the height of a cylinder is increasing at a constant rate of 9 inches per second. the volume remains a constant 1318 cubic inches. at the instant when the radius of the cylinder is 99 inches, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v

Answer: 20x

Step-by-step explanation:

The required probability can thus be expressed as a common fraction  [tex]$\frac{3}{21}$[/tex]

The probability of two distinct members of the set[tex]$\{ 3, 7, 21, 27, 35, 42, 51 \}$[/tex] being multiplied and the product being a multiple of 63 can be expressed as a fraction,

The total number of possible outcomes when two numbers are randomly selected and multiplied is [tex]$\binom{7}{2} = \frac{7!}{2! 5!} = 21$[/tex].

The number of outcomes where the product is a multiple of 63 is [tex]$\binom{3}{2} = \frac{3!}{2! 1!} = 3$[/tex]

Therefore, the probability that the product is a multiple of 63 is  [tex]$\frac{3}{21}$[/tex]

The required probability can thus be expressed as a common fraction [tex]$\frac{3}{21}$[/tex].

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

If the derivative of a function is positive, then the function is increasing. If the derivative of a function is negative, then the function is decreasing.

1. Take a function, f(x).

2. Take the derivative of the function, f'(x).

3. If f'(x) is greater than 0, then the function is increasing.

4. If f'(x) is less than 0, then the function is decreasing.

To determine if a function is increasing or decreasing, the derivative of the function must be found. The derivative of a function is written as f'(x). If the derivative is greater than 0, then the function is increasing. If the derivative is less than 0, then the function is decreasing. This is because an increasing function has a positive slope, and a decreasing function has a negative slope. The derivative is the slope of the function, so if the derivative is positive, the function is increasing, and vice versa.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

[tex] {2x}^{4} = 50 \\ = > {x}^{4} = \frac{50}{2} \\ = > {x}^{4} = 25 \\ = > {x}^{4} - 25 = 0 \\ = > ( {x}^{2} + 5)( {x}^{2} - 5) = 0 \\ = > {x}^{2} - 5 = 0 \\ > (x - 5)(x + 5) = 0 \\ = > x = 5 \: \: and \: \: - 5[/tex]

Answer:

5, -5

Hope it helps.

Please send your query through comment section.

The US tax policy encourage long-term investments by providing a lower tax rate for long-term gains.

Therefore the answer is d. by providing a lower tax rate for long-term gains.

In the United States, the tax code provides a lower tax rate for long-term capital gains, which are gains on investments held for more than one year, as a way to encourage long-term investments. This means that when an investor sells an asset that they have held for more than one year, they will pay a lower tax rate on the gain than they would if they had held the asset for less than one year. This provides an incentive for investors to hold on to their investments for a longer period of time, rather than engaging in short-term buying and selling.

To know more on tax policy

https://brainly.com/question/24195988

#SPJ4

Answer:

Step-by-step explanation:

2(x + 3)=5x + 6 - 3x true or never true?

2(x + 3)=5x + 6 - 3x

2x + 6 = 2x + 6

2x - 2x = 6 - 6

0 = 0

Probability that the person randomly chosen from the town's population is under 18 or employed part time is the probability of a randomly chosen person is under 18 plus the probability of a randomly chosen person is  employed part-time subtracting the probability that they are both under 18 and employed part-time.

In order to find the probability that a person is under 18 or employed part-time, you would need to know the proportion of the population that is under 18 and the proportion of the population that is employed part-time. Then you can use the following formula:

P(under 18 or part-time) = P(under 18) + P(part-time) - P(under 18 and part-time)

Where P(under 18 and part-time) is the probability that a person is under 18 and employed part-time at the same time.

To know more on probability

https://brainly.com/question/21537697

#SPJ4

Mathematics focuses on geometry, numbers, and form. For such, axioms and definitions are needed to describe the study's subjects. On the basis of those definitions and axioms, properties are proved using logic.

Mathematical logic help you in using a phone, sending a fax, or operating a vehicle and many other things.

