A snail moves at a speed of 1. 2 feet per minute. the snail will move 12 yards in half an hour
There are 60 minutes in an hour, so half an hour is 30 minutes.
The snail moves at a speed of 1.2 feet per minute. Therefore, in 30 minutes, it will travel:
1.2 feet/minute * 30 minutes = 36 feet.
To convert feet to yards, we need to divide by 3 since there are 3 feet in a yard:
36 feet / 3 = 12 yards.
Therefore, .
the snail's speed may seem slow to us, it's important to remember that different animals have different speeds that are adapted to their particular ecological niche.
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Please help...I have absolutely no idea what Im doing.
By handing the survey to every third person, Kyle used a: 1. nonrandom sampling.
Each student in his class had an unequal chance of being selected to receive the survey.
A statement that best explain why Kyle's survey may be biased is: 3. Two out of every three students entering Kyle's class didn't receive the survey.
What are the types of sampling?In Mathematics and Statistics, there are different types of sampling used by researchers and these include the following;
Stratified sampling.Cluster sampling.Random sampling.Convenience sampling.Systematic sampling.Based on the information provided about the survey conducted by Kyle, we can reasonably infer and logically deduce that a systematic sampling method (nonrandom sampling) was adopted.
Consequently, the survey may be considered as being biased because each student in Kyle's class had an unequal chance of being selected to receive the survey.
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Need help with this project
The function that represents the graph below is given as follows:
c. y = 4x³.
How to obtain the function which defines the graph?Before defining the function which defines the graph, we must obtain the domain and the range of the function, as follows:
Domain -> set of input values assumed by the function -> x values -> all real values in the graph.Range -> set of output values assumed by the function -> y values -> all real values in the graph.As the function has a range of all real values, we know that it is a cube function and not a square function, removing options a and b.
The function is positive and negative as follows:
Positive: positive values of x.Negative: negative values of x.Hence the function has a positive leading coefficient, meaning that option c is the correct option.
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Please help me. Offering brainlest!
Answer:
64cm³
Step-by-step explanation:
Surface area of a cube is 6a²
6a² = 96
Divide both sides by 6
a² = 16
Square root of both sides
a = 4cm
Volume of a cube is a³
Volume =4³
Volume 64cm³
A carton of juice has spilled on a tile floor. The juice flow can be expressed with the function , where t represents time in minutes and j represents how far the juice is spreading. The flowing juice is creating a circular pattern on the tile. The area of the pattern can be expressed as .
Part A: Find the area of the circle of spilled juice as a function of time, or . Show your work. (6 points)
Part B: How large is the area of spilled juice after 2 minutes? You may use 3.14 to approximate in this problem. (4 points)
Use the equation editor in your responses. (10 points)
Finding the area of the circle of spilled juice as a function of time is: j(t) = πr(t)²
What is Equation?An equation is mathematical statement that asserts equality of two expressions. It contains one or more variables, and typically consists of terms on either side of equals sign.
Part A:
Let the radius of the circular pattern be r at time t. Then, we have:
j = πr²
Taking the derivative of both sides with respect to time, we get:
dj/dt = 2πr(dr/dt)
Since the rate of change of the radius is unknown, we can express it in terms of the rate of change of j:
dr/dt = (1/2πr)(dj/dt)
Substituting this expression for dr/dt back into our original equation, we get:
j = πr²
dj/dt = π(2r)(dr/dt)
dj/dt = 2πr(dr/dt)
dj/dt = 2πr(1/2πr)(dj/dt)
dj/dt = dj/dt
Therefore, the area of the spilled juice as a function of time is:
j(t) = πr(t)²
Part B:
If we assume that the rate of change of the radius is constant over the first 2 minutes, we can use the formula for the area of a circle to find the area of the spilled juice after 2 minutes:
j(2) = πr(2)²
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can someone help?? Need the answer ASAP !!
