Answer: C
Step-by-step explanation: after rotating, if you split it in half horizontally, you have two cones
The three-dimensional figure formed when the triangle is rotated around the dashed line through B and C is a cone.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
When we rotate a two-dimensional shape around an axis, we create a three-dimensional solid. This process is known as "revolution" or "rotational symmetry".
In this particular case, we have a triangle that can be rotated around the line segment that connects points B and C. If we were to rotate the triangle around this axis, we would create a three-dimensional solid. To figure out what kind of solid this is, we can think about the cross-sections that would be created if we were to slice through the solid perpendicular to the axis of rotation.
If we were to slice through the solid perpendicular to the axis of rotation, we would get a circle. This means that the solid created by rotating the triangle is a cylinder.
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Evaluate the definite integral
∫ (t^5 - 2t^2)/t^4 dt
To evaluate the definite integral of the given function, ∫ (t^5 - 2t^2)/t^4 dt, follow these steps:
1. Simplify the integrand: Divide each term by t^4.
(t^5/t^4) - (2t^2/t^4) = t - 2t^(-2)
2. Integrate each term with respect to t.
∫(t dt) - ∫(2t^(-2) dt) = (1/2)t^2 + 2∫(t^(-2) dt)
3. Apply the power rule to the remaining integral.
(1/2)t^2 + 2(∫t^(-2+1) dt) = (1/2)t^2 + 2(∫t^(-1) dt)
4. Integrate t^(-1) with respect to t.
(1/2)t^2 + 2(ln|t|)
Now, since we need to evaluate the definite integral, we should have the limits of integration. Let's assume the limits of integration are a and b. Then, apply the Fundamental Theorem of Calculus:
[(1/2)b^2 + 2(ln|b|)] - [(1/2)a^2 + 2(ln|a|)]
This expression gives the value of the definite integral for the given function within the limits a and b.
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This table shows the time it takes students in Homeroom 203 to get to school each morning: 1 Time Less than 10 min 10-19 min 20-29 min 30-39 min 40-49 min 50 min or more Find the experimental probability of a student in this homeroom taking a certain number of minutes to get to school. Make a probability distribution for this data. Number of Students 3, 5, 10, 7, 2, 3
Answer:
Step-by-step explanation:
To find the experimental probability of a student in Homeroom 203 taking a certain number of minutes to get to school, we need to divide the number of students who take that amount of time by the total number of students in the homeroom.
The total number of students in the homeroom is:
3 + 5 + 10 + 7 + 2 + 3 = 30
The probability of a student taking less than 10 minutes to get to school is:
3/30 = 0.1 or 10%
The probability of a student taking 10-19 minutes to get to school is:
5/30 = 0.166 or 16.6%
The probability of a student taking 20-29 minutes to get to school is:
10/30 = 0.333 or 33.3%
The probability of a student taking 30-39 minutes to get to school is:
7/30 = 0.233 or 23.3%
The probability of a student taking 40-49 minutes to get to school is:
2/30 = 0.066 or 6.6%
The probability of a student taking 50 minutes or more to get to school is:
3/30 = 0.1 or 10%
To make a probability distribution, we can list the possible outcomes (in this case, the time it takes to get to school) and their corresponding probabilities:
Time (min) Probability
Less than 10 0.1
10-19 0.166
20-29 0.333
30-39 0.233
40-49 0.066
50 or more 0.1
Note that the probabilities add up to 1, which is what we expect for a probability distribution.
a cylinder has a radius of 3.8 meters it’s volume is 154 cubic meters
Answer:
h ≈ 3.39
Step-by-step explanation:
V = πr^2h
h = V/πr^2
h = 154/ π · 3.8^2
h ≈ 3.39472
A sphere with a radius of 6 in. is repeatedly filled with water and emptied into a cylinder with a radius of 6 in. and a height of 18 in.. how many times is the sphere emptied into the cylinder until the cylinder is full of water?