Logic models are composed of mathematical constructs. When it comes to supporting its conclusions, mathematics employs logic. The "science" of reasoning is logic. It deals with arguments, hence learning what constitutes a strong argument is a need for becoming a logician.

Logic can also be applied in everyday conversation about non-mathematical subjects. The amount of reasoning required is typically much more for mathematical inquiries than for non-mathematical ones.

Therefore, logic is a technique that mathematicians (as well as other individuals) employ when it comes to supporting their claims. Proof involves logic.

Mathematical logic has a direct impact on our daily life now more than ever. I'm not only referring to the marks pupils receive or the number of required mathematical subjects. I'm referring to using a phone, sending a fax, or operating a vehicle. I'm referring to making a home, purchasing medication for your family, and enjoying music.

To learn more about mathematical logic in daily life link is here

brainly.com/question/28052598

#SPJ4

It can be concluded that -

A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.

Given is that each day for three weeks, Kenisha records the number of eggs her chickens lay. The frequency table attached at the end shows her data.

[1] -

Number of days for which layed eggs are 5 or more -

5 + 5 + 2 = 12

[2] -

The greatest number of eggs laid down are equivalent to 7.

Therefore, it can be concluded that -

To solve more questions on frequency table, visit the link below -

brainly.com/question/28931302

#SPJ1

Answer:

To find the greatest number of tickets Jessica can buy, we can solve the inequality for t.

First, we divide both sides of the inequality by 5:

32/5 ≥ t

Then, we can simplify by dividing 32 by 5:

6.4 ≥ t

The result tells us that t, the number of tickets, must be less than or equal to 6.4

Since t represents the number of tickets, it must be a whole number, so the greatest number of tickets Jessica can buy is 6.

Answer:

6 tickets (t)

Step-by-step explanation:

32/$5=6 2/5 so 6 tickets (t)

For the given scenario appropriate answer is A: 1, 7, 34, 7, 1, which is the best indicator that the variable is modeled with a normal approximation

A normal distribution is the sampling distribution of averages or proportions from a large number of independent trials that approximately follows the normal curve. The expectation of a sample proportion or average is the corresponding population value.

The normal approximation is used to approximate probabilities because it is often easier to use the area under the normal curve compared to the sum of many discrete values.

"

Complete question:

Clara recorded 50 numerical observations on a certain variable and then calculated the mean x¯ and the standard deviation s for the observations. To help decide whether a normal model is appropriate, she created the following chart. The figure presents a number line. The number line has four tick marks labeled from left to right as x bar minus 2 s, x bar minus s, x bar plus s, and x bar plus 2 s. The 4 tick marks create 5 intervals on the number line. From left to right the intervals are labeled a, b, c, d, and e. The intervals at the ends of the number line, a and e, appear to be the same length, the intervals labeled b and d appear to be the same length and the interval in the middle, labeled c, appears to be twice the length of interval b. In Clara’s chart, the letters a,b,c,d,and e represent the number of observations falling in each interval. Which of the following list of counts for a,b,c,d,and e, respectively, is the best indicator that the variable can be modeled with a normal approximation?

A 1, 7, 34, 7, 1

B 1, 10, 28, 10, 1

C 2, 8, 30, 8, 2

D 2, 4, 38, 4, 2

E 5, 5, 30, 5, 5

"

You can learn more about normal approximation at

https://brainly.com/question/28194998

#SPJ4

So, on solving the provided question, we can say that to decrease that the Type II error, it is necessary to increase both the significance level and the sample size of voters.

When the experimenter fails to rule out a false null hypothesis, they commit a type II error, also referred to as a false-negative.Type II errors can also be decreased by increasing the significance level used throughout the testing method.

By employing more stringent criteria, the power of the testing technique can be increased while significantly reducing a type II error.

By raising the significance level employed throughout the testing procedure, Type II mistakes can also be reduced.

To know more about Type II error visit:
https://brainly.com/question/16012410

#SPJ4

The property of real numbers illustrated by the equation -2(x+4)=-2x-8 is option C: Distributive property.

