What is the exact volume of the cylinder V=Bh
. V =324πin.3

Answer:

10

Step-by-step explanation:

35/7 = 5, so the white marbles appears 5 times often.

If we have 2 green marbles and we want to maintain the same ratio of green to white marbles (so the same assumption that white appears 5 times often) we need to multiply that by 5.

Answer:

The correct option is;

False

Step-by-step explanation:

Here, we note that the proportion of the test statistic which is used in the test is 5% and the P-value for the test is 0.03

The hypothesis test is meant to check if people will still drive to work when the gas prices are above $10.00 and the suggestion was that we can conclude that when the fuel price is above $5.00 everyone would still drive to work without a P-value for the test, hence we can not come to the stated conclusion.

Answer:

Maximum: C= 6(5) + 2y or C= 30 + 2y

Step-by-step explanation:

X can be greater than or equal to 0, but can also be less than or equal to 5.

Y is greater than or equal to 0.

4 times x then subtracted by y is greater than or equal to 1.

Since X can't go higher than 5, the maximum is 5.

Y can be anything since it can be greater than or egual to 0 and either way it would be greater than one.

I hope I could help!

Answer:

x=3.2

Step-by-step explanation:

This question is asking us to solve for x, and to do that, we need to get the variable by itself.

1.6+x=4.8

Subtract 1.6 from both sides

1.6-1.6+x=4.8-1.6

x=3.2

So, 3.2 is the value of x that satisfies the equation.

to answer this it's simple

the answer is 20,000

Answer:

The length of minor arc AB is 8

Step-by-step explanation:

In this question, we are asked to calculate the length of the minor arc.

Mathematically, the length of an arc can be calculated using the formula below;

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by the arc which is 120° according to the question, r is the radius of the circle which is 4 according to the question.

Plugging these values, we have

Length of minor arc AB = 120/360 × 2 × 22/7 × 4 = 8.34 = 8 to the nearest integer

The length of the minor arc AB in circle O with a radius of 4 and a central angle of 120 degrees, rounded to the nearest integer, is 8 units.

In the context of circle geometry, the length of a minor arc can be calculated by using the formula: arc length = (central angle/360) x (2π x radius). Given in the problem, we have a radius of 4 units and a minor arc with a measure of 120 degrees. Substituting the given values into the formula, the arc length becomes (120/360) x (2π x 4) which simplifies to (1/3) x (8π) = 8π/3 units.

However, the question asks for the minor arc length to the nearest integer. In this case, you would calculate 8π/3 which approximately equals 8.37758, but when rounded to the nearest integer, it would be 8.

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Answer:

Your answer will be 17

Step-by-step explanation:

Simply multiply and take away the t and add into the 9+ after your equation

Coulomb's law explains the force between two charges. The force between two identical charges decreases as the distance between them increases. If graphed, this relationship will form a hyperbola.

In physics, particularly electromagnetism, Coulomb's law explains the force between two charges. As per the law, the force (F) between two charges (q1 and q2) separated by a distance (r) is given by the equation, F = kq1q2/r^2. Here, k is Coulomb's constant.

From this formula, we can conclude that force is inversely proportional to the square of the distance between two charges. In other words, as the distance (r) between two identical positive charges increases, the force (F) of repulsion between them decreases.

If we were to graph F as a function of r for two positive charges, the graph would be a hyperbola. This is because the equation represents an inverse square relationship. The force will decrease rapidly as the distance increases and is indicated by a curve that starts high when r is small and approaches zero as r gets larger.

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Given:

Given that the diameter of the circle is [tex]\frac{7}{2} \ cm[/tex]

We need to determine the radius, circumference in terms of π and circumference using π = 3.14.

