6) There are many cylinders with a height of 4 inches.
Let rrepresent the radius in inches and V represent the
volume in cubic inches.
Complete the table relating the radius and volume of cylinders
with height 4 inches. Round each number to the nearest cubic
inch.

The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

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Answer:

179 + 49+ 139 = 367

Step-by-step explanation:

A shopkeeper purchased a bag for Rs 800 and umbrella for 400.if s/he sold the bag at 15% profit and umbrella at 15% loss,find his/her profit or loss percent in whole transaction.

pls help

Answer:

$3,570

Step-by-step explanation:

Simple interest = principal × rate × time / 100

Principal = $3,500

Rate = 2%

Time = 1 year

Simple interest = principal × rate × time / 100

= (3500 × 2 × 1) / 100

= 7000 / 100

= 70

Simple interest = $70

Total amount that Luke's sister will repay = principal + simple interest

= $3,500 + $70

= $3,570

Total amount that Luke's sister will repay = $3,570

The least three numbers that when added together give a number multiple of 7 are:

2, 3 and 7

Prime numbers are numbers that have only two divisors, but these two divisors are always the same number and the number 1.

If we want to know a number that comes from the sum of three prime numbers and that in turn is divisible by 7, then let's identify the prime numbers from 0 to 20:

2, 3, 5, 7, 11, 13, 17, 19

Let's start with the lowest ones:

The three numbers are: 2, 3 and 7.

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The first six terms of the sequence defined by an = (5n -1 )/3n+1 Q1 = a1= 1, a2=1.286 , a3=1.4, a4=1.462 , a5=1.5 ,a6=1.526 . Therefore, the sequence has a limit of 5/3.

To find the first six terms of the sequence defined by an = (5n -1 )/3n+1, we need to substitute the values of n=1, 2, 3, 4, 5, and 6 into the expression given.

Then we will have the values of the first six terms of the sequence:

a1 = (5(1) - 1)/(3(1) + 1) = 4/4 = 1

a2 = (5(2) - 1)/(3(2) + 1) = 9/7 ≈ 1.286

a3 = (5(3) - 1)/(3(3) + 1) = 14/10 = 1.4

a4 = (5(4) - 1)/(3(4) + 1) = 19/13 ≈ 1.462

a5 = (5(5) - 1)/(3(5) + 1) = 24/16 = 1.5

a6 = (5(6) - 1)/(3(6) + 1) = 29/19 ≈ 1.526

To find whether the sequence appears to have a limit or not, we can observe the values of the sequence. As we can see, the values of the sequence are increasing, but they do not seem to be increasing without bound.

Therefore, the sequence appears to have a limit. Using the limit formula, we can find the limit of the sequence as follows: lim n→∞ (5n - 1)/(3n + 1) = lim n→∞ [(5/n) - (1/n)] / [(3/n) + (1/n)] = lim n→∞ [5 - 1/n] / [3 + 1/n] = 5/3

So, the sequence has a limit of 5/3.

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Answer:

Step-by-step explanation:

1. Identify the slope.

2. Identify the point.

3. Substitute the values into the point-slope form, y − y 1 = m ( x − x 1 ) .

4. Write the equation in slope-intercept form.

Answer:

33

Step-by-step explanation:

Answer:

Part A) $9.96

Part B) $7.47

Step-by-step explanation:

Given:

If 2 Ice cream = $4.98

Step:

Then Let's find how much is 1 Ice cream.

To find the cost of 1 Ice cream divide the $4.98 by 2

which gives you 2.49

Now:

Part A) How much will 4 pints of ice cream cost?

2.49 x 4 = $9.96

Hence, 4 pints of ice cream cost → $9.96

Part B) How much will 3 pints of ice cream cost?

2.49 x 3 = $7.47

Hence, 3 pints of ice cream cost → $7.47

[RevyBreeze]

Answer:

15+7=22

Step-by-step explanation:

Set up the equations.

Answer:

a - incorrect

b - correct

c - correct

d - incorrect

e - correct

Step-by-step explanation:

Answer:

-270

Step-by-step explanation:

Answer:

\(6x^2+17x-45\)

Step-by-step explanation:

Our equation is

\(\left(2x+9\right)\left(3x-5\right)\)

Simplify

\(6x^2-10x+27x-45\)

Combine like terms

\(6x^2+17x-45\)

Brainliest please

True. We expect most of the data in a data set to fall within 2 standard deviations of the mean of the data set.

In a normal distribution, which is a common assumption for many data sets, it is expected that approximately 68% of the data falls within 1 standard deviation of the mean, and approximately 95% falls within 2 standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.

The empirical rule is based on the properties of a normal distribution, which is symmetric and bell-shaped. It states that the majority of the data is concentrated around the mean, with the spread of the data increasing as we move further away from the mean. Within 2 standard deviations of the mean, we capture a large portion of the data, approximately 95%. This means that most of the data points are expected to fall within this range.

However, it's important to note that this statement assumes a normal distribution and may not hold true for all data sets. In cases where the data does not follow a normal distribution or has outliers, the proportion of data falling within 2 standard deviations may differ.

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The required shortest distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.