The sphere must be emptied into the cylinder 3 times to completely fill it with water.
We will use the formulas for theSo, the sphere must be emptied into the cylinder 3 times to completely fill it with water. and the volume of a cylinder to find out how many times the sphere needs to be emptied into the cylinder until it is full.
Step 1: Find the volume of the sphere.
The formula for the volume of a sphere is V_sphere = (4/3)πr^3, where r is the radius.
Given that the radius of the sphere is 6 inches, we can calculate its volume:
V_sphere = (4/3)π(6)^3 = (4/3)π(216) ≈ 904.78 cubic inches
Step 2: Find the volume of the cylinder.
The formula for the volume of a cylinder is V_cylinder = πr^2h, where r is the radius and h is the height.
Given that the radius of the cylinder is 6 inches and the height is 18 inches, we can calculate its volume:
V_cylinder = π(6)^2(18) = π(36)(18) ≈ 2038.51 cubic inches
Step 3: Determine how many times the sphere must be emptied into the cylinder.
To find out how many times the sphere needs to be emptied into the cylinder, divide the volume of the cylinder by the volume of the sphere:
Number_of_times = V_cylinder / V_sphere = 2038.51 / 904.78 ≈ 2.25 times
Since we cannot empty the sphere partially, we'll round up to the nearest whole number:
Number_of_times = 3 times
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Consider right angle triangle ABC, right angled at B. If AC=17 units and BC+8 units determine all the trigonometric ratios of angle C
The trigonometric ratios of angle C are sin C = 15/17, cos C = 8/17, and tan C = 15/8.
Since triangle ABC is a right triangle with a right angle at B, and we know AC = 17 units (hypotenuse) and BC = 8 units (adjacent side to angle C), we can use the Pythagorean theorem to find the length of the remaining side, AB (opposite side to angle C).
The Pythagorean theorem states: AB² + BC² = AC²
Plugging in the values we know:
AB² + 8² = 17²
AB² + 64 = 289
To find AB:
AB² = 289 - 64 = 225
AB = √225 = 15 units
Now we can determine the trigonometric ratios of angle C:
1. sine (sin C) = opposite/hypotenuse = AB/AC = 15/17
2. cosine (cos C) = adjacent/hypotenuse = BC/AC = 8/17
3. tangent (tan C) = opposite/adjacent = AB/BC = 15/8
So the trigonometric ratios of angle C are:
sin C = 15/17, cos C = 8/17, and tan C = 15/8.
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Sabine rode on a passenger train for 480 miles between 10:30 A. M. And 6:30 P. M. A friend in a different city
The speed of the train is 60 miles per hour.
Sabine travel 480 miles on a passenger train between 10:30 A.M. and 6:30 P.M. What is speed of train?We calculate in two steps:
Calculate the speed of the trainTo calculate the speed of the train, we need to use the formula:
Speed = Distance / Time
Here, the distance travelled by the train is 480 miles, and the time taken is 8 hours (from 10:30 A.M. to 6:30 P.M.). So, we can calculate the speed of the train as:
Speed = 480 miles / 8 hours
Speed = 60 miles per hour
Therefore, the speed of the train is 60 miles per hour.
Explain the solutionSabine rode on a passenger train for 480 miles between 10:30 A.M. and 6:30 P.M.
To calculate the speed of the train, we used the formula Speed = Distance / Time, where Distance is 480 miles and Time is 8 hours (since the journey was between 10:30 A.M. and 6:30 P.M.).
Substituting the values, we get the speed of the train as 60 miles per hour.
This means that the train travelled at a speed of 60 miles per hour throughout the journey, covering a distance of 480 miles in 8 hours.