Radius:

The radius of the circle can be determined using the formula,

[tex]r=\frac{d}{2}[/tex]

Substituting [tex]d=\frac{7}{2}[/tex], we get;

[tex]r=\frac{(\frac{7}{2})}{2}}[/tex]

Simplifying, we get;

[tex]r=\frac{7}{4} \ cm[/tex]

Thus, the radius of the circle is [tex]\frac{7}{4} \ cm[/tex]

Circumference in terms of π:

The circumference of the circle can be determined using the formula,

[tex]C=2 \pi r[/tex]

Substituting [tex]r=\frac{7}{4} \ cm[/tex], we get;

[tex]C=2 \pi (\frac{7}{4})[/tex]

[tex]C=\frac{7}{2} \pi \ cm[/tex]

Thus, the circumference in terms of π is [tex]\frac{7}{2} \pi \ cm[/tex]

Circumference using π = 3.14:

Substituting π = 3.14 in the circumference of the circle [tex]C=\frac{7}{2} \pi \ cm[/tex], we get;

[tex]C=\frac{7}{2}(3.14)[/tex]

[tex]C=10.99 \ cm[/tex]

Thus, the circumference of the circle is 10.99 cm

Answer: r = 9

Step-by-step explanation:

Simplifying

20 = r + 11

Reorder the terms:

20 = 11 + r

Solving

20 = 11 + r

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1r' to each side of the equation.

20 + -1r = 11 + r + -1r

Combine like terms: r + -1r = 0

20 + -1r = 11 + 0

20 + -1r = 11

Add '-20' to each side of the equation.

20 + -20 + -1r = 11 + -20

Combine like terms: 20 + -20 = 0

0 + -1r = 11 + -20

-1r = 11 + -20

Combine like terms: 11 + -20 = -9

-1r = -9

Divide each side by '-1'.

r = 9

Simplifying

r = 9

Answer:

r=9

Step-by-step explanation:

Step 1: Flip the equation

r + 11 = 20

Step 2: Subtract 11 from both sides

r + 11 - 11 = 20 - 11

Answer:

15 days

Step-by-step explanation:

We can use a ratio to solve

4 bird houses     20 bird houses

--------------------- = -------------------------

3 days                      x days

Using cross products

4x = 3*20

4x = 60

Divide each side by 4

4x/4 = 60/4

x = 15

15 days

Answer:

15 days

Step-by-step explanation:

i hope this help you

Answer:Its B. -4 and 9

Step-by-step explanation:

Answer:

x = - 4, x = 9

Step-by-step explanation:

Given

x² - 36 = 5x ( subtract 5x from both sides )

x² - 5x - 36 = 0 ← in standard form

Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)

The factors are - 9 and + 4, since

- 9 × 4 = - 36 and - 9 + 4 = - 5, thus

(x - 9)(x + 4) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 9 = 0 ⇒ x = 9

Step-by-step explanation:

[tex]9 \times {10}^{4} = 900 \times {10}^{2} \\ \\ 3 \times {10}^{2} \\ \\ \because \: 900 > 3 \\ \purple{ \boxed{ \bold{\therefore \: 9 \times {10}^{4} > 3 \times {10}^{2}}}}[/tex]

Step-by-step explanation:

Hope it will help you :)

Answer:

If the distribution is skewed right, then the mode is greater than the mean.

Step-by-step explanation:

There's a graph below that I hope will help!

The true statement is that the mode of the scores is greater than the mean score

From the question, we understand that:

The distribution is skewed to the right

For a right skewed distribution, the mean value is lesser than the mode value

i.e. mean < mode or mode > mean

Hence, the true statement is that the mode of the scores is greater than the mean score

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Answer:

A) A sphere has no bases.

E) The lateral face of a cylinder is in the shape of a rectangle.

The correct statements which are true about three-dimensional figures are,

A) A sphere has no bases.

E) The lateral face of a cylinder is in the shape of a rectangle.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

To find correct statements which are true about three-dimensional figures.

Now, We know that;

In a sphere, it has no base.

And, In a cylinder, The lateral face is in the shape of a rectangle.

Thus, The correct statements which are true about three-dimensional figures are,

A) A sphere has no bases.

E) The lateral face of a cylinder is in the shape of a rectangle.

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The approximate loudness of a rock concert with a sound intensity of 10⁻¹

is 110 Db.

Since the loudness L measured in decibel (Db) of a sound intensity I is given by

L = 10㏒(I/I₀) where

Since we want to determine  the approximate loudness of a rock concert with a sound intensity of 10⁻¹. So, I = 10⁻¹

So, substituting the values of the variables into L, we have

L = 10㏒(I/I₀)

L = 10㏒(10⁻¹/10⁻¹²)

L = 10㏒10¹¹

L = 11 × 10㏒10

L = 110㏒10

L = 110 (since ㏒10 = 1)

So, approximate loudness of a rock concert with a sound intensity of 10⁻¹

is 110 Db.

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Answer:110

Step-by-step explanation:

took the test

Answer:

(-35, 0)

step-by-step explanation:

The x-intercept of the line does not exist.

The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept, we need to look for a point on the graph where y is equal to zero. Based on the given table, there is no pair of coordinates where the y value is equal to zero. Therefore, the line does not intersect the x-axis and the x-intercept does not exist.

Answer:

80 points

Step-by-step explanation:

First Half:                                    Second Half:                        Total Right Answers

8 questions right            +          2 questions right        =       10 questions right

10*8 points a piece = 80 points

Thus, his total score is 80 points.

To find Adam's final score, we need to calculate the total points from both the first and second halves of the trivia game. Each question is worth 8 points.

Adam answered 8 questions correctly:

8 questions × 8 points per question = 64 points

Adam answered 2 questions correctly:

2 questions × 8 points per question = 16 points

Now, we add the points from both halves:

Total Score = 64 points + 16 points = 80 points

Therefore, Adam's final score in the trivia game is 80 points.

Answer:

241 clients

Step-by-step explanation:

His problem can be solved using the principle of proportionality or rule three.

We can take advantage of the proportion between respondents who tell us the number of respondents and how many expect to go on vacation and the total number of workers, therefore:  

                         Respondents /// Whole company

Vacations                  21                          x

Total                          45                        516

then x equals:

x = (516 * 21) / (45)

x = 240.8

x = 241 clients

This means that approximately 241 clients expect to go on vacation throughout the company.

Answer:

241

Step-by-step explanation:

its the answer for khan academy

hope this helps

by the use of elimination method

make all coefficients of subject to be eliminated similar..by multiplying the coefficients with one another

for eqn(i)

5(-10y+9x=-9)

-50y+45x=-45

for eqn(ii)

9(10y+5x=-5)

90y+45x=-45

-50y+45x=-45

90y+45x=-45

...subtract each set from the other...

we get

-140y+0=0

y=0

from eqn(i)

10y+5x=-5

0+5x=-5

x= -1

Answer:

D

Step-by-step explanation:

Answer:

D. For each student, there are 5 markers.

Step-by-step explanation:

A class of 25 students shares a set of 100 markers.

5 students are absent.

Therefore,

No. of students present = 25 - 5 = 20

No. of markers = 100

No. of markers each student gets = 100/20 = 10/2 = 5

Hence, each student gets 5 markers.

Answer:

C. f(x)=5x^2-4x+5 is the correct answer on edge 2021

Answer:

0.68 * 62 = 42.16 kilos

Step-by-step explanation:

0.32 * 62 = 19.84

62 - 19.84 = 42.16 kilos

0.68 * 62 = 42.16 kilos

Answer:

42.16kg

Step-by-step explanation:

32% of 62= 19.84

62-19.84=42.16

Answer:

(a) The required recurrence relation for  the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].

(b)The salary of the employee will be $83421.88 in 2017.

(c) [tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]

Step-by-step explanation:

Summation of a G.P series

[tex]\sum_{i=0}^n r^i= \frac{r^{n+1}-1}{r-1}[/tex]

(a)

Every year the salary is increasing 5% of the salary of the previous year plus $1000.

Let [tex]a_n[/tex] represents the salary of the employee of n years after 2009.

Then [tex]a_{n-1}[/tex] represents the salary of the employee of (n-1) years after 2009.

Then [tex]a_n= a_{n-1}+5\%.a_{n-1}+1000[/tex]

             [tex]=a_{n-1}+0.05a_{n-1}+1000[/tex]

             [tex]=(1+0.05)a_{n-1}+1000[/tex]

            [tex]=1.05a_{n-1}+1000[/tex]

The required recurrence relation for  the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].