What is Distributive property?

The distributive law of multiplication and addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed.

The given equation is -2(x+4)=-2x-8.

According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC.

In the equation it can be clearly seen that the form is distributive form as -

A = -2

B = x

C = 4

Therefore, the equation uses distributive property.

To learn more about Distributive property from the given link

https://brainly.com/question/2807928

#SPJ1

Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100. For(B) 8181 values of n is q + r divisible by 11.

5 digit Number:

A 5 digit number is a 5 digit number where the first digit is 1 or greater than 1 and the remaining digits can be any digit from 0 to 9. It starts at ten thousand (10,000) and goes up to 99,999 (99,999).

Given:

Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100.

When a five digit number is divided by 100, we get first three digits as quotient and last two digits as remainder. Therefore q can be any integer from 100 to 999 and r can be from 0 to 99

So for each value of 9 x 100 = 900 , possible value will be q = 100/11 = 9

Now,

q + r ≡ 0 (mod 11) will be possible values of r.

Since there is one extra , 900 / 11 = = 81

Hence, q + r ≡ 0 (mod 11)

So, possible values of n such that q + r = 0(mod 11) is 9 x 100 + 1 x 81

So, it will be 8100 + 81 = 8181

Learn more about Quotient:

https://brainly.com/question/429188

#SPJ4

Answer:

To determine if Tim is correct in stating that he has paid his fair share of the total cost, we need to calculate the total cost of the dinner and compare it to the cost of the desserts Tim paid for.

Will paid for 2 pizzas at a cost of $3.75 each, for a total of 2 * $3.75 = $7.50

Tim paid for 3 desserts at a cost of $1.09 each, for a total of 3 * $1.09 = $3.27

The total cost of the dinner is $7.50 + $3.27 = $10.77

To check if Tim has paid his fair share, we need to compare the cost of the desserts he paid for ($3.27) to the total cost of the dinner ($10.77)

$3.27 is 30.3% of $10.77, meaning Tim paid for around 30% of the dinner.

In this case, it's not fair to say that Tim has paid his fair share of the total cost, since he paid for only around 30% of the dinner, and as such, this cost should be split among the three of them.

It would be more accurate to say that Tim has paid a portion of the dinner, but not his fair share.

The model that shows 5 * 3/5 = 3 can be shown by sketching the boxes and shading the given parts.

The model of multiplication is a visual representation used to show multiplication without algebraic calculation. The model includes boxes and squares to indicate the multiplication.

Draw 3 boxes to represent 3 groups, and then place 8 in each box to represent 8 things in each group in order to multiply 3 by 8. There are several methods to draw this model.

We deduced from the model that the unknown value (?) may be determined by dividing the number of boxes (three, which stand for three groups) by the eight items.

Learn more about model multiplication here:

https://brainly.com/question/1928793

#SPJ1

There are a total of 126 different committees that can be formed with at least three women.

The number of different committees that can be formed with at least three women from a group of six women and three men can be calculated using the Combination formula. The Combination formula is defined as follows:

C(n,r)=n!/r!(n-r)!

where n is the total number of elements in the group and r is the number of elements to be selected from it.

In this case, n = 9 (6 women + 3 men) and r = 5 (the size of the committee).

Therefore, the number of different committees that can be formed with 3 women is:

C(9,5) = 9!/(5!*(9-5)!) = 9!/5!*4! = 126

Therefore, there are a total of 126 different committees that can be formed with at least three women.

Learn more about Combination here:

https://brainly.com/question/13715183

#SPJ4

The coordinates of the point P along the directed line segment AB are (-6, -4).

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.

Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(1(-2) + 4(-7))/(1 + 4)],  [(1(0) + 4(-5))/(1 + 4)]

P(x, y) = [(-2 - 28)/(5)],  [(0 - 20)/5]

P(x, y) = [-30/5],  [(-20)/(5)]

P(x, y) = [-6, -4]

Read more on line ratio here: brainly.com/question/14457392

#SPJ1

Answer: 148

Step-by-step explanation: To find the surface area, add up all the side areas. Since we know that the opposite side of one side is the same, we can do 2(4 *5) + 2(6*5) + 2(4*6). This will get 148.