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Please help
Michael thought he could only run 5 laps around the track but he was actually able to run 8 laps what was his percent error round to the nearest percent
To calculate the percent error, we need to use the following formula:
percent error = (|measured value - actual value| / actual value) x 100%
1. Determine the difference between the actual value (8 laps) and the estimated value (5 laps).
Actual value = 8 laps
Estimated value = 5 laps
Difference = Actual value - Estimated value = 8 - 5 = 3 laps
2. Divide the difference by the actual value:
Percent error (decimal) = Difference / Actual value = 3 laps / 8 laps = 0.375
3. Convert the decimal to a percentage by multiplying by 100:
Percent error = 0.375 * 100 = 37.5%
4. Round to the nearest percent:
Percent error ≈ 38%
So, Michael's percent error in estimating his laps around the track was approximately 38%.
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state the parent function of g(x) and describe how the graph of (x) is related to its parent function (questions 3,4,5)
The parent functions of the function equations are x³, x⁴ and x²
Stating the parent functionsThe transformed functions 3 - 5 represent the given parameter
To derive the parent functions, we need to determine the degree of the transformed and use this degree as a guide
By definition, the degree of a function is the highest power in the function
So, we have
Question 3
g(x) = (1/2x + 2)³ + 5
The degree here is 3
This means that the function is a cube function
The parent function of a cube function is y = x³
So, the parent function is g(x) = x³
Question 4
g(x) = x⁴ - 4
The degree here is 4
This means that the function is a polynomial function shifted down by 4 units
The parent function of this is y = x⁴
So, the parent function is g(x) = x⁴
Question 5
g(x) = 1/2(x - 1)² - 4
The degree here is 2
This means that the function is a quadratic function
The parent function of a quadratic function is y = x²
So, the parent function is g(x) = x²
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Find the mad for this set of data.
swim team
name
age (years) mean
absolute
deviation
1
3
9
10
maddox
enrique
13
10
gloria
9
10
1
mckenna
10
.
10
0
10
10
0
mad =
?
✓ done
asher
hannah
danielle
9
10
1
10
10
0
katy
10
10
0
11
10
1
timothy
gentry
9
10
1
The MAD for this set of data is 0.8.
To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:
Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1
Next, we find the absolute deviation of each age from the mean:
|13 - 10.1| = 2.9
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|9 - 10.1| = 1.1
Then, we find the average of these absolute deviations:
MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8
Therefore,To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:
Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1
Next, we find the absolute deviation of each age from the mean:
|13 - 10.1| = 2.9
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|9 - 10.1| = 1.1
Then, we find the average of these absolute deviations:
MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8
Therefore, the MAD for this set of data is 0.8.
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Can you explain what is the horizontal tangent plane and how
should I use the tangent plane equation to answer this question,
thanks.
equation: f(a,b) + f(1)(x-a) + f(2)(y-b) = z
The value of the function at that point is equal to the z-coordinate of the point on the plane.
How to use the tangent plane equation to find the equation of a tangent plane?A horizontal tangent plane is a plane that is parallel to the x-y plane and tangent to a surface at a point where the slope in the horizontal direction is zero.
To use the tangent plane equation to find a horizontal tangent plane, we need to find the partial derivatives of the function with respect to x and y, evaluate them at the point of interest, and check if they are both zero.
If they are both zero, then the tangent plane is horizontal and the equation simplifies to f(a,b) = z.
The tangent plane equation is given by:
f(a,b) + f(1)(x-a) + f(2)(y-b) = z
where (a,b) is the point where the tangent plane intersects the surface, and f(1) and f(2) are the partial derivatives of the function with respect to x and y, evaluated at (a,b).
To use this equation to find the horizontal tangent plane, we first find the partial derivatives f(1) and f(2), and evaluate them at the point where we want to find the tangent plane. If f(1) and f(2) are both zero at that point, then the tangent plane is horizontal and the equation simplifies to:
f(a,b) = z
This means that the value of the function at that point is equal to the z-coordinate of the point on the plane.
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I need help with this one
solve for x
Answer:
x = 2
Step-by-step explanation:
A secant is a straight line that intersects a circle at two points.