(b)

Given, [tex]a_0=\$50,000[/tex]

[tex]a_n=1.05a_{n-1}+1000[/tex]

Since 2017 is 8 years after 2009.

So, n=8.

∴ [tex]a_8[/tex]

[tex]=1.05 a_7+1000[/tex]

[tex]=1.05(1.05a_6+1000)+1000[/tex]

[tex]=1.05^2a_6+1.05\times 1000+1000[/tex]

[tex]=1.05^2(1.05a_5+1000)+1.05\times 1000+1000[/tex]

[tex]=1.05^3a_5+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^3(1.05a_4+1000)+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^4a_4+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^4(1.05a_3+1000)+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^5a_3+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^5(1.05a_2+1000)+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^6a_2+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^6(1.05a_1+1000)+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^7a_1+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^7(1.05a_0+1000)+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^8a_0+1.05^7\times1000+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^8a_0+(1.05^7+1.05^6+1.05^5+1.05^4+1.05^3+1.05^2+1.05+1)1000[/tex]

[tex]=1.05^8 \times 50,000+\frac{1.05^8-1}{1.05-1}\times 1000[/tex]

[tex]=1.05^8\times 50,000+20,000(1.58^8-1)[/tex]

[tex]=70,000\times 1.05^8-20,000[/tex]

≈$83421.88

The salary of the employee will be $83421.88 in 2017.

(c)

Given, [tex]a_0=\$50,000[/tex]

[tex]a_n=1.05a_{n-1}+1000[/tex]

We successively apply the recurrence relation

[tex]a_n=1.05a_{n-1}+1000[/tex]

    [tex]=1.05^1a_{n-1}+1.05^0.1000[/tex]

   [tex]=1.05^1(1.05a_{n-2}+1000)+1.05^0.1000[/tex]

   [tex]=1.05^2a_{n-2}+1.05^1.1000+1.05^0.1000[/tex]

   [tex]=1.05^2(1.05a_{n-3}+1000)+(1.05^1.1000+1.05^0.1000)[/tex]

   [tex]=1.05^3a_{n-3}+(1.05^2.1000+1.05^1.1000+1.05^0.1000)[/tex]

                    ...............................

                   .................................

  [tex]=1.05^na_{n-n}+\sum_{i=0}^{n-1}1.05^i.1000[/tex]

 [tex]=1.05^na_0+1000\sum_{i=0}^{n-1}1.05^i[/tex]

 [tex]=1.05^n.50,000+1000.\frac{1.05^n-1}{1.05-1}[/tex]

 [tex]=1.05^n.50,000+20,000.(1.05^n-1)[/tex]

 [tex]=(50,000+20,000)1.05^n-20,000[/tex]

 [tex]=70,000 . \ 1.05^n-20,000[/tex]

[tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]

The employee’s salary is dictated by the recurrence relation where S_n = S_(n-1) + 1000 + 0.05*S_(n-1). This formula is used to iteratively calculate the salary increase each year, providing an accurate salary for any given year after 2009. However, an explicit formula for this scenario may not be straightforward due to the increment's dependency on the previous year's salary.

The subject of this problem is recurrence relation, a mathematical concept that uses a formula to establish the relationship between successive terms in a numerical sequence. The employee's salary problem can be expressed by the following recurrence:

S_n = S_(n-1) + 1000 + 0.05*S_(n-1), where S_n represents the salary in year n and S_(n-1) refers to the prior year's salary.

To calculate the salary in 2017, you start with the initial salary in 2009 and apply the formula for each subsequent year. After doing this for 8 years (2017 being 8 years past 2009), the salary is found to be $60,796.32.

Unfortunately, a simple explicit formula may not exist for this scenario because of percentage increment based on the previous year's salary. However, the salary can be accurately calculated for any given year using the recurrence relation established in Part (a).

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Final answer:

The number of possible four-digit PIN combinations for an ATM, where no repetition of the same four digits is allowed, is 5040. This is calculated by multiplying the number of choices for each digit position, which are 10, 9, 8, and 7 respectively.

Explanation:

Calculating ATM PIN Code Combinations

To determine the number of possible four-digit PIN combinations for an ATM that does not allow the repetition of the same four digits (such as 5555), we have to consider how many choices we have for each digit. Since there are 10 possible digits (0-9) for each placement and repetition of the same four digits is not allowed, the first digit can be any of the 10 digits, the next digit can also be any of the 10 digits (except for the first digit), and so on.

The number of combinations can be calculated using factorial notation. For the first digit, there are 10 possibilities. For the second digit, there are 9 remaining possibilities (since the digit cannot be the same as the first), for the third digit, there are 8 possibilities, and for the fourth digit, there are 7 possibilities.

The calculation then becomes 10 x 9 x 8 x 7, which equals 5040 possible combinations. This shows that there are numerous ways to create a unique four-digit code without repeating the same digit four times.

Answer:

The answer is C.

Step-by-step explanation:

You can do it by solving both equations :

y = x³ - 8

Let y=0,

x³ - 8 = 0

x³ = 8

x = ³√8

= 2

x² + 5x + 6 = 0

(x+3)(x+2) = 0

x = -3

x = -2

So the domain for 1st equation is 2 and 2nd equation is -2 & -3.

In 1st equation, the answer cannot be option A & B and in 2nd equation, the answer is B.

Answer:

A) domain: x cannot equal −3, −2

Step-by-step explanation:

y = x^3 − 8

________

x^2 + 5x + 6

The function is undefined when the denominator goes to zero

x² + 5x + 6 = 0

x² + 3x + 2x + 6 = 0

x(x + 3) + 2(x + 3) = 0

(x + 2)(x + 3) = 0

x = -3, -2

Domain can take any value except -2 and -3

Answer:

The probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean cannot be calculated.

Step-by-step explanation:

As given in the question statement, the distribution of delivery times is strongly skewed to the right. The population distribution is skewed to right. Too much skewed distribution can cause the statistical model to work ineffectively and affects its performance. The probability can also not be calculated because the sample size is too small. Small sample size affects the results and makes them less reliable because it results in a higher variability and likelihood of skewing the results.

Answer:

We cannot calculate this probability because the sampling distribution is not normal.

Step-by-step explanation:

Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.

Answer:

The sample needs to be at least n = 897 in size.

Step-by-step explanation:

Given

Confidence Level = 95%

Let p = those who had laptop

p = 70% = 0.7

Margin of Error = 3% = 0.03

Let n = required sample.

To estimate the proportion of laptop owners with 95% confidence, first the z-value is calculated. [tex]z_{(a/2)}[/tex]

Given that confidence level = 95%

α  =  1 − 95 %

α  =  1 − 0.95  

α =  0.05  

So;

[tex]z_{(a/2)}[/tex] = [tex]z_{(0.05/2)}[/tex]

[tex]z_{(a/2)}[/tex] = [tex]z_{(0.025)}[/tex]

From the z table

[tex]z_{(0.025)} = 1.96[/tex]

Using formula for margin of error

[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]

where p + q =1

q = 1 - p

q = 1 - 0.7

q = 0.3

So,

[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]

[tex]0.03 = 1.96 * \sqrt{\frac{0.7 * 0.3}{n} }[/tex] --- Make n the subject of formula

First, square both sides

[tex]0.03^{2} = 1.96^{2} * {\frac{0.7 * 0.3}{n} }[/tex] ------ Multiply both sides by [tex]{\frac{n}{0.03^{2}}}[/tex]

[tex]0.03^{2} * {\frac{n}{0.03^{2}}} = 1.96^{2} * {\frac{0.7 * 0.3}{n} } * {\frac{n}{0.03^{2}}}[/tex]

[tex]n = 1.96^{2} * {\frac{0.7 * 0.3}{0.03^{2}} }[/tex]

[tex]n = {\frac{0.806736}{0.0009} }[/tex]

[tex]n = 896.473[/tex]

Hence, the sample needs to be at least n = 897 in size.