If 15% of adults in a certain country work from home, then probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.05 .

the percent of students that work from home is (p) = 15% = 0.15  ;

the number of adults in the sample is (n) = 350  ;

to find the probability , we first need to find the mean and standard deviation ;

So , mean [tex](\mu)[/tex] = [tex]n\times p = 350\times 0.15 = 52.5[/tex] ;

and Standard Deviation[tex](\sigma)[/tex] = [tex]\sqrt{np(1-p)} = \sqrt{3550\times 0.15 \times 0.85} = 6.68[/tex] ;

We need to calculate the probability that fewer than 42 out of a random sample of 350 adults will work from home ,

which means ; [tex]P(X < 42-0.5) = P(X < 41.5)[/tex] ,

So , the probability will be the p value of Z when x= 41.5 ;

we know that ; [tex]z= \frac{X-\mu}{\sigma}[/tex] ;

substituting the values of mean and standard deviation ;

⇒ [tex]Z = \frac{41.5-52.5}{6.68}[/tex] ;

On solving ,

we get ;

⇒ [tex]Z = -1.65 ;[/tex] and the p value at z = -1.65 is 0.05 .

Therefore , the required probability is 0.05 or 5% .

Learn more about Probability here

https://brainly.com/question/19054425

#SPJ4

x questions are the leaves and 4 of the following words in sentence of your own experience are the plants that are the plants that are the plants that are the plants that are

Answer:

a) To find out how many pounds a 137 ounce baby weighs, we divide the weight in ounces by the number of ounces per pound.

137 ounces / 16 ounces/pound = 8.5625 pounds

Therefore, a 137 ounce baby weighs 8.5625 pounds.

b) To find out how much heavier the second baby is, we first convert the weight of the second baby from pounds to ounces.

We know there are 16 ounces in one pound, so we can multiply 9.375 (9 3/8) by 16 to find out how many ounces the second baby weighs.

9.375 * 16 = 150.4 ounces

Now we can subtract the weight of the first baby from the weight of the second baby to find out the difference in weight.

150.4 - 137 = 13.4 ounces

Therefore, the second baby is 13.4 ounces heavier than the first baby.

Answer:

He was driving at 66 2/3 miles per hour

Step-by-step explanation:

200/3 = 66 2/3

a. The sample mean for U is 21.55 and the sample mean for F is 8.39.

b. sample median for U is 17 and the sample median for F is 8.

c. trimmed mean for U is 17 and the trimmed mean for F is 7.95.

d. trimmed percentage for U is 18.18% and the trimmed percentage for F is 13.33%.

a) Sample mean can be calculated by adding values and dividing the sum by the number of the values.

< Strong > Mean(U) < / Strong > =

[tex]\frac{6.0 +5.0 + 11.0 + 33.0 + 4.0+5.0+80.0+18.0 + 35.0+17.0+23.0}{11}[/tex] = 21.55

< Strong > Mean(F) < / Strong > =  [tex]\frac{2.0 + 15.0 + 12.0 + 8.0 + 8.0 + 7.0 + 6.0 + 19.0 + 3.0+9.8+22.0+9.6+2.0+2.0+0.5}{15}[/tex] = 8.39

b) Sample median is the middle value of a sorted sample:

Sorted(U)= [ 4.,  5.,  5.,  6., 11., 17., 18., 23., 33., 35., 80.]

Sorted(F)=[ 0.5,  2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. , 22.]