A segment is part of a line that connects two points.
According to the Intersecting Secants Theorem, the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.
The given diagram shows two secant segments that intersect at an exterior point.
One secant segment is (6x - 1 + 7) and its external part is 7.The other secant segment is (x + 3 + 9) and its external part is 9.Therefore, according to the Intersecting Secants Theorem:
[tex](6x-1+7) \cdot 7=(x+3+9) \cdot 9[/tex]
Solve for x:
[tex]\begin{aligned}(6x+6) \cdot 7&=(x+12) \cdot 9 \\42x+42&=9x+108\\42x+42-9x&=9x+108-9x\\33x+42&=108\\33x+42-42&=108-42\\33x&=66\\33x\div33&=66\div33\\x&=2 \end{aligned}[/tex]
Therefore, the value of x is x = 2.
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 Solve for the value of p
If p : q = 2/3 : 2 and p : r = 3/4 : 1/2 , calculate the ratio p : q : r Giving your answer in its simplest form.
please help i mark it as brainly
If p : q = 2/3 : 2 and p : r = 3/4 : 1/2 , the ratio of p : q : r in its simplest form is 32 : 27 : 24.
To calculate the ratio p : q : r, we need to first find the values of p, q, and r. We can use the given proportions to set up a system of equations and solve for the variables.
From the first proportion, we know that:
p/q = 2/3 : 2
We can simplify this by cross-multiplying:
p = (2/3) * 2q
p = (4/3)q
From the second proportion, we know that:
p/r = 3/4 : 1/2
Again, we can cross-multiply and simplify:
p = (3/4) * r/(1/2)
p = (3/2)r
Now we have two equations for p in terms of q and r. We can substitute these into each other and solve for q and r:
(4/3)q = (3/2)r
r/q = (8/9)
q/r = (9/8)
Now we have the ratios of r to q and q to r. We can use these to find the ratio of p, q, and r:
p : q : r = p : q * (9/8) : r * (8/9)
Substituting the values we found for p in terms of q and r:
p : q : r = (4/3)q : q * (9/8) : r * (8/9)
Simplifying:
p : q : r = 32 : 27 : 24
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You ask your best friend to lend you Rs.300 to buy your favorite toy she says she can lend you the money. Only if you give her an extra three rupees for every three months the past before you return it.
Your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.
What is rate of interest?The amount a lender charges a borrower for the use of assets, such as money, consumer goods, or physical assets, is known as an interest rate. It is a fraction of the loan's principal, which is the amount borrowed to cover the cost of the purchase or the deposit made with a bank or other financial institution.
If your best friend is charging you an extra ₹3 for every three months that pass before you return the money, then after nine months, you will owe her an extra ₹9 in addition to the original ₹300.
So the total amount you must pay her if you return the ₹300 after nine months would be ₹309.
To calculate the annual rate of interest she is charging you, we can use the formula:
Annual Interest Rate = (Total Interest / Principal) x (12 / Number of Months)
Where the Principal is the original amount borrowed (₹300), the Total Interest is the extra amount you owe her (₹9), and the Number of Months is the time period for which you borrowed the money (9 months).
Plugging in the values, we get:
Annual Interest Rate = (9 / 300) x (12 / 9) = 0.04 or 4%
So, your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.
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The complete question is:
You ask your best friend to lend you ₹300 to buy your favourite toy. She says she can lend you the money only if you give her an extra ₹3 for every three months that pass before you return it. What is the total amount you must pay her if you return it after nine months? What is the annual rate of interest she is charging you?
What function does the graph represent?
Answer:
B
Step-by-step explanation:
Since the graph is facing down, there will be a negative sign.
In parenthesis it says (x + 1) which means you move one unit left
On the outside it says +2 which means you move the graph 2 units up
PART B Corey repeats his process 10 more times and gets these results: 3 green balls, 2 orange balls and 5 purple balls. Explain a possible reason for this outcome.
Based on the results of Corey repeating his process 10 more times, a possible reason for this outcome with 3 green balls, 2 orange balls, and 5 purple balls could be that there is a higher probability of selecting a purple ball compared to the other colors.
Here's a step-by-step explanation:
1. Corey conducted an experiment where he repeated a process 10 times.
2. During these trials, he obtained the following results: 3 green balls, 2 orange balls, and 5 purple balls.
3. The distribution of colors suggests that there is a higher probability of selecting a purple ball (5/10) than a green ball (3/10) or an orange ball (2/10).
4. This outcome could be due to factors such as a larger number of purple balls in the pool from which Corey is selecting or some other bias in the process that increases the likelihood of selecting a purple ball.
In conclusion, the possible reason for the outcome with 3 green balls, 2 orange balls, and 5 purple balls is that there might be a higher probability of selecting a purple ball during Corey's repeated trials.
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TRUE or FALSE:
1. Each exterior angle of a regular hexagon is acute
2. The sum of the interior angles of a polygon is not necessarily a multiple of 180
3. In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle
1. The statement "Each exterior angle of a regular hexagon is acute" is True.
2. The statement "The sum of the interior angles of a polygon is always a multiple of 180" is False.
3. The statement "In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle" is True.
1. TRUE: Each exterior angle of a regular hexagon is acute.
A regular hexagon has six equal sides and six equal interior angles. The sum of the interior angles of a hexagon is (6-2) * 180 = 720 degrees. Since it's a regular hexagon, each interior angle is 720/6 = 120 degrees. The exterior angles are supplementary to the interior angles, so each exterior angle is 180 - 120 = 60 degrees. Since 60 degrees is less than 90 degrees, each exterior angle is acute.
2. FALSE: The sum of the interior angles of a polygon is always a multiple of 180.
The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of vertices (or sides). As you can see, the result is always a multiple of 180.
3. TRUE: In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle.
For a regular polygon, the measure of an exterior angle can be calculated as 360/n, where n is the number of vertices (or sides). As the number of vertices increases, the measure of an exterior angle decreases, since they are inversely proportional.
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WILL GIVE BRAINLIEST! A line contains the points R (-5, -3) S (-1, -1) and T (x, 3). Solve for x. Be sure to show and explain all work
The x-coordinate of point T is 7. Thus, point T is (7, 3).
To solve for x, we will use the concept of slope. The slope between any two points on a line remains constant. Let's find the slope between points R(-5, -3) and S(-1, -1):
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-1 - (-3)) / (-1 - (-5))
m = (2) / (4)
m = 1/2
Now, we will use the slope between points S(-1, -1) and T(x, 3):
m = (3 - (-1)) / (x - (-1))
1/2 = (4) / (x + 1)
Now, we will solve for x:
1/2 (x + 1) = 4
x + 1 = 8
x = 7
So, the x-coordinate of point T is 7. Thus, point T is (7, 3).
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Bricks are going to be packed into a crate which has a space inside of 2.8m3. The volume of each brick is 16000cm3. Given that an exact number of bricks that can be packed into the crate. how many bricks can it hold
The crate can hold 175 bricks.
What is the maximum number of bricks that can be packed into a crate with an internal volume of 2.8 m³, given that the volume of each brick is 16000 cm³?
First, we need to convert the volume of the crate from cubic meters to cubic centimeters because the volume of each brick is given in cubic centimeters.
1 m = 100 cm
Volume of crate = 2.8 m3 = 2.8 x (100 cm)3 = 2,800,000 cm3
Now we can find the number of bricks that can be packed into the crate by dividing the volume of the crate by the volume of each brick:
Number of bricks = Volume of crate / Volume of each brick
= 2,800,000 cm3 / 16,000 cm3
= 175 bricks
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Cuánto interés ganará lesli si presta l 5000 a pagar en 3años? al:5%simple anual. 10%simple anual. 5%compuesto anual
Lesli ganará $750 de interés si presta $5000 a pagar en 3 años al 5% de interés simple anual.