The slope and the y-intercept of the line that is perpendicular to y = 5x - 2 and passes through the origin are given as follows:
Slope of -1/5.Intercept of zero.How to obtain the slope and the intercept of the perpendicular line?The line for this problem is given as follows:
y = 5x - 2.
Meaning that the slope and the intercept are given as follows:
Slope of 5.Intercept of -2.When two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope of the line perpendicular to y = 5x - 2 is given as follows:
5m = -1
m = -1/5.
The line also passes through the origin, meaning that when x = 0, y = 0, hence the intercept is of zero.
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Break-Even Sales
Anheuser-Busch InBev SA/NV (BUD) reported the following operating information for a recent year (in millions):
The anticipated break-even number of barrels for the following year is 254.40 million per barrel.
a) To compute the break-even number of barrels for the current year, we need to first calculate the total fixed costs and the total variable costs for the year.
Total Fixed Costs = Selling, general, and administrative expenses - Variable Selling, general, and administrative expenses + Operating Income before special items
Total Fixed Costs = 14,439 - (0.5 * 14,439) + 13,275
Total Fixed Costs = $20,494.5 million
Total Variable Costs = Cost of goods sold - Variable Cost of goods sold
Total Variable Costs = 17,803 - (0.75 * 17,803)
Total Variable Costs = $4,450.75 million
Now, we can calculate the contribution margin per barrel as follows:
Contribution Margin per Barrel = (Sales - Variable Costs) / Number of Barrels
Contribution Margin per Barrel = ($45,517 - $4,451) / 500
Contribution Margin per Barrel = $82.132 million / barrel
To find the break-even number of barrels, we can use the following formula:
Break-even Number of Barrels = Total Fixed Costs / Contribution Margin per Barrel
Break-even Number of Barrels = $20,494.5 million / $82.132 million per barrel
Break-even Number of Barrels = 249.53 million barrels
Therefore, the break-even number of barrels for the current year is 249.53 million.
To compute the anticipated break-even number of barrels for the following year, we need to consider the increase in fixed costs due to the new distribution and general office facilities. Assuming all other costs and per-barrel amounts remain constant, the new total fixed costs would be:
New Total Fixed Costs = Total Fixed Costs + Increase in Fixed Costs
New Total Fixed Costs = $20,494.5 million + $400 million
New Total Fixed Costs = $20,894.5 million
Using the same contribution margin per barrel as in the current year, we can calculate the anticipated break-even number of barrels for the following year:
b) Anticipated Break-even Number of Barrels = New Total Fixed Costs / Contribution Margin per Barrel
Anticipated Break-even Number of Barrels = $20,894.5 million / $82.132 million per barrel
Anticipated Break-even Number of Barrels = 254.40 million barrels
Therefore, the anticipated break-even number of barrels for the following year is 254.40 million.
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The correct question would be:
Break-Even Sales Anheuser-Busch InBev SA/NV (BUD) reported the following operating information for a recent year (in millions): $45,517 Sales Cost of goods sold Selling, general, and administrative expenses $17,803 14,439 (32,242) Operating income $13,275 *Before special items In addition, assume that Anheuser-Busch InBev sold 500 million barrels of beer during the year. Assume that variable costs were 75% of the cost of goods sold and 50% of selling, general, and administrative expenses. Assume that the remaining costs are faced. For the following year, assume that Anheuser-Busch InBev expects pricing variable costs per barrel and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $400 million
a. Compute the break-even number of barrels for the current year. In computing variable and fixed costs and per-barrel amounts, round to two decimal places. Round the break-even number of barrels to one decimal place. million barrels
b. Compute the anticipated break-even number of barbels for the following year Round to one decimal place in millions of barrels million barrels.
What value of y makes the equation true? y+2.91=11
A) 8.1
B) 8.09
C) 9.1
D) 13.91
Answer:
Step-by-step explanation:
If Y+2.91=11, simply subtract 2.91 from 11. 11-2.91 is 8.09. Y is 8.09.