Median(U)=17, which is the 6th (middle) value

Median(F)=8, which is the 8th (middle) value

c) If we delete the smallest and largest observation, we have:

U= [  5.,  5.,  6., 11., 17., 18., 23., 33., 35., ]

F= [ 2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. ]

Using the above equation for the new samples, we have:

TrimmedMean(U)= 17

TrimmedMean(F)=7.95

d) Trimming percentages can be found by dividing the number of removed values by the old sample size

That is, for U: [tex]\frac{2}{11} = 0.18[/tex] 18.18%

for F: [tex]\frac{2}{15} = 0.13[/tex] ,13.33%

Read more about the Sample mean :

https://brainly.com/question/29441200

#SPJ4

Answer:

B

Step-by-step explanation:

-3x + 2y =  ?  You forgot to put what this equals, but it does not matter.

3x + 6y = 9

       9y = ?

When we add -3x and 3x the x's drop out.

The smallest bouncy prime is 2.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.

A number n is said to be a bouncy prime if it is prime, and the sum of the positive divisors of n (also known as the sum of divisors function, denoted f(n)) is also prime.

The smallest prime number is 2. The sum of divisors of 2 is

1+2 = 3

which is also prime, so 2 is a bouncy prime.

Since 2 is the smallest prime and it is a bouncy prime, the smallest bouncy prime is 2.

To know more on prime numbers

https://brainly.com/question/10751577

#SPJ4

On solving the provided question, we can say that curvaturein t=1;[tex]curvate=(36+36+4)1/2/(1+4+9)3/2=761/2/143/2[/tex]

Curvature is one of many ideas in mathematics that are strongly related to geometry. According to common sense, curvature is the deviation of a curve or face from a plane or a straight line. In mathematics, curvature refers to the rate at which a curve changes direction in relation to the distance traveled along the curve. The pace at which a curve spins is generally referred to as its curvature. The direction of the curve is indicated by the tangent line or velocity vector, which means that the curvature is roughly equal to the rate of rotation of the tangent line or velocity vector.

t=1

curvate=|r'(t) x r"(t)|/|r'(t)|3 (x mean vector product of r'(t) and r"(t))

[tex]r'(t)=(1,2t, 3t2)\\r''(t)=(0,2,6t)\\r'(t) x r"(t)=(6t2 , -6t, 2)\\|r'(t) x r"(t)|=(36t4+36t2+4)1/2\\|r'(t)|=(1+4t2+9t4)1/2\\|r'(t)|3=(1+4t2+9t4)3/2\\curvate=(36t4+36t2+4)1/2/(1+4t2+9t4)3/2\\curvate in t=1\\curvate=(36+36+4)1/2/(1+4+9)3/2=761/2/143/2[/tex]

To know more about curvature visit:

https://brainly.com/question/30106465

#SPJ4

In the right triangle the value of x is solved to be  4

The figure attached is a right triangle and the value of x can be worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The problem is described in a right angle triangle as below

hypotenuse = x

adjacent = 10 miles

The value of x is calculated using cos, CAH

cos 60 = Adjacent / hypotenuse

cos 60 = 2 / x

x = 2 / cos 60

x = 4

Learn more about SOH CAH TOA here:

https://brainly.com/question/29402966

#SPJ1

The z-score corresponding to an observation is -1.64 and option b is the correct answer.

The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from the mean serve as the unit of measurement for Z-score. The score for a data point is equal to the mean score if the Z-score is 0. A result that deviates by one standard deviation from the mean is indicated by a Z-score of 1.0.

The z-score is given by the following formula:

z = 4.5 - 5.7/ 0.61

z = -1.64

Hence, the z-score corresponding to an observation is -1.64 and option b is the correct answer.

Learn more about z-score here:

https://brainly.com/question/15016913

#SPJ4

On solving the provided question, we can say that the polynomial value is P(x) + Q(x)= -11x2 + 4x + 14

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

the polynomials

Let P(x) = (9 - 3x2) and Q(x) = (-8x2 + 4x + 5)

P(x) = -3x2 + 9 --- (1)

Q(x) = -8x2 + 4x + 5 --- (2)

the polynomials

P(x) + Q(x) = (-3 - 8)x2 + 4x + (9 + 5)

P(x) + Q(x)= -11x2 + 4x + 14

To know more about polynomials visit:

https://brainly.com/question/11536910

#SPJ4