The slope is defined as the ratio measure of rise to measure of the run.

Here,
The shortest possible distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.

This is because, if the doorway is 1.3 feet above the parking lot, the ramp will need to rise 1.3 feet in order for a person or vehicle to be able to enter the building. The length of the ramp will be equal to the rise, so in this case, the shortest possible distance between the building and the end of the ramp would be 1.3 feet.

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Answer:

the answer is -72-41

Step-by-step explanation:

Answer:

\( \displaystyle A _{ \text{vinyl record }} \approx 490 {cm}^{2} \)

Step-by-step explanation:

we are given the circumstances of a vinyl record

we want to figure out the area

in order to do so we should figure out redious first

recall that,

\( \displaystyle \rm C = 2\pi r\)

given that, C=78.5

thus substitute:

\( \displaystyle \rm 78.5= 2\pi r\)

divide both sides by 2π:

\( \displaystyle r = \frac{78.5}{2\pi} \)

we have figured out r now we'll figure out the area

remember that,

\( \displaystyle A _{ \text{circle}} = \pi {r}^{2} \)

substitute the value of r

\( \displaystyle A _{ \text{vinyl record }} = \pi { \bigg(\frac{78 .5}{2\pi} \bigg)}^{2} \)

by using calculator we acquire

\( \displaystyle A _{ \text{vinyl record }} = 490 {cm}^{2} \)

The executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

Let x be the number of days the executive stayed in London, y be the number of days he stayed in Paris, and z be the number of days he stayed in Rome.

We can set up the following equations to represent the given information:

180x + 230y + 160z = 2660 (hotel bills)

110x + 120y + 90z = 1520 (meal expenses)

x = y + z (he spent as many days in London as he did in Paris and Rome combined)

We can rearrange the third equation to get y + z - x = 0 and substitute it into the first two equations to eliminate x:

180x + 230y + 160z = 2660

110x + 120y + 90z = 1520

-180y - 180z + 180x = 0

Adding the first and third equations gives us:

360x + 50y - 20z = 2660

Adding the second and third equations gives us: 290x - 60y - 90z = 1520

We can now solve for x by multiplying the first equation by 3 and the second equation by 5 and subtracting them:

1080x + 150y - 60z = 7980

-1450x + 300y + 450z = 7600

----------------------------------

1630x - 150y - 510z = 380

Solving for x gives us:

x = (150y + 510z + 380) / 1630

Substituting this back into the third equation gives us:

y + z - (150y + 510z + 380) / 1630 = 0

Multiplying by 1630 and rearranging gives us:

1480y + 490z = 380

We can now solve for y by multiplying the first equation by 490 and the second equation by 50 and subtracting them:

490(360x + 50y - 20z) = 490(2660)

50(290x - 60y - 90z) = 50(1520)

---------------------------------------------------

19600x + 24500y - 9800z = 1303400

-14500x + 3000y + 4500z = 76000 --------------------------------------------------

4100x - 21500y - 14300z = 1227400

Solving for y gives us:

y = (4100x + 14300z - 1227400) / 21500

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480(4100x + 14300z - 1227400) / 21500 + 490z = 380

Multiplying by 21500 and rearranging gives us:

606800x + 2054200z - 1817320000 = 0

Solving for z gives us:

z = (1817320000 - 606800x) / 2054200

Substituting this back into the equation x = y + z gives us:

x = y + (1817320000 - 606800x) / 2054200

Multiplying by 2054200 and rearranging gives us: 606800x^2 - 2054200xy - 2054200x + 1817320000y + 3707618640000 = 0

Using the quadratic formula, we can find the value of x:

x = (2054200y + 2054200 ± √[(2054200y + 2054200)^2 - 4(606800)(1817320000y + 3707618640000)]) / (2*606800)

Plugging in the value of y from earlier gives us:

x = (2054200(4100x + 14300z - 1227400) / 21500 + 2054200 ± √[(2054200(4100x + 14300z - 1227400) / 21500 + 2054200)^2 - 4(606800)(1817320000(4100x + 14300z - 1227400) / 21500 + 3707618640000)]) / (2*606800)

Simplifying and solving for x gives us:

x = 10

Substituting this back into the equation x = y + z gives us:

10 = y + z

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480y + 490(10 - y) = 380

Solving for y gives us:

y = 6

Substituting this back into the equation 10 = y + z gives us: 10 = 6 + z

Solving for z gives us:

z = 4

Therefore, the executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

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Answer:

f=1

Step-by-step explanation:

Let start off with doing -f plus 4f which gives you 3f. The equation would now be 2+3f=8-3f. Add 3f so you can cancel out the -3f and add the 3f to the other 3f. Now your equation is 2+6f=8. Cancel out do by doing -2. (Don't forget to to it to the 8 also.) Now your equation is 6f=6. Divide 6 from both sides to get 1. (You divide because you want to get f alone.

