Janine is planning on creating a water-based centerpiece for each of the 30 tables at her wedding reception. She has already purchased a cylindrical vase for each table. The radius of the vases is 6 cm and the height is 28 cm. She intends to fill them halfway with water and then add a variety of colored marbles until the waterline is approximately three-quarters of the way up the cylinder. She can buy bags of 100 marbles in 2 different sizes, with radii of 9 mm or 12 mm. A bag of 9 mm marbles costs $3 and a bag of 12 mm marbles costs $4.
a. If Janine only bought 9 mm marbles how much would she spend on marbles for the
whole reception? What if Janine only bought 12 mm marbles? (Note: 1 cm cubed = 1 ml)
b. Janine's parents, who are paying for the wedding, have told her she can spend at d
most dollars on marbles. Write a system of equations and/or inequalities that she can use to determine how many marbles of each type she can buy.
c. Based on your answer to part (b), how many bags of each size marble should Janine buy if she has $180 and wants to mix in as many small marbles as possible?
d. Janine wants to paint the marbles with blue paint. If it requires 10 ml of paint to cover 1 square foot of surface area, how much paint is needed to paint all the marbles?

The estimate for the mean time spent dancing is given as follows:

27 minutes.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

In this problem, we have a grouped frequency chart, hence, using the midpoint rule, the observations are given as follows:

Hence the mean is given as follows:

M = (11 x 6 + 25 x 18 + 23 x 30 + 15 x 42 + 6 x 54)/(11 + 25 + 23 + 15 + 6)

M = 27.

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The solution for y in sqrt(2x + y - 3z) = 5 is y = -2x + 3z + 25. Option A

To solve for y in the equation: sqrt(2x + y - 3z) = 5,

we need to isolate y on one side of the equation by squaring both side of the equation

=(sqrt(2x + y - 3z))^2 = 5^2

=2x + y - 3z = 25

We can solve for y by subtracting 2x and adding 3z to both sides:

y = 25 - 2x + 3z

y = -2x + 3z + 25

Therefore, the solution for y is y = -2x + 3z + 25

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The correct sample space for the gumballs in Julia's bag is: Sample space = {lemon-lime, watermelon, grape}

What is the proper sample space for the gumballs she has in her bag?

The correct sample space for the gumballs in Julia's bag is:

Sample space = {lemon-lime, watermelon, grape}

This is because the sample space represents all possible outcomes or options in an experiment. In this case, the experiment is selecting a gumball from the bag. The three options in the bag are lemon-lime, watermelon, and grape gumballs, so those are the only possible outcomes and they form the sample space. The other options listed in the answer choices, such as numbers or repeated gumball types, do not accurately represent the possible outcomes in this situation.

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Answer:

The video will receive 32,768 views

Step-by-step explanation:

0.8 times 40,960 equals to our answer 32,768 just how 0.8 times 80,000 equals to the 2nd days answer; 64,000

Answer:

(C) 51,200

Step-by-step explanation:

1) 100,000 x 80%

2) 80,000 x 80%

3) 64,000 x 80%

4) 51,200

So, after each day being multiplied by 80 percent the video will receive 51,200 views on the fourth day.

Answer:

The slope is 1/3
The y-intercept is (0,4)
The answer in slope-intercept form: y= 1/3x + 4

Step-by-step explanation:

The slope is 1/3 meaning you rise up 1 and run 3.

The y-intercept is (0,4) Since that's the only thing crossing the Y-Axis

Slope intercept-form Expressed as: y=mx+b

The answer in slope-intercept form: y= 1/3x + 4

Answer:

Step-by-step explanation:

Answer:

$1,297.50

Step-by-step explanation:

For the first week:

15.5 hours x $30/hour = $465

For the second week:

27.75 hours x $30/hour = $832.50

To find the total amount:

$465 + $832.50 = $1,297.50

Answer:

Step-by-step explanation:

You want the area of a sector with radius 5 m subtending an arc of 198°. You also want the radius of a 270° sector with area 363π square inches.

The area of a sector can be found using the formula ...