Answer:
B) 8.09
Equation:
y + 2.91 = 11
To solve for the value of y, we need to isolate y on one side of the equation by performing the same operation on both sides.
Start by subtracting 2.91 from both sides:
y + 2.91 - 2.91 = 11 - 2.91
Finally, all we need to do is simplify:
y = 8.09
Therefore, the value of y that makes the equation true is 8.09.
What is the correct way to name the following image?
The correct way to name the image is Southwest Vector BA, indicating the direction of the vector from B to A.
How do we name the vector diagram?
Vector BA : This notation indicates that the vector starts at point B and ends at point A, and it is read as "vector B-A" or "B-A vector". The order of the letters reflects the direction of the arrow, from B to A.
Arrow SW or SW arrow: This notation indicates the direction of the vector, which is towards the southwest, and it is read as "arrow southwest" or "southwest arrow". The order of the letters reflects the direction of the vector, from the northwest to the southeast.
Southwest Vector BA : This notation combines both the direction and the points of the arrow, and it is read as "southwest vector B-A" or "B-A southwest vector". The order of the words reflects the direction of the vector, from the northwest to the southeast, and the order of the letters reflects the starting and ending points of the arrow.
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Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 27 , 45 , 75 , . . . 27,45,75,...
The sum of the first 8 terms of the sequence is 720.
What is sequence ?A sequence is a set of numbers that are arranged in a specific order, according to some rule or pattern. Each number in the sequence is called a term, and the position of the term in the sequence is called its index or subscript. Sequences can be either finite or infinite.
According to the given information :We can see that this is an arithmetic sequence with a first term a = 27 and a common difference d = 18. To find the sum of the first 8 terms of the sequence, we can use the formula for the sum of an arithmetic sequence:
Sn = n/2[2a + (n-1)d]
where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
Plugging in the values we know, we get:
S8 = 8/2[2(27) + (8-1)(18)]
= 4[54 + 126]
= 4(180)
= 720
Therefore, the sum of the first 8 terms of the sequence is 720.
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gcf of 17,22, and 46
Answer:
1
Step-by-step explanation:
17 is a prime number, so only 1 and 17 are its factors. 17 is not a factor of either 22 or 46, but 1 is.
Find value of x in simplest form
The value of x in its simplest form is x = 67√2 = 94.75.
What is sine function?The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilise the sine function. The ratio between the side perpendicular to the angle and the hypotenuse is known as the sine of an angle in a right-angled triangle.
The relation between the opposite side and the hypotenuse is given by the sine function.
Thus,
sin (45) = opposite side / hypotenuse = 67 / x
1 / √2 = 67/x
x = 67√2 = 94.75
Hence, the value of x in its simplest form is x = 67√2 = 94.75.
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(a) Assume that the carrying capacity for the US population is 800 million. Use it and the fact that the population was 282 million in 2000 to formulate a logistic model for the US population. (Let t = 0 correspond to the year 2000. Use k for your constant.
P(t) = _____ millions
(b) Determine the value of k in your model by using the fact that the population in 2010 was 309 million.
k= _____
(c) Use your model to predict the US population in the years 2100 and 2300.
year 2100:
million
year 2300:
million
(d) Use your model to predict the year in which the US population will exceed 600 million.
By looking at the logistic model of US population, it can be said that the population will exceed 600 million by the year 2148.
(a) The logistic model for the US population is given by P(t) = (C/1 + Ae^(-kt)), where C is the carrying capacity, A is a constant, k is a constant, and t is time. Given that the carrying capacity for the US population is 800 million and the population was 282 million in 2000, we can formulate the logistic model as follows:
P(t) = (800/1 + Ae^(-kt))
To find the value of A, we can plug in the initial conditions. Let t = 0 correspond to the year 2000 and P(0) = 282:
282 = (800/1 + Ae^(0))
282 = (800/A + 1)
A = (800/282) - 1
A = 1.84
Therefore, the logistic model for the US population is:
P(t) = (800/1 + 1.84e^(-kt))
(b) To determine the value of k in the model, we can use the fact that the population in 2010 was 309 million. Let t = 10 correspond to the year 2010 and P(10) = 309:
309 = (800/1 + 1.84e^(-10k))
1.84e^(-10k) = (800/309) - 1
e^(-10k) = 0.593/1.84
-10k = ln(0.593/1.84)
k = -0.076
Therefore, the value of k in the model is k = -0.076.
(c) To predict the US population in the years 2100 and 2300, we can plug in the values of t = 100 and t = 300 into the model:
P(100) = (800/1 + 1.84e^(-100(-0.076))) = 535.7 million
P(300) = (800/1 + 1.84e^(-300(-0.076))) = 762.2 million
Therefore, the predicted US population in the year 2100 is 535.7 million and in the year 2300 is 762.2 million.
(d) To predict the year in which the US population will exceed 600 million, we can set P(t) > 600 and solve for t:
(800/1 + 1.84e^(-kt)) > 600
1.84e^(-kt) < (800/600) - 1
e^(-kt) < 0.333/1.84
-kt < ln(0.333/1.84)
t > -ln(0.333/1.84)/k
Using the value of k from part (b), we get:
t > -ln(0.333/1.84)/(-0.076) = 147.7
Therefore, the population of US will exceed 600 million by the year 2148.
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g(x) = 4x - 1
f(x) = x + 3
Find (gof)(x/2)
For the function (g o f)(x/2) the value is obtained as 2x + 11.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function g(x) is given as g(x) = 4x - 1.
The function f(x) is given as f(x) = x + 3.
To find (g o f)(x/2), we need to first find f(x/2) and then substitute this value into g(x) in place of x.
f(x) = x + 3
So, f(x/2) = (x/2) + 3
Now, substitute this into the equation of g(x) in place of x -
g(x) = 4x - 1
g(f(x/2)) = 4(f(x/2)) - 1
= 4((x/2) + 3) - 1 (substituting f(x/2))
= (4x/2 + 12) - 1
= 2x + 11
Therefore, the value is (g o f)(x/2) = 2x + 11.
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what is the distance between the two points (−8,−3) and (−1,4) in simplest radical form
Answer:
the distance between the two points (-8,-3) and (-1,4) is 7sqrt(2) units.
Step-by-step explanation:
We can use the distance formula to find the distance between the two points:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the given coordinates:
d = sqrt((-1 - (-8))^2 + (4 - (-3))^2)
d = sqrt(7^2 + 7^2)
d = sqrt(2 x 7^2)
d = 7sqrt(2)
Therefore, the distance between the two points (-8,-3) and (-1,4) is 7sqrt(2) units.
An account with an initial balance of $1250 earns interest that is compounded quarterly. If no other deposits or withdrawals are made, the
account will have a balance of $1406.08 after 9 months. Find the annual interest rate.
Answer:
If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate. Expert Answer.
1 answer
·
Top answer:
Given that P=1,250A=1,406.08n=9 month
Step-by-step explanation:
PLEASE HELP MEEEE I NEEED HEELPPPPP
Answer:
I think its (C) - 2/3
the surface area of the cylinder is 420 in^2. what is its base area ? use 3.14 for pie and round the answer to the nearest hundredth.
The surface area of the cylinder is 420 in^2. The base area of the cylinder is 67.02 in².
Given that the surface area of the cylinder is 420 in², we have to find its base area.
To find the base area of the cylinder, we have to use the formula for the surface area of the cylinder.
The formula is:
Surface area of the cylinder = 2πr(r + h)
Here, π = 3.14,
r is the radius of the base of the cylinder, and h is the height of the cylinder.
Since the base is a circle, the area of the base is given by the formula:
A = πr²We can calculate the radius of the cylinder using the given surface area.
