Answers
Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.
Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.
Radius (r) = 8 cm / 2 = 4 cm
Height (h) = 19 cm
So, V1 = π(4 cm)²(19 cm)
≈ 3032.07 cm³
Container #2:
Radius (r) = 5 cm
Height (h) = 12 cm
Using the formula:
V2 = π(5 cm)²(12 cm)
≈ 942.48 cm³
Container #3:
Diameter (d) = 12 cm
Radius (r) = 12 cm / 2 = 6 cm
Height (h) = 10 cm
V3 = π(6 cm)²(10 cm)
≈ 1130.97 cm³
Now, Comparing the volumes:
V1 ≈ 3032 cm³
V2 ≈ 942 cm³
V3 ≈ 1131 cm³
Learn more about Volume here:
https://brainly.com/question/28058531
#SPJ1
Related Questions
A missile is moving 1810 m/s at a 20.0° angle. It needs to hit a target 19,500 m away in a 32.0° direction in 9.20 s. What is the magnitude of the acceleration that the engine must produce?
Answers
Answer:
Aprox: 465.4 ms/2
Step-by-step explanation:
To find the magnitude of the acceleration the engine must produce, we'll break down the missile's motion into its horizontal and vertical components.
Given:
Initial velocity (V₀) = 1810 m/s
Launch angle (θ) = 20.0°
Target distance (d) = 19,500 m
Target direction (φ) = 32.0°
Time of flight (t) = 9.20 s
First, let's find the horizontal and vertical components of the missile's initial velocity (V₀x and V₀y).
V₀x = V₀ * cos(θ)
V₀y = V₀ * sin(θ)
V₀x = 1810 m/s * cos(20.0°) ≈ 1712.4 m/s
V₀y = 1810 m/s * sin(20.0°) ≈ 618.8 m/s
Now, let's find the horizontal and vertical displacements (dx and dy) of the missile using the time of flight (t) and the target distance (d).
dx = d * cos(φ)
dy = d * sin(φ)
dx = 19,500 m * cos(32.0°) ≈ 16,402.8 m
dy = 19,500 m * sin(32.0°) ≈ 10,236.8 m
Next, let's calculate the acceleration needed in the x-direction (ax) and y-direction (ay) to cover the horizontal and vertical displacements in the given time.
ax = (2 * dx) / t²
ay = (2 * dy) / t²
ax = (2 * 16,402.8 m) / (9.20 s)² ≈ 391.7 m/s²
ay = (2 * 10,236.8 m) / (9.20 s)² ≈ 257.7 m/s²
Finally, to find the magnitude of the acceleration, we can use the Pythagorean theorem:
acceleration magnitude (a) = √(ax² + ay²)
a = √(391.7 m/s²)² + (257.7 m/s²)² ≈ 465.4 m/s²
Therefore, the magnitude of the acceleration that the engine must produce is approximately 465.4 m/s².
hat amount did she get back? (h) Ujeli had 11 pencils. She kept 3 pencils for herself and divided the remaining pencil equal among 4 of her friends. How many pencils did she give to each of them?
Answers
Answer:
2
Step-by-step explanation:
Ujeli had 11 pencils and she kept 3 so 11-3 = 8
so that means that the remaining pencil were dived by 4 (8÷2) = 2
A girl is on a bridge 38.9 m high. She throws a rock straight down at -12.5 m/s. How long does it the rock to hit the ground
Answers
Answer:
3.14 seconds
Step-by-step explanation:
1-56.
The owner of Universal Widgets has two teams of employees and
wants to know which team is working the "best." The assistant
manager gathered data for the number of widgets made per team
member on various days. He presented the data to the owner as
two boxplots, shown at right. The owner is confused.
a. Help the owner decide which team is working the "best"
by comparing center, shape, spread, and outliers.
b. Which team had a smaller standard deviation? Explain.
200
150
100
30
Team I
Answers
Center: We can compare the medians of the two boxplots to get an idea of the center. From the boxplots, we see that the median of Team I is around 110 widgets per team member, while the median of Team II is around 90 widgets per team member. This suggests that Team I is working better in terms of productivity.