  A= 1/2r²θ . . . . where θ is in radians

  A = 1/2(5 m)²(198π/180) = (55/4)π m²

The area of sector TOP is 55π/4 = 13.75π square meters.

Solving the area equation for the radius of the sector, we find ...

  r = √(2A/θ)

The radius of the circle with a 270° sector that has an area of 363π in² is ...

  r = √(2·363π/(3/2π)) = √(4·121) = 22

The radius of the circle is 22 inches.

Answer:

Step-by-step explanation:

You want functions that have the given list of asymptotes and intercepts.

The functions of interest here are built as rational functions of products of linear terms. Each numerator linear term (x -p) will make the function have a zero (x-intercept) of x=p. Each denominator linear term (x -p) will make the function have a vertical asymptote at x=p. The horizontal asymptote will be the value of the ratio of the leading numerator and denominator terms as x gets large in magnitude.

The x-intercepts at -2 and 4 mean the numerator factors are (x +2) and (x -4).

The vertical asymptotes at -1 and 3 mean the denominator factors are (x +1) and (x -3).

In order to make the function have a horizontal asymptote of -1, the ratio of leading terms (x²/x²) must have a coefficient of -1.

One function that meets the requirements is ...

  [tex]f(x)=-\dfrac{(x+2)(x-4)}{(x+1)(x-3)}[/tex]

The vertical asymptotes at -5 and 4/3 mean the denominator factors are (x +5) and (3x -4). (We could use (x-4/3), but we prefer integers in the expression.)

The ratio of leading terms (1/x²) is positive for x not between the asymptotes, so we need a negative coefficient.

One function that meets requirements is ...

  [tex]f(x)=-\dfrac{1}{(x+5)(3x-4)} = -\dfrac{1}{3x^2+11x-20}[/tex]

Answer:

6.174 x 10^11

Step-by-step explanation:

We can find the value of k by substituting a known value of x and solving for k.

Let's choose x = 0, then:

f(0 + 3) = (0)² + ke-21

f(3) = ke-21

Since we don't know the value of f(3), we cannot solve directly for k. However, we can use another piece of information: the function f(x) is defined as f(x) = x³ - 1.

Let's substitute x = 0 into the definition of f(x):

f(0) = 0³ - 1

f(0) = -1

Now, we can use this information to find f(3):

f(3) = (3)³ - 1

f(3) = 27 - 1

f(3) = 26

Substituting this back into the original equation:

f(3) = ke-21

26 = ke-21

Solving for k:

k = 26e^21

Therefore, the value of k is approximately 6.174 x 10^11.

1/3

The notation P(x) is used to describe the probability of event x occurring.

Divisors

Before we can do the probability question, we need to find the divisors of 6. Divisors are numbers that can evenly divide another number. The factors and divisors of a number are the same. So, 6 has 4 divisors:

All of these values are on a 6-sided dice. So, in this probability question, there are 4 unsuccessful outcomes.

Probability

The probability of a simple event is the number of successful outcomes divided by the number of possible outcomes. In this situation, there are 6 possible outcomes, each side of the dice. Four of these outcomes do not satisfy the given condition (not a divisor of 6). Thus, there are 2 successful outcomes.

The probability of rolling a number that is not a divisor of 6 is 1/3.

Answer:

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

Let the original price of the bicycle be x.

Set up an equation to reflect the discount:

Solve the given equation for x:

Hence the original price is $112.38.

Answer:

Step-by-step explanation:

Solve first inequality

4x-4 < 8

4x < 12

x < 12/4

x < 3

Solve second inequality

9x+5 > 23

9x > 18

x > 18/9

x > 2

So 2 < x < 3

In interval notation (2 , 3)

Answer: 48% = 1200/x

Step-by-step explanation:

Using the given information, Thursday game generates $2240.00 and Saturday game generates $2413.00.

How much money did Thursday game generate? $2240.00

How much money did Saturday game generate? $2413.00

From the question, we are to determine how much money was taken in at each game.

From the given information, the two games together earn $4653.00 for the team.

Thursday game generates $173.00 less than Saturday's game

Let T represent Thursday game and S represent Saturday game.

Then,

We can write the equations

T + S = $4653.00       --------- (1)

S - T = $173.00           --------- (2)

From the second equation, we can write that

S = $173.00 + T          --------- (3)

Substitute into the first equation

T + S = $4653.00

T + $173.00 + T = $4653.00

2T = $4653.00 - $173.00

2T = $4480

T = $4480/2

T = $2240.00

Substitute into the third equation

S = $173.00 + T

S = $173.00 + $2240.00

S = $2413.00

Hence, Thursday game generates $2240.00 and Saturday game generates $2413.00

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Answer:

Step-by-step explanation:

The required slope of WZ is 3/2 for the given situation.

Since WXYZ is a rectangle, WZ is perpendicular to XY, and the slope of WZ is the negative reciprocal of the slope of XY.

The slope of the line is defined as the angle of the line. It is denoted by m

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The slope of XY is:

m = (y₂ - y₁)/(x₂ -x₁ ) = (-7 - (-5))/(-1 - (-4)) = -2/3

The negative reciprocal of -2/3 is:

-1/(-2/3) = 3/2

Therefore, the slope of WZ is 3/2.

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The area of the shaded triangle is  220 in²

The perimeter of the shaded triangle is 92. 48 in

Note that the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that the parameters are given as;

Substitute the values

Area = 1/2 × 40 × 11

Multiply the values

Area = 440/2

Divide the values

Area = 220 in²

The perimeter would be given as;

Perimeter = a + b + c

Substitute the values

Perimeter = 11 + 40 + 41. 48 = 92. 48 in

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Answer:

Step-by-step explanation:

Step 1 - 3 Tires at $50ea = 3*50 = 150
Total Change to Funds: $150
Step 2 - Returned one tire at $50 =
Total Change to Funds: $150 - $50 = $100

Step 3 - Ahab found a $5 bill

Total Change to Funds: $100-$5 = $95

Step 4 - Purchased (2) Jackets at $40ea = 2*40=$80
Total Change to Funds: $95 + $80 = $175

150-50+5-80 = 175

Answer:

The center of the circle is (3, -2) ((three, negative two)).

The radius of the circle is 5 (five).

The equations in terms of f(x) to match each graph with its transformations should be written as follows;

Graph 1 ⇒ f(x) + 4

Graph 2 ⇒ -f(x - 4)

Graph 3 ⇒ f(x - 7)

Graph 4 ⇒ f(x + 2) - 5

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to write an equation that models Graph 1, we would have to apply a vertical translation to f(x) by 4 units up.

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Answer:

$7760

Step-by-step explanation:

To find the total average credit card debt for the year 2000, we need to substitute t = 5 into the given expression:

404t + 5740 = 404(5) + 5740

= 2020 + 5740

= 7760

Answer: 2

Step-by-step explanation:

The number of trees that are less than 6 feet tall according to the given stem and leaf plot is 2. The stem value of 5 represents trees that are 5 feet tall, and the leaf values of 1 and 2 indicate that there are two trees in total with a height less than 6 feet. Therefore, the answer is 2.

Answer:

A to B would be plus 6cm. so 11cm

Step-by-step explanation:

if we look at the comparison from the first image and the bigger one we see that the differences 6cm apart so the answer is plus 6cm (11cm) in all

Pls give brainlist me the world

Have a good day :)

Answer:

98 pages

Step-by-step explanation:

Make a proportion according to the given information:

56 pg - 4 min

x pg - 7 min

Cross-multiply to find x:

[tex]x = \frac{7 \times 56}{4} = \frac{392}{4} = 98[/tex]

Answer:

→ 125^x = 5^3x + 4

→ (5^3)x = 5^3x + 4

→ 5^3x = 5^3x + 4

→ 0 = 4

→ x ∈ Ø

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of six sides on the die, two are the desired results, which are 1 or 6, hence the probability is given as follows:

p = 2/6

p = 1/3.

Hence, out of 60 trials, the expected number of successes is given as follows:

E(X) = 60 x 1/3

E(X) = 20.

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Answer:

In 2040, the population will be 800,000.

In 2060, the population will be 1,600,000.

In 2080, the population will be 3,200,000.

Step-by-step explanation:

The population of a country doubles every 20 years.

The population in 2020 was 400,000.

We need to find out the population of the country in 2040, 2060, and 2080.

exponential growth formula also known as the compound interest formula

A = P(1 + r/n)^(nt)

where:

A is the final amount after time t

P is the initial principal or population

r is the annual interest rate or growth rate

n is the number of times the interest or growth is compounded per year

t is the number of years

If the population of a country doubles every 20 years, it means that the growth rate is constant at 3.5% per year (because 2^(1/20) = 1.035).

To calculate the population in future years, we can use the formula:

Population = Initial Population * (1 + Growth Rate)^(Number of Years / 20)

a) To find the population in 2040, we need to calculate the number of years from 2020 to 2040, which is 20 years. Therefore:

Population in 2040 = 400,000 * (1 + 0.035)^(20/20) = 400,000 * 2 = 800,000

b) To find the population in 2060, we need to calculate the number of years from 2020 to 2060, which is 40 years. Therefore:

Population in 2060 = 400,000 * (1 + 0.035)^(40/20) = 400,000 * 4 = 1,600,000

c) To find the population in 2080, we need to calculate the number of years from 2020 to 2080, which is 60 years. Therefore:

Population in 2080 = 400,000 * (1 + 0.035)^(60/20) = 400,000 * 8 = 3,200,000

Therefore, the population of the country in 2040 will be 800,000, in 2060 will be 1,600,000, and in 2080 will be 3,200,000, assuming a constant growth rate.

chatgpt

Answer:

A. 800 000

B. 1 600 000

C. 3 200 000

Step-by-step explanation:

If you ever wondered how many people will be living in your city in the future, you can use some simple math to find out. All you need is the formula x(t) = x0 x (1 + r)^t, where x(t) is the population after time t, x0 is the initial population, r is the growth rate and t is the time in years.

For example, let's say your city had 400 000 people in 2020 and it doubles every 20 years. That means the growth rate is r = 0.0353, which you can find by solving for r when x(t) = 2x0 and t = 20.

Now you can plug in different values of t to see how many people will be living in your city in 2040, 2060 and 2080. You get:

x(20) = 400 000 x (1 + 0.0353)^20 = 800 000

x(40) = 400 000 x (1 + 0.0353)^40 = 1 600 000

x(60) = 400 000 x (1 + 0.0353)^60 = 3 200 000

Wow, that's a lot of people! You better start looking for a bigger house or a quieter neighborhood. Or maybe you can move to another city with a lower growth rate. Or maybe you can invent a time machine and go back to 2020 when things were simpler. The choice is yours!

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

The most important variable in the human body is likely dependent on the specific context and system being considered.

Length, viscosity, and diameter are all important variables in the human body, but it is difficult to say which one is the most important as each plays a different role in different bodily systems.

Length, for example, is important in skeletal muscle physiology, where it determines the force and velocity of muscle contractions. Viscosity is important in the circulatory system, where it affects blood flow and the ability of the blood to transport oxygen and other nutrients. Diameter is also important in the circulatory system, as it determines the resistance to blood flow and the distribution of blood to different organs and tissues.

Therefore, the most important variable in the human body is likely dependent on the specific context and system being considered.

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Using the scale factor of the dilation, the measure of line U'V' is calculated as: 5 units

Dilation is a transformation that changes the size of a geometric figure, either making it larger or smaller, while preserving its shape and orientation.

If line UV is dilated by a scale factor of 1/3 to form line U'V', it means that the length of U'V' is one-third of the length of UV.

Since the length of UV is 15, the length of U'V' can be found by multiplying 15 by 1/3:

U'V' = (1/3) x 15

Simplifying the expression, we get:

U'V' = 5

Therefore, the measure of line U'V' is 5.

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