420 = 2πr(r + h)420
= 2 × 3.14 × r(r + h)420
= 6.28 r² + 6.28 rh
Now we need to assume some value of h. For example, if we take h = 7, then we have:
420 = 6.28 r² + 6.28 r (7)
420 = 6.28 r² + 43.96 or
6.28 r² + 43.96 r - 420 = 0
Now we can solve this quadratic equation to find the value of r. Using the quadratic formula:
r = [-b ± sqrt(b² - 4ac)] / 2a
Putting a = 6.28, b = 43.96, and c = -420, we get:
r = [-43.96 ± sqrt(43.96² + 4(6.28)(420))] / 2(6.28)
r = [-43.96 ± sqrt(3291.84)] / 12.56r = (-43.96 + 57.40) / 12.56 or
r = (-43.96 - 57.40) / 12.56r = 1.10 or r = -1.82
We can discard the negative value of r, so we have:r = 1.10
Now we can calculate the base area of the cylinder using the formula for the area of a circle.A = πr²A = 3.14 × (1.10)²A = 3.14 × 1.21A = 3.80 (rounded to the nearest hundredth)
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Shirley's water bottle is half full. She pours
it into another bottle that is one-third full,
and it fills that bottle. If the second bottle
holds 2 quarts, how much did the first
bottle hold?
Answer:
Shirley's water bottle holds 4 quarts when it is half full.
Step-by-Step-Explanation
If the second bottle is one-third full and holds 2 quarts, then it means that it can hold a total of 2 / (1/3) = 6 quarts when completely full.
Let's call the amount of water in Shirley's bottle "x" quarts. We know that when she pours it into the second bottle, it becomes completely full with 6 quarts. So we can set up the equation:
x + 2 = 6
Solving for x, we get:
x = 6 - 2
x = 4
The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2). The graph of the equation, shown below.
What is the term graph means?The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.
For the given equation,
[tex]h=3Sin [\frac{\pi }{2} (t+2)] +5[/tex]
Follow the steps for drawing the graph,
Choose a range of values for t that we want to graph. Since the period of the oscillation is 2 seconds, we can choose a range of t values that spans one or more full periods of the oscillation.Substitute each t value into the equation to find the corresponding h value. For example, when t = 0,[tex]h = 3 Sin [\frac{\pi }{2} (0 + 2)] + 5 = 3 Sin [\pi] + 5 = 5[/tex]
This means that when the ball is at the midpoint of its oscillation (i.e., at time t = 0), its height is 5 feet above the equilibrium position.
Plot the (t, h) pairs as points on a graph, with t values on the x-axis and h values on the y-axis.Connect the plotted points with a smooth curve to create the graph of the equation.The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2).Using these steps, we can create the graph of the equation, which looks like the below diagram.
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Histograms Suppose we have a table called data with two numerical columns, "x" and·y. Consider the following scatter plot, which was generated by calling data.scatter('x', 'y') 2.0 1.5 1.0atos- 0.0 Histogram A: E 25 D 20 E 15 10 0 1 2 3 1 4 Histogram B: 40 C 30 20 a 10 0.0 0.5 1.0 1.5 .02.5 3.0 Question 1. One of these two lines of code generated Histogram A, and the other generated Histogram B . data.hist('x) data.hist'y) Which line generated Histogram A? Which generated Histogram B? Explain. Write your answer here. Question 2. Suppose we run this line of code new_data -Table().with_columns( data.column(x)5, y, data.column(y') We then run new_data.hist(x). What does the new histogram look like?
The shape of the histogram will remain the same but will stretch horizontally.
1. Histograms Suppose that the line of code data.hist('x') generated Histogram A and the line of code data.hist('y') generated Histogram B. This is because Histogram A shows the distribution of the x values and Histogram B shows the distribution of the y values.
The x-axis of Histogram A corresponds to the x values and the y-axis corresponds to the frequency of those values. Similarly, the x-axis of Histogram B corresponds to the y values and the y-axis corresponds to the frequency of those values.
2. The new histogram generated by running new_data.hist('x') will look similar to Histogram A, but the x values will be multiplied by 5. This means that the x-axis will have larger values and the bars will be shifted to the right. The y-axis, which corresponds to the frequency of the x values, will remain the same.
The overall shape of the histogram will also remain the same, but it will be stretched horizontally.
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Write an equation of the line below.
Answer: y=3/2x+4
Step-by-step explanation: The equation for the line below is [tex]y=\frac{3}{2}x +4[/tex]
This equation is correct because the formula is y=mx+b. m is the slope and you can see the slope is [tex]\frac{3}{2}[/tex] and x is to represent that the number is the slope. The b, or +4 represents where the line crosses over the x-axis.
The equation is [tex]y=\frac{3}{2}x +4[/tex]
Let me know if you have any other questions about this problem.
-Your Brainly Helper!
WHAT IS THE ANSWER?
HELP ME PLeese
Answer:
Step-by-step explanation:
An African elephant weighs 5,500 pounds. How many ounces is that?
An African elephant weighs 88,000 ounces. To convert pounds to ounces, we need to know the conversion factor between the two units.
There are 16 ounces in one pound, which means we can convert pounds to ounces by multiplying the weight in pounds by 16. A pound is equal to 28 grams. A one-quarter ounce contains seven grams. A half-ounce has 14 grams in it. One-eighth of an ounce has 3.5 grams.
In this case, the African elephant weighs 5,500 pounds. To find out how many ounces that is, we can multiply 5,500 by 16:
5,500 pounds x 16 ounces/pound = 88,000 ouncesTherefore, the African elephant weighs 88,000 ounces.
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You pick a card at random, put it back, and then pick another card at random.
2
3
4
5
6
What is the probability of picking a 4 and then picking a number greater than 4?
Write your answer as a percentage.
Answer:8%
Step-by-step explanation:Since the cards are put back after each pick, the two picks are independent events.
The probability of picking a 4 on the first pick is 1/5, as there is one card with a value of 4 out of five cards in total.
The probability of picking a number greater than 4 on the second pick is 2/5, as there are two cards with values greater than 4 (5 and 6) out of five cards in total.
The probability of both events occurring (picking a 4 and then a number greater than 4) is the product of the probabilities of each event:
1/5 x 2/5 = 2/25
So the probability of picking a 4 and then picking a number greater than 4 is 2/25.
To express this as a percentage, we can multiply by 100:
2/25 x 100 = 8%
Therefore, the probability of picking a 4 and then picking a number greater than 4 is 8%.
Question 18
5 pts
An airplane flying into a headwind travels 1176.00 miles in 4 hours and 54 minutes. On the return flight, the
distance is traveled in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both
remain constant.
plane speed = 282 mph; wind speed = 274 mph
plane speed = 267.00 mph; wind speed = 27.00 mph
plane speed = 282 mph; wind speed = 27.00 mph
plane speed = 244 mph; wind speed = 256 mph
plane speed = 244 mph; wind speed = 27.00 mph
Using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The distance travelled = 1176.00 miles
Time taken = 4 hours and 54 minutes = 4*60 + 54 = 294 minutes
The times taken for return flight = 4 hours = 240 minutes
Let,
x = speed of the plane
y = speed of the wind
In a headwind the speed reduces.
So the relative speed of the plane is (x-y)
distance = speed * time
1176 = (x-y) * 294
x-y = 4
Now for the return flight, the wind is tailwind and the speed increases.
So the relative speed of the plane is (x+y).
1176 = (x+y) * 240
x + y = 4.9
Now we have a system of equations.
x - y = 4
x + y = 4.9
Adding,
2x = 8.9
x = 4.45 miles/min = 4.45 * 60 miles/hour = 267 miles/hour
and
y = 4.9 - x = 4.9 - 4.45 = 0.45 miles/min = 0.45*60 = 27 miles/hour
Therefore using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
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There are 70 students traveling to a soccer tournament. All of the vans can take 9 students each. How many vans are needed to take all of the students to the tournament?
Answer:
They need 8 vans.
Step-by-step explanation:
8 × 9 is 72. If you have 8 vans that carry 9 students each, you will have room for 72 students. Then you have enough room for 70 students.
If you only have 7 vans you can only transport 7 × 9, or 63 students. That is not enough. They need 8 vans.
16. The population of the United States in July of 2000 was 282.2 million people. A year later in July of 2001
the population was 284.8 million.
Find an exponential model, in the form of P(t)= a(b)', that models the population of the United States in
millions of people. The variable t represents the number of years since July of 2000. Round your value of b
to the nearest thousandth.
Step-by-step explanation:
284.8 = 282.2 ( b)^1 1 is the number of years....looking for 'b'
284.8 / 282.2 = b = ~ 1.009
P(t) = 282.2 ( 1.009)^t where P(t) is in millions and :
The variable t represents the number of years since July of 2000. Round your value of b to the nearest thousandth.
please help me on this please
Answer:
[tex]\boxed{\mbox{\large{\quad 54\quad }}} \quad\text{ 25\% of last year's attendance}\\\\\boxed{\mbox{\large{\quad 216\quad }}}\quad\text{100\% of last year's attendance}\\\\[/tex]
Step-by-step explanation:
If we let x be the number of attendees last year then since this year's attendees 270 is 125% of x we get
125% of x = 270
125% as a decimal = 125/100 = 1.25
So we get the equation
1.25x = 270
Divide by 1.25 to get
1.25x/1.25 = 270/1.25
x = 216
So there were a total of 216 attendees last year
25% of last year attendees = 0.25 x 216 = 54
What are the solutions to the following quadratic?
5x² + 18x=25x+15+3x²
(x+5)(2x-3)
O (5,-3/2)
(x - 5)(2x+3)
(-5,3/2)
Answer:
We can start by simplifying both sides of the equation:
5x² + 18x = 25x + 15 + 3x²
2x² - 7x - 15 = 0
Now we need to factor this quadratic equation:
2x² - 7x - 15 = (2x + 3)(x - 5)
Setting each factor equal to zero gives us the solutions:
2x + 3 = 0 or x - 5 = 0
Solving for x, we get:
x = -3/2 or x = 5
Therefore, the solutions to the quadratic equation are x = -3/2 and x = 5.
So, the correct answer is (x - 5)(2x+3).
URGENT ‼️ rephrased my exponential growth word problem now i need help on how to set up my equation
The Population of salmonella doubles in size every 25 hours.
There are about 10 grams of salmonella enterica bacteria in
"one cell, determine how many
cells have increased after 75 hours.
The population of salmonella enterica after 75 hours is 80 grams, which is equivalent to 8 cells. That is, the population of salmonella enterica has increased from 1 cell to 8 cells after 75 hours.
What is exponential growth?Exponential growth is a pattern of growth that is rapid and often exponential. It occurs when the rate of change in a variable is proportional to the variable's current value. This means that a small change in the variable can result in a large increase or decrease in its value over a short period of time.
The population of salmonella enterica bacteria doubles every 25 hours. This means that each hour, the population of the bacteria increases by a factor of two. To calculate the number of bacteria after 75 hours, we need to apply the concept of exponential growth. Exponential growth is a process by which the value of a variable increases exponentially, or multiplicatively, over time.
Assuming that the population of salmonella enterica was initially 10 grams, the population after 75 hours can be calculated using the equation:
Population = 10 * 2⁽⁷⁵÷²⁵⁾
The population after 75 hours is thus 10 * 2³ = 80 grams. This means that the population of salmonella enterica has increased from 10 grams to 80 grams after 75 hours.
Since each cell of salmonella enterica has a mass of 10 grams, the population after 75 hours can also be calculated in terms of cells. The population of salmonella enterica after 75 hours is 80 grams, which is equivalent to 8 cells. That is, the population of salmonella enterica has increased from 1 cell to 8 cells after 75 hours.
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