Shape: We can compare the shapes of the two boxplots to see if there are any differences in the distributions. From the boxplots, we see that both teams have roughly symmetric distributions, with no significant skewness.
Spread: We can compare the interquartile ranges (IQRs) of the two boxplots to get an idea of the spread. From the boxplots, we see that the IQR of Team I is around 30 widgets per team member, while the IQR of Team II is around 40 widgets per team member. This suggests that Team I has a smaller spread and is more consistent in their productivity.
Outliers: We can compare the number of outliers in the two boxplots to see if there are any extreme values. From the boxplots, we see that both teams have a similar number of outliers, with a few points outside the whiskers.
Based on these comparisons, we can conclude that Team I is working better than Team II in terms ofproductivity. Team I has a higher median, a smaller spread, and a similar number of outliers compared to Team II.
b. To determine which team had a smaller standard deviation, we need to calculate the standard deviation for each team. However, the boxplot only gives us information about the quartiles, the median, and the outliers, and not the individual data points. Therefore, we cannot directly calculate the standard deviation from the boxplot.
However, we can make an inference based on the spread of the boxplots. We saw in part (a) that the IQR of Team I is smaller than the IQR of Team II. Since the IQR is a measure of spread that includes the middle 50% of the data, we can infer that the standard deviation of Team I is likely smaller than the standard deviation of Team II. This is because a smaller IQR suggests that the data is more tightly clustered around the median, which would result in a smaller standard deviation.
Therefore, based on the boxplots, we can infer that Team I had a smaller standard deviation than Team II.
does anyone have answers to Practice: Unit Rates for Ratios with Fractions Level G iready and the quiz? I will give a lot of points and brainliest answer
Answers
6 c of flour per c of water
Which fraction represents Raul's speed in miles per hour?
What is Raul's speed in miles per hour?
8 over 4/5
10
What is the rate in cups of corn starch per cup of water?
3/8
What is the price per pound of the dried apricots?
$6
What is Ellie's speed in miles per minute?
1/12 mi/min
At that rate, what is the price of 2 tons of gravel?
128
While direct answers to iReady tasks are not provided, guidance for tackling problems involving unit rates and ratios with fractions was presented. The concept to calculate the unit rate involves dividing the first quantity by the second quantity. One should work towards solving these problems independently to reinforce the learning.
Explanation:I'm sorry, but I cannot provide direct answers to your iReady task; it would not be fair or beneficial to your learning. However, I can guide you in how to tackle problems involving unit rates and ratios with fractions. With a unit rate, you're finding a ratio that compares a quantity to one unit of another quantity. The method typically involves dividing the first quantity by the second one.
For example, if you have a problem that says '6 cookies cost $1.50, what is the unit rate?', you would solve it by dividing 1.50 (the cost) by 6 (the number of cookies) to find the unit cost of a single cookie. This gives you a unit rate of $0.25 per cookie. If your questions on iReady involve complex fractions or operations, follow the same concept but use the relevant operation (multiplication, division, etc.). Practice moving toward solving these problems independently to improve your understanding of the concept.
Learn more about Unit Rates and Ratios with Fractions here:https://brainly.com/question/33490440
#SPJ2
A native wolf species has been reintroduced into a national forest. Originally, 46 wolves were transplanted. Assuming that the population is growing exponentially at a rate of 5.6%, how long will it take for the population to reach 150 wolves? Round your answer to the first decimal place.
Answers
Nt = N0 × (1 + r)^t
where Nt is the population at time t, N0 is the initial population, r is the growth rate, and t is the time.
In this case, N0 = 46, r = 0.056 (since the growth rate is given as a percentage, we need to divide by 100 to get the decimal equivalent), and we want to find t when Nt = 150. So we can plug in these values and solve for t:
150 = 46 × (1 + 0.056)^t
Divide both sides by 46:
150/46 = (1 + 0.056)^t
Take the natural log of both sides:
ln(150/46) = t × ln(1 + 0.056)
Solve for t:
t = ln(150/46) / ln(1 + 0.056) ≈ 8.6 years
Therefore, it will take approximately 8.6 years for the wolf population to reach 150 individuals.
An artist made a cone of stainless steel, then sliced it into three pieces. what is the volume of the largest piece? PLEASE SHOW WORK AND EXPLAIN HOW YOU GOT YOUR ANSWER I WILL MARK YOU BRAINLIEST!!!
Answers
The volume of the largest piece is 10, 597. 5 cm³
How to determine the volumeThe largest part of the cone takes the shape of a cylinder.
Now, the formula for calculating the volume of a cylinder is expressed as;
V = πr²h
The parameters of the formula are enumerated as;
V is the volume of the cylinder.r is the radius of the cylinder.h is the height of the cylinder.Now, substitute the values, we get;
Diameter = 2 radius
Radius = 30/2
Radius = 15cm
Height = 15cm
Now, substitute the values, we get;
Volume = 3.14 × 15² ×15
Find the square value and substitute, we have;
Volume = 10, 597. 5 cm³
Learn more about volume at: https://brainly.com/question/1972490
#SPJ1
Write a system of linear equations for the graph below. really need lots of help with this!
i also need the y's
Answers
Answer:
friend with this information you cannot know the answer you have to say everything says about that mathematical problem
What is the area of a rectangle whose width is n feet and who’s length is 2 feet more than 3 times it’s width in terms of n?
Answers
Answer: The length of the rectangle is given as "2 feet more than 3 times its width."
Let's break it down step by step:
The width of the rectangle is n feet.Three times the width is 3n.Two feet more than 3 times the width is 3n + 2.
The formula for the area of a rectangle is length multiplied by width. So, in terms of n, the area of the rectangle would be:
Area = Length × Width
= (3n + 2) × n
= 3n^2 + 2n
Therefore, the area of the rectangle, in terms of n, is 3n^2 + 2n.
In a laboratory experiment, the population of bacteria in a petri dish started off at
4900 and is growing exponentially at 8% per hour. Write a function to represent the
population of bacteria after t hours, where the rate of change per minute can be
found from a constant in the function. Round all coefficients in the function to four
decimal places. Also, determine the percentage rate of change per minute, to the
nearest hundredth of a percent.
Answers
1. The function representing the population of bacteria after t minutes is P(t) = 4900× [tex]e^{(0.08(t/60)}[/tex]
2. The percentage rate of change per minute is approximately 0.13%.
How did we find the function and percentage rate?
The general form of an exponential growth function ⇒ P(t) = P0 ×[tex]e^{(rt)}[/tex]
P(t) is the population at time t,
P0 is the initial population,⇒4900
r is the growth rate ⇒ 8%
t is the time.
Therefore, our function in terms of hours (t) becomes:
P(t) = 4900 × [tex]e^{(0.08t)}[/tex]
To find per minute, there are 60 minutes in an hour,
∴ t becomes t/60
P(t) = 4900× [tex]e^{(0.08(t/60))}[/tex]
We know the rate of change per hour is 8%, so the rate of change per minute will be 8% divided by 60, which is
[tex]e^{(0.08/60)-1}[/tex] × 100 = 0.13%.
Find more exercises on exponential growth function;
https://brainly.com/question/14344314
#SPJ1
Can u help me please fill in the square
Answers
The equation of the circle is (x + 4)² + (y - 1)² = 81
Given is an equation of a circle we need to convert it in standard form,
x² + y² + 8x - 2y = 64,
To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.
The standard form of a circle equation is:
(x - h)² + (y - k)² = r²
where (h, k) represents the center of the circle, and r represents the radius.
Let's convert the given equation to standard form step by step:
x² + y² + 8x - 2y = 64
Rearrange the equation to group the x-terms and y-terms:
x² + 8x + y² - 2y = 64
Now, complete the square for the x-terms.
Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:
x² + 8x + 16 + y² - 2y = 64 + 16
Simplify:
(x + 4)² + y² - 2y = 80
Complete the square for the y-terms.
Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:
(x + 4)² + y² - 2y + 1 = 80 + 1
Simplify:
(x + 4)² + (y - 1)² = 81
Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.
Hence the equation of the circle is (x + 4)² + (y - 1)² = 81
Learn more about equation of a circle click;
https://brainly.com/question/29104982
#SPJ1
what is greatest common factor of -x^2+6x-19
Answers
The greatest common factor of -x^2 + 6x - 19 is 1.
To find the greatest common factor (GCF) of the polynomial [tex]-x^2 + 6x - 19,[/tex] we need to factorize the polynomial and identify the common factors among its terms.
First, let's examine the polynomial and see if we can factor it further:
[tex]-x^2 + 6x - 19[/tex]
The polynomial does not appear to have any common factors among its terms.
It cannot be factored using simple integer factors.
In this case, we can say that the GCF of the given polynomial is 1.
It is important to note that the GCF represents the highest degree of common factors that can be factored out from all terms of a polynomial. In this particular case, the polynomial does not possess any common factors that can be factored out.
It's worth mentioning that this polynomial is already in its simplest form and cannot be factored further.
However, if the polynomial had common factors that could be factored out, such as common binomial factors or other mathematical patterns, the GCF would differ from 1.
But in this case, the polynomial does not exhibit any common factors beyond 1.
For similar question on greatest common factor.
https://brainly.com/question/25266622
#SPJ8
A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
Answers
The work done in stretching the spring from 10 centimeters to 40 centimeters is 9000 joules.
To determine the work done in stretching the spring from 10 centimeters to 40 centimeters, we need to understand the relationship between force, displacement, and work.
In this case, we are given that a force of 450 newtons stretches the spring by 30 centimeters.
We can use this information to calculate the spring constant (k) using Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement it undergoes.
Hooke's Law: F = kx
Where:
F is the force applied,
k is the spring constant, and
x is the displacement of the spring.
We can rearrange the equation to solve for k:
k = F / x
k = 450 N / 30 cm
k = 15 N/cm
Now that we have the spring constant, we can calculate the work done in stretching the spring from 10 cm to 40 cm using the formula for work:
Work [tex]= (1/2)k(x2^2 - x1^2)[/tex]
Where:
k is the spring constant,
x1 is the initial displacement, and
x2 is the final displacement.
Plugging in the values:
Work [tex]= (1/2)(15 N/cm)(40 cm^2 - 10 cm^2)[/tex]
Work [tex]= (1/2)(15 N/cm)(1200 cm^2)[/tex]
Work [tex]= (1/2)(15 N/cm)(1200 cm^2)[/tex]
Work = 9000 N·cm or 9000 joules (since 1 N·cm = 1 joule)
For similar question on spring.
https://brainly.com/question/28203351
#SPJ8
b) 9 mm 6 mm 7 mm surface area for this question
Answers
The surface area of the rectangular prism is 318 square mm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
9 mm by 6 mm by 7 mm
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (9 * 6 + 9 * 7 + 6 *7)
Evaluate
Area = 318
Hence, the area is 318 square mm
Read more about surface area at
brainly.com/question/26403859
#SPJ1
Question
The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?
A pair of equations is shown below:
y = 3x − 5
y = 6x − 8
Part A: Show all of your steps of how you will use substitution to determine the values for x and y. (4 points)
Part B: What is the solution, or ordered pair, for the two equations?
Answers
Part A: equate the expressions 6x - 8 = 3x - 5
collect the like terms 6x -3x = -5 + 8
Divide by the coefficient x = 1
Part B: The values are (1, -3)
How to determine the valuesTo determine the value of the variables, we need to consider the equations.
From the information given, we have the equations given as;
y = 3x − 5
y = 6x − 8
Now, equate the expressions, we get;
6x - 8 = 3x - 5
collect the like terms, we have;
6x - 3x = -5 + 8
add or subtract the like terms
3x = 3
Divide by the coefficient
x = 1
Substitute the value
y= 6(1) - 9
expand the bracket
y = 6 - 9 = -3
Learn more about substitution at: https://brainly.com/question/22340165
#SPJ1
2. The table includes results from polygraph experiments. In each case, it was known if the
subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the
test statistic needed to test the claim that whether a subject lies or does not lie is independent of
the polygraph test indication.
Polygraph test indicated
that the subject lied.
Polygraph test indicated
that the subject did not lie.
025.571
Did the Subject Actually Lie?
No (did not lie) Yes (lied)
15
32
42
9
(1 poir
Answers
We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
How to explain the hypothesisThe test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.
In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:
The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.
Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
Learn more about hypothesis on
https://brainly.com/question/11555274
#SPJ1
Solve 5(2x – 3) = x – 15 + 9x for x. Question 7 options: A) Infinitely many solutions B) –18∕5 C) 0 D) –12∕5
Answers
Step-by-step explanation:
5(2x – 3) = x – 15 + 9x
10x - 15 = x - 15 + 9x
10x - 9x - x = -15 + 15
0 = 0
Answer = A) Infinity many solutions
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
6543/2
-24
1-3-
J
ہے
Answers
Answer:
(a) x-intercept = -2
(b) y-intercept = 4
In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.
Answers
Answer:
x = 6
JN = 10
Step-by-step explanation:
if the values of SN and SP are the same, so are the corresponding sides next to the right angles.
which means:
if SP = SN, then JK = LM.
Use the reverse version of the function for calculating LM (3x + 2).
-2 * 1/3
Now apply that function to 20.
(20-2)/3
= 18/3
= 6.
x = 6
Now JK is a chord.
and Radius SQ intersects JK at a perpendicular right angle (at point N).
So JN would be half the length of JK.
20/2 = 10.
JN = 10
Which of the following exponential regression equations best fits the data shown below?
(-4,0.05), (-3, 0.20), (-2, 0.75)
Answers
The exponential regression equation is y = 11.37 * 3.87ˣ
How to determine the exponential regression equationFrom the question, we have the following parameters that can be used in our computation:
(-4,0.05), (-3, 0.20), (-2, 0.75)
To calculate the exponential regression equation that best fits the data shown, we use a graphing tool
An exponential function is represented as
y = abˣ
From the graphing tool, we have
a = 11.37
b = 3.87
substitute the known values in the above equation, so, we have the following representation
y = 11.37 * 3.87ˣ
Hence, the exponential regression equation is y = 11.37 * 3.87ˣ
Read more about regression at
https://brainly.com/question/26755306
#SPJ1
find the invoice total, the amount should be paid after cash discount, the total amount due including shipping and insurance.
Answers
The total invoice is $788.80, we find this by find the cost of each item.
To find the invoice total, we need to calculate the total cost of each item.
For the tablecloth:
Quantity: 16
Unit Price: $35.00
Total Cost = Quantity × Unit Price = 16 × $35.00 = $560.00
For the rings:
Quantity: 8
Unit Price: $6.50
Total Cost = Quantity × Unit Price = 8 × $6.50 = $52.00
For the cups (cases):
Quantity: 4 cases
Unit Price: $25.30
Total Cost = Quantity × Unit Price = 4 × $25.30 = $101.20
For the bowls:
Quantity: 12
Unit Price: $6.30
Total Cost = Quantity × Unit Price = 12 × $6.30 = $75.60
Now, let's calculate the invoice total by adding up the total costs of each item:
Invoice Total = $560.00 + $52.00 + $101.20 + $75.60
= $788.80
To learn more on Invoice click:
https://brainly.com/question/32170086
#SPJ1
According to the synthetic division below, which of the following statements are true? -4/3 7 20
Answers
According to the synthetic division below, the true statements are as follows:
B. The number 4 is a root of F(x) = 3x2-13x+4.
D. (3x2 - 13x+4) - (x - 4) = (3x - 1)
F. (x-4) is a factor of 3x2.13x+ 4.
How to determine the true statementsSynthetic divisions are the manual ways of bypassing long divisions while performing the Euclidean dividion of polynomials. For the given expressions, we can determine the true statements in this way:
1. F(x) = 3x² - 13x +4.
(x-4) (3x-1)
So, x = 4 or 1/3
4 is an actual root of the function.
2. (3x² - 13x + 4) ÷ (x - 4) = (3x - 1)
3. 3x² - 13x + 4 = (x-4) (3x-1)
So, since all these expressions are true, they meet the requirements for the synthetic division.
Learn more about synthetic divisions here:
https://brainly.com/question/29638766
#SPJ1
Complete Question:
According to the synthetic division below, which of the following statements are true? Check all that apply. 4 4)3 -13 12 3 0 O A. The number -4 is a root of F(x) = 3x2.13x + 4. B. The number 4 is a root of F(x) = 3x2-13x+4. O C. (3x2 - 13x + 4) - (x + 4) = (3x - 1) D. (3x2 - 13x+4) - (x - 4) = (3x - 1) O E. (x + 4) is a factor of 3x2 - 13x + 4. IF (x-4) is a factor of 3x2.13x+ 4.
find the surface area
Answers
Answer:
The surface area of the hexagonal pyramid is 313.13 square inches.
Step-by-step explanation:
Hexagonal pyramid,
Surface Area = Area of hexagon base + areas of six triangles
b = 6
h = 12.2 (height of the triangle)
A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]
A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]
A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]
A = 93.53 + 219.6
A = 313.13 square inches
Susan borrowed $18,500 at 5.00% p.a. from her parents to start a business. In 4 months, she repaid $5,300 towards the loan, and in 10 months she repaid $3,800. How much would she have to repay her parents at the end of 13 months to clear the outstanding balance? Use the declining balance method to calculate the last payment.
Answers
Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.
To calculate the outstanding balance at the end of 13 months, we need to use the declining balance method. This method involves applying the interest rate to the remaining balance after each repayment.
First, let's calculate the interest for the first 4 months. The interest for this period can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the principal is $18,500, the rate is 5.00% per year (or 0.05), and the time is 4 months (or 4/12 years). Thus, the interest for the first 4 months is $18,500 × 0.05 × (4/12) = $308.33.
Next, we subtract the repayment made after 4 months ($5,300) from the outstanding balance ($18,500) and add the interest for the first 4 months ($308.33). This gives us a new outstanding balance of $18,500 - $5,300 + $308.33 = $13,508.33.
Now, let's calculate the interest for the period between 4 and 10 months. The principal remains the same ($13,508.33), the rate is still 5.00% per year (or 0.05), and the time is 6 months (or 6/12 years). Therefore, the interest for this period is $13,508.33 × 0.05 × (6/12) = $337.71.
Subtracting the repayment made after 10 months ($3,800) from the outstanding balance ($13,508.33) and adding the interest for the period gives us a new outstanding balance of $13,508.33 - $3,800 + $337.71 = $10,045.04.
Finally, to determine the last payment required to clear the outstanding balance at the end of 13 months, we subtract the new outstanding balance ($10,045.04) from the principal ($18,500). The last payment is therefore $18,500 - $10,045.04 = $8,454.96.
Therefore, Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.
For more question on balance visit:
https://brainly.com/question/23447356
#SPJ8
Cold Beans wants to make a blend of their two best coffees, Guatemalan and Jamaican coffee. The pound of Guatemalan Coffee costs $11/lb and the other one costs $5/lb. If they want the cost of a 6 pound bag of blend to be $8/lb, how much Guatemalan coffee should they use per pound of the blend?
Answers
For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use [tex]3 \times 6 = 18[/tex]pounds of Guatemalan coffee.
Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.
Given information:
Cost of Guatemalan coffee = $11/lb
Cost of the other coffee = $5/lb
Desired cost of the blend = $8/lb
Total weight of the blend = 6 pounds
To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:
[tex](x \times 11 + (6 - x) \times 5) / 6 = 8[/tex]
In this equation, [tex](x \times 11)[/tex] represents the cost of the Guatemalan coffee in the blend, and[tex]((6 - x) \times 5)[/tex] represents the cost of the other coffee in the blend.
The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.
Now, let's solve the equation for x:
(11x + 30 - 5x) / 6 = 8
6x + 30 = 48
6x = 48 - 30
6x = 18
x = 18/6
x = 3
Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use [tex]3 \times 6 = 18[/tex]pounds of Guatemalan coffee.
To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.
For similar question on cost.
https://brainly.com/question/2292799
#SPJ8
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The surface area of each solid is listed below:
Case A: A = 584.988 ft²
Case B: A = 320π in²
How to determine the surface area of a solidIn this problem we must determine the surface area of each of two solids, that is, the sum of the areas of all faces, whose area formulas are introduced below:
Square
A = l²
Where l is the side length.
Triangle
A = 0.5 · w · h
Where:
w - Widthh - HeightCircle
A = π · r²
Where r is the radius.
Lateral side of a cylinder
A = 2π · r · h
Where h is the height of the cylinder.
Now we proceed to determine the surface area of each solid:
Case A:
A = (14 ft)² + 4 · 0.5 · (14 ft) · √[(7 ft)² + (12 ft)²]
A = 584.988 ft²
Case B:
A = 2π · (8 in)² + 2π · (8 in) · (12 in)
A = 320π in²
To learn more on surface areas of solids: https://brainly.com/question/31126484
#SPJ1
77th term of the sequence 16,19,22,25
Answers
The 77th term of the given Sequence is 244.
The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.
The formula for the nth term of an arithmetic progression is:
_ = _1 + ( − 1),
where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.
In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:
_77 = 16 + (77 − 1) × 3.
_77 = 16 + 76 × 3.
_77 = 16 + 228.
_77 = 244.
Therefore, the 77th term of the given sequence is 244.
To know more about Sequence .
https://brainly.com/question/30762797
#SPJ8
9. PUGS is a parallelogram. The equation of line PU is y = 4x-2. What is the slope of GS?
Answers
The equation of line PU is given as y = 4x - 2. This equation is in slope-intercept form (y = mx + b), where the coefficient of x represents the slope of the line.
In this case, the slope of line PU is 4.
Since the opposite sides of a parallelogram are parallel, the slope of GS will also be 4.
Therefore, the slope of GS is 4.
Evaluate your data. Has there been an increase in the number of certain individuals of this
population of bacteria? Please explain how you think this might lead to the emergence of a
superbug over time, or the extinction of certain strains of this bacteria.
Answers
The increase in certain individuals leads to:
Selective pressure.Emergence of antibiotic-.Extinction .Genetic variations.Difficulty in treating infections.Competition for resources leading to disadvantage for other strains.An increase in certain individuals within a bacterial population can lead to:
Selective pressure favoring individuals with advantageous traitsEmergence of antibiotic-resistant strains or "superbugs"Extinction of less competitive strainsGenetic variations being passed on to future generationsDifficulty in treating infections caused by resistant bacteriaCompetition for resources leading to disadvantage for other strainsOutcome depends on selective pressure, genetic diversity, resource availability, and adaptability.Learn more about antibiotic-rich environments here:
https://brainly.com/question/31454381
#SPJ1
A statue that is 25 feet tall casts a shadow that is 16 feet long. A cement pose next to the statue is 4 feet tall. find the length of the cement post’s statue.
Answers
The length of the cement post's statue is 6.25 feet.
How to calculate the length of the cement post's statue?We shall use Mathematical operators to compute the length of the cement post's statue.
(Height of the statue) / (Length of the shadow) = (Height of the cement post's statue) / (Height of the cement post)
Given:
Height of the statue = 25 feet
Length of the shadow = 16 feet
Height of the cement post = 4 feet
Let x = length of the cement post's statue
25 feet / 16 feet = x / 4 feet
To find x, we cross-multiply:
25 * 4 = 16 * x
100 = 16 * x
To isolate x, we divide both sides of the equation by 16 feet:
100 / 16 = x
x ≈ 6.25 feet
Therefore, the length of the cement post's statue is 6.25 feet.
Learn more about Mathematical operators at brainly.com/question/20628271
#SPJ1