Answer:

B) \(9d^8\)

Step-by-step explanation:

To find the expression equivalent to \((3d^4)^2\), we must simplify the given expression. This can be done by applying an exponent rule:

\((a*b)^x=a^xb^x\)

In the context of our problem, we would have:

\((3*d^4)^2\)

Therefore, when that exponent is distributed, we get:

\((3^2d^8)\)

Simplified, we have:

\(9d^8\)

9514 1404 393

Answer:

Step-by-step explanation:

Arithmetic sequence

The terms of an arithmetic sequence have common difference. If the missing term is x, then the difference between terms is the same:

  x -250 = 10 -x

  2x = 260 . . . . . . add 250+x to both sides

  x = 130 . . . . . . . . divide by 2

The missing term of an arithmetic sequence is 130.

(the common difference is -120)

__

Geometric sequence

The terms of a geometric sequence have a common ratio. If the missing term is x, then the ratios between terms are the same:

  x/250 = 10/x

  x^2 = 2500 . . . . . . . multiply both sides by 250x

  x = ±√2500 = ±50 . . . take the square root

The missing term of a geometric sequence is +50 or -50.

(the common ratio is ±1/5)

Answer:

42

Step-by-step explanation:

1

29

+13

 42

Answer:

m+13=29

m=29-13

m=16

Step-by-step explanation:

Answer: its 2πr

Step-by-step explanation:

Answer:

(- 2, 2 )

Step-by-step explanation:

Given the 2 equations

y = x + 4 → (1)

y = - 2x - 2 → (2)

Substitute y = x + 4 into (2)

x + 4 = - 2x - 2 ( add 2x to both sides )

3x + 4 = - 2 ( subtract 4 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

Substitute x = - 2 into either of the 2 equations abd evaluate for y

Substituting into (1)

y = - 2 + 4 = 2

solution is (- 2, 2 )

Answer:

Approximately 0.1894 or 18.94% of the population is less than 10.0.

Step-by-step explanation:

On use the z-score formula and the standard normal distribution.

a. To compute the z-value associated with 14.3, we use the formula:z = (x - μ) / σWhere:

x = 14.3 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (14.3 - 12.2) / 2.5

z = 2.1 / 2.5

z ≈ 0.84

Therefore, the z-value associated with 14.3 is approximately 0.84.

b. To obtain the proportion of the population between 12.2 and 14.3, we need to get the area under the standard normal distribution curve between the corresponding z-scores.

Using a standard normal distribution table or a calculator, we can find the area associated with each z-score.The z-value for 12.2 can be calculated using the same formula as in part a:

z1 = (12.2 - 12.2) / 2.5

z1 = 0 / 2.5

z1 = 0

The z-value for 14.3 is already known from part a: z2 ≈ 0.84.

Now, we obtain the proportion by subtracting the area associated with z1 from the area associated with z2:

Proportion = Area(z1 < z < z2)

Using a standard normal distribution table or a calculator, we obtain:

Area(z < 0) ≈ 0.5000 (from the table)

Area(z < 0.84) ≈ 0.7995 (from the table)

Proportion = 0.7995 - 0.5000

Proportion ≈ 0.2995

Therefore, approximately 0.2995 or 29.95% of the population is between 12.2 and 14.3.

c. To obtain the proportion of the population less than 10.0, we need to get the area under the standard normal distribution curve to the left of the corresponding z-score.Using the z-score formula:z = (x - μ) / σ

Where:

x = 10.0 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (10.0 - 12.2) / 2.5

z = -2.2 / 2.5

z ≈ -0.88

Now, we obtain the proportion by looking up the area associated with z ≈ -0.88 using a standard normal distribution table or a calculator:

Area(z < -0.88) ≈ 0.1894 (from the table)

Therefore, approximately 0.1894 or 18.94% of the population is less than 10.0.

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y = 5x + 35

When x = 0, we substitute x = 0 into the equation above and then solve for y

y = 5(0) + 35

y = 0+ 35

y = 35

when x =3, substitute into the equation and then solve for y

y = 5(3) + 35

y = 15 + 35

y = 50

when x=-7, substitute x=-7 into the equation above and then solve for y

y = 5(-7) + 35

y = -35+ 35

y=0

x y (x,y)

0 35 (0, 35)

3 50 (3, 50)

-7 0 (-7, 0)

The simplified form of the polynomial is \(-(a^2 / (6b^3)).\)

Polynomials are algebraic expressions that consist of variables and coefficients. The variables are often referred to as "indeterminates." The word polynomial comes from the terms "poly" and "nomial," which mean "many" and "terms," respectively. When you combine exponents, constants, and variables using mathematical operations such as addition, subtraction, multiplication, and division (excluding division by a variable), you get a polynomial. Depending on the number of terms it has, a polynomial can be categorized as a monomial, binomial, or trinomial.

To simplify this expression, we can use the following rules of exponents:

\(a^m/a^n = a^{(m-n) }\)(when the bases are the same)

\(a^{-m} = 1/a^m\\(1/b^m) = b^{-m}\)

Using these rules, we can simplify the expression as follows:

\(-6a^3b^{-1}/36ab^2 = - (6/36) \times a^{(3-1)} \times b^{(-1-2)}\\\\= - (1/6) \times a^2 \times b^{(-3)}\\\\= - (a^2 / (6b^3))\)

Therefore, the simplified form of the expression is \(-(a^2 / (6b^3)).\)

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation: