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 500[/tex]

     The standard deviation is  [tex]\sigma = 100[/tex]

The  percent of people who write this exam obtain scores between 350 and 650    

    [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]

Generally  

               [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

   [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]

   [tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]

   [tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]

From the z-table  [tex]P(Z < -1.5 ) = 0.066807[/tex]

   and [tex]P(Z < 1.5 ) = 0.93319[/tex]

=>    [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]

=>  [tex]P(350 < X 650 ) = 0.866[/tex]

Therefore the percentage is  [tex]P(350 < X 650 ) = 86.6\%[/tex]

What are the coordinates of the point (2,-4) under the dilation D-2?

A) (8,-4)
B) (4,-8)
C) (-8,4)
D) (-4,8)​

Answers

Answer:

D) (-4,8)

Step-by-step explanation:

Multiply both coordinates by -2

Answer:

(-4,8)

Step-by-step explanation:

I found a school pdf with the answer key to this exact equation and thats the answer

hello, if someone can give me a hand with this upper and lower bound excercise please? l get 3 marks of 5 but l cant find what l am missing please thanks

Answers

Answer:   maximum "safe"  Force = 415.58 N

Step-by-step explanation:

Length = 1.2 m

lower bound is 1.15 (because it rounds up to 1.2)

upper bound is 1.24 (because it rounds down to 1.2)

Note: 1.25 would round up to 1.3

width = 2.5 m

lower bound is 2.45 (because it rounds up to 2.5)

upper bound is 2.54 (because it rounds down to 2.5)

Note: 2.55 would round up to 2.6

Pressure = 150 N/m²

lower bound is 147.5 (because it rounds up to 150)

upper bound is 152.4 (because it rounds down to 150)

Note: 152.5 would round up to 155

Max "safe" Force means minimum Area and minimum Pressure (lower bounds)

Force = Area x Pressure

           = length x width x Pressure

           = 1.15 x 2.45 x 147.5

           = 415.58

i need help quick!!!

Answers

Answer: A,C, and D

Step-by-step explanation:

Answer:

the answer to this question may be option B, C and D

Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below: Write the number shown on the calculator display in standard form. A. 60,466,176 B. 600,000,000 C. 6,000,000,000 D. 60,000,000,000

Answers

Answer:

d. 60000000000

Step-by-step explanation:

Answer:

The answer is D. 60,000,000,000

Step-by-step explanation:

ayuda por favorrrrrrrrrrrrr

Answers

Answer:

1. a)

2. e)

3. c)

Step-by-step explanation:

1.

HD^2 = 9^2 - 7^2

HD^2 = 32

AD^2 = HD^2 + 2^4

AD^2 = 36

AD = 6

2.

PT^2 = 8(8 + OE)

144 = 64 + 8OE

OE = 10

R = OE = 10

3.

x^2 = 41^2 - 9^2

x = 40

9. Marvin Gate bought some fencing from a wholesaler for $6,000. The wholesaler offered a trade discount of 35%. What was the original price?
(Round to the nearest cent.)
A. $6,230.77
O B. $9.230.77
O C. $6,930.77
D. 55,930 77
Mark for review (Will be highlighted on the review page)

Answers

Answer:

B - %9230.77

Step-by-step explanation:

the original price of the fencing before the trade discount was approximately $9,230.77.

To find the original price of the fencing before the trade discount, we need to calculate the amount that corresponds to a 35% decrease from the discounted price.

Let's denote the original price as "P". The discounted price is given as $6,000.

The discounted price is calculated by subtracting the discount amount from the original price:

Discounted price = Original price - Discount amount

The discount amount is determined by multiplying the original price by the discount rate:

Discount amount = Original price × Discount rate

Given that the discount rate is 35% (or 0.35), we have:

Discount amount = P × 0.35

Substituting the discounted price of $6,000, we can write the equation as:

$6,000 = P - (P × 0.35)

Simplifying the equation:

$6,000 = P(1 - 0.35)

$6,000 = P(0.65)

To solve for P, we divide both sides of the equation by 0.65:

P = $6,000 / 0.65

P ≈ $9,230.77

Therefore, the original price of the fencing before the trade discount was approximately $9,230.77.

The correct answer is B. $9,230.77.

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A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x-2)=48 What is the length, x, of the garden?

Answers

Answer:

[tex]x {}^{2} - 2x = 48[/tex]

[tex]x { }^{2} - 2x - 48 = 0[/tex]

using quadratic formula,

[tex] - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} \div 2a[/tex]

[tex]2 + \sqrt{196} \div 2[/tex]

[tex]2 + 14 \div 2[/tex]

[tex]x = 8[/tex]

or

[tex]x = - 6[/tex]

A class with n kids lines up for recess. The order in which the kids line up is random with eachordering being equally likely. There are three kids in the class named John, Betty, and Mary. The useof the word "or" in the description of the events, should be interpreted as the inclusive or. That is"A or B" means thatAis true,Bis true, or bothAandBare true.Give an expression for each of the probabilities below as a function ofn. Simplify your final expressionas much as possible so that your answer does not include any expressions of the form (a/b).Requried:a. What is the probability that Betty is first in line or Mary is last in line? b. Explain the method used to calculate probability.

Answers

Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

Given this pair of probabilities, the probability that Mary is the first is  n(A) = n-1!, while the probability that Betty is last is  n(A) = n-1!

There are n! ways of making this arrangement

We have probability of A: Betty is the first person in this line

Probability of B: Mary is the last person

A U B = p(A) + p(B) - p(A ∩ B)

n(A) = n-1 that is given that Betty is the first person on the line.

then n(A) = n-1!

As the last person on the line P(B) = n-1!

Probability of (A∩B) =( n-2)!  this has Mary as the first and Betty as the last person.

Remaining students that would have to be on this line are n-2

Prob(A∪B) = n(A ∪ B)/n!

= 2(n-2)/n(n-1)

What is the probability theory in Mathematics?

This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.

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HELP ME!

A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?

Answers

Answer: approx 1196 students.

Step-by-step explanation:

As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)

2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.

95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392

Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.

N=2392:2=1196

How is a reflection different than a rotation

Answers

Answer:

different

Step-by-step explanation:

reflection is basically like a mirror where it reflects you. rotation is when an object spins/rotates.

A reflection is the flipping of a point or figure over a line of reflection (the mirror line). A rotation is the turning of a figure or object around a fixed point.

Hi people if someone gives me a hint please. Show algebraically that the product of two consecutive numbers is always even l wrote n (n+1) is always an even number But doesnt recognise it as 100% right thanks for any help

Answers

Step-by-step explanation:

Consider the following rules.

even + odd = odd

even - odd = odd

even × odd = even

even ÷ odd = even (if divisible)

Now for the two consectives terms...

One will surely be even and the other, odd.

So using the rule

Their product will always be odd

Hope it helps....

BRAINLIEST PRETTY PLEASE!!

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP​

Answers

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d }    = 30

       5(2a  + 4d )d           = 60

       10a    + 20d             = 60

reduce to lowest term to easy calculation by dividing through by 10

                      a + 2d       = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉  = ⁹/₂(2a + 8d )   = 69

        9(2a  + 8d )    = 30 + 69

            18a + 72d   = 99 x 2

            18a + 72d   = 198

divide through by 18 to reduce to lowest time

                a  + 4d    = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

                 a + 2d = 6

                 a + 4d = 11

                     -2d  = -5

                          d = ⁵/₂.

Now substitute  for d to get a

               a  + 2(⁵/₂) = 6

                a + 5       = 6

                           a   = 6 - 5

                            a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.

What is sequence?

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given:

The sum of the first 5 terms of an AP is 30,

Write the equations as shown below,

S₅ = ⁵/₂(2a + ( n - 1 )d }  = 30

5(2a  + 4d )d = 60

10a    + 20d = 60

reduce to lowest term to easy calculation by dividing through by 10

a + 2d = 6

T₉  = ⁹/₂(2a + 8d )   = 69  (sum of the next 4 terms inclusive)

9(2a  + 8d )  = 30 + 69

18a + 72d  = 99 x 2

18a + 72d = 198

a  + 4d    = 11

Solve the equation as shown below,

d = ⁵/₂, and   a = 1.

Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.

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How should a musician effectively convey emotions or ideas in a performance?

Answers

Answer:

Within the factors hindering expression in music, tempo is the most important number of factors such as your mood.

Step-by-step explanation:

If one wants to convey a message, they should try these:

a) Use real life

b) introduce symbolism

c) convey sensory disruption, e.t.c.

Hope these helps.

A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?

Answers

Answer:

  17 by 21 inches

Step-by-step explanation:

The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...

  L + W = 38

  LW = 357

__

Solution:

  W(38 -W) = 357 . . . . . substitute for L

  -(W^2 -76W) = 357 . . expand on the left

  -(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square

  (W -19)^2 = 4 . . . . . . . write as a square

  W -19 = ±√4 = ±2 . . . take the square root; next, add 19

  W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other

The dimensions are 17 by 21 inches.

A baseball is hit 3 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the maximum height. Round your answer to the nearest integer.

Answers

Answer:

53

Step-by-step explanation:

i used an angle of 45 degrees.

Distance from ground = 3feets

Angle = 45⁰

U is the initial velocity = 80ft/sec

g = 32

The question wants us to vfind maximum height

We have

r(t) = (80cos45⁰)ti + [3 + 80sin45⁰]t - 0.5(32)t²

We know cos 45 is also sin45 = 1/√2

r(t) = (40√2)ti + [3+40√2]t - 16t²

When we differentiate with respect to t:

r'(t) = (40√2)i + (40√2 - 32t)

= 40√2 =32t

t = 40√2/32

t= 20√2/16

We put the value of t into (3 + 40√2)t -16t²

When we substitute and simplify this we have

3 + 56.57 + 1.77 -16 +8

= 53.34

Which is approximately 53.

write 32 1/2 in radical form​

Answers

Answer:

Nothing further, the simplest answer is 32 1/2

Step-by-step explanation:

Verify that the Divergence Theorem is true for the vector field F on the region E. F(x,y,z)=3xi+xyj+2xzk, E is the cube bounded by the planes x=0, x=1, y=0, y=1, z=0 and z=1

Answers

Answer: 9/2

Step-by-step explanation: Find explanation in the attached file

What is (-i)^6 ? Please don’t guess. Thanks

Answers

D) -1

i is (-1)^1/2, so (-i)^6 is ((-1)^1/2)^6 which is (-1)^3=-1.

Answer:

-1

Step-by-step explanation:

Hello, please consider the following.

[tex](-i)^6=(-1)^6\cdot(i^2)^3=1\cdot (-1)^3=\boxed{-1}\\[/tex]

Thank you

A technician is testing light bulbs to determine the number of defective bulbs. The technician records the table below to show the results. Result of Light Bulb Test Number of Bulbs Tested 14 28 84 336 Number of Defective Bulbs Found 1 2 6 ? The technician expects to find 24 defective bulbs when 336 are tested. Which statement explains whether the technician’s reasoning is correct, based on the information in the table?

Answers

Answer:

He should find 24 defective lightbulbs.

Step-by-step explanation:

1. Divide the number of defective bulbs by the total number of bulbs for each section.

2. Make sure the number you get is the same each time.

3. Divide the guessed number of bulbs (24) by the total number of bulbs (336)

4. If the number you got for step 4 matches the number you got for step 3, then he is right

Answer:

The answer is A

Step-by-step explanation:

on NCCA

A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5
questions if you guess randomly on each question?

Answers

The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.

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Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs.

Answers

Answer: 1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar for both recipes.

Step-by-step explanation:

Dante is baking two recipes.

A cookie recipe, that needs 1.5 cups of sugar.

A brownie recipe, that needs 1.25 cups of sugar.

So the total sugar that he needs is:

The sugar for the cookies + the sugar for the brownies:

The equation is:

1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar.

Suppose that a sample mean is .29 with a lower bound of a confidence interval of .24. What is the upper bound of the confidence interval?

Answers

Answer:

The upper bound of the confidence interval is 0.34

Step-by-step explanation:

Here in this question, we want to calculate the upper bound of the confidence interval.

We start by calculating the margin of error.

Mathematically, the margin of error = 0.29 -0.24 = 0.05

So to get the upper bound of the confidence interval, we simply add this margin of error to the mean

That would be 0.05 + 0.29 = 0.34

Look at the figure below. which ratio represents tan 0?
A -5/4, B -4/5, C -3/4, D 3/5.

Answers

The correct answer is D) 3/5

The required value of the tanФ is given as -3/4. C option is correct.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What are trigonometric equations?

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Tan(180 - Ф) = -tanФ = perpendicular / base

From figure,  perpendicular= 12 and  base = 16
-tanФ = 12 / 16
tanФ = -3/4

Thus, the required value of the tanФ is given as -3/4. C option is correct.

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A classroom has 35 students. If the ratio of boys to girls was 5:2, , how many girls were in the class

Answers

Answer:

35/14

Step-by-step explanation: 35/14

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

Answer:

10 girls.

Step-by-step explanation:

Boys: 5x

Girls: 2x

next... 5x + 2x = 35

7x= 35

x=5

Answer. 10 girls.

Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043 Keith reads that the mean nap is 22 minutes. The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. 1.39 or 1.43 or 2.88 or 0.70

Answers

Answer:

The  t-statistic is [tex]t = 0.6956[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 22 \ minutes[/tex]

       The standard deviation is  [tex]s = 7.043[/tex]

       The  given data is  23, 35, 17, 30, 20, and 19.

Generally the sample mean is mathematically evaluated as

      [tex]\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}[/tex]

     [tex]\= x =24[/tex]

The t-statistic is mathematically evaluated as

       [tex]t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }[/tex]

=>   [tex]t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }[/tex]

=>   [tex]t = 0.6956[/tex]

Answer: 0.70

Step-by-step explanation:

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