How much interest will Leslie earn if she lends $5000 to be paid back in 3 years at a simple annual interest rate of 5%, 10%, and a compound annual interest rate of 5%?Para calcular el interés que ganará Leslie en diferentes escenarios, consideraremos los siguientes casos:
A) Tasa simple anual del 5%:
El interés simple se calcula multiplicando el capital prestado por la tasa de interés y el tiempo en años.
Interés = Capital x Tasa x Tiempo
Interés = 5000 x 0.05 x 3 = $750
B) Tasa simple anual del 10%:
De manera similar al caso anterior, el interés se calcula como:
Interés = 5000 x 0.10 x 3 = $1500
C) Tasa compuesta anual del 5%:
En el caso de la tasa de interés compuesta, los intereses se acumulan en cada período. La fórmula para calcular el monto total es:
Monto = Capital x (1 + Tasa)^Tiempo
Monto = 5000 x (1 + 0.05)^3 = $5788.75
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The water hose fills A bucket at 1/3 per minute how many minutes does it take to fill a 2 gallon bucket
It will take 6 minutes for the water hose to fill the 2-gallon bucket at a rate of 1/3 gallon per minute.
To determine the time required to fill a 2-gallon bucket using a water hose that fills at a rate of 1/3 gallon per minute, you can use a simple calculation.
First, identify the fill rate of the hose, which is 1/3 gallon per minute. Now, consider the bucket's capacity, which is 2 gallons. To find out how many minutes it takes to fill the bucket, divide the total capacity of the bucket by the fill rate:
Time (minutes) = Bucket capacity (gallons) / Fill rate (gallons per minute)
In this case:
Time (minutes) = 2 gallons / (1/3 gallons per minute)
To solve this, you can multiply the numerator and denominator by the reciprocal of the fill rate:
Time (minutes) = 2 gallons * (3 minutes per gallon)
Time (minutes) = 6 minutes
So, it will take 6 minutes for the water hose to fill the 2-gallon bucket at a rate of 1/3 gallon per minute.
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A squirrel and a chipmunk are each collecting pinon nuts for the winter. They have each saved an equal amount. How many pinon nuts would the squirrel have to give the chipmunk so that the chipmunk would have ten more pinon nuts than the squirrel?
Please help me
Let x be the number of pinon nuts each animal has collected. To make the chipmunk have ten more pinon nuts than the squirrel, the squirrel would have to give the chipmunk 10 pinon nuts.
So, after the exchange, the squirrel would have x - 10 pinon nuts, and the chipmunk would have x + 10 pinon nuts.
Since they are each giving an equal amount, the total number of pinon nuts remains the same. Therefore, we can set up the equation:
x + (x - 10) = 2x - 10
Simplifying and solving for x, we get:
2x - 10 = 2x
-10 = 0
This is a contradiction, so there is no solution that satisfies the conditions of the problem.
Therefore, the problem is not well-defined and there is no answer.
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PLEASE HELP
Find X
(7x+3) 78° 152°
By using concept of interior angle we find the value of X is -7.14 degrees.
The above problem involves finding the value of x in a triangle with two known angles measuring 78° and 152°.
The sum of the interior angles of any triangle is always 180°, so we can use this fact to set up an equation involving the third angle, which is given as 7x +3 degrees.
To solve for x, we first simplify the equation by combining the known angles:
78° + 152° + (7x + 3)° = 180°
Next, we can simplify by adding the two known angles:
230° + 7x° = 180°
This simplifies to:
7x° = -50°
Finally, we can solve for x by dividing both sides by 7:
x = [tex]\frac{-50^\circ}{7}$$[/tex]
Therefore, x is approximately -7.14 degrees.
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As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price to that your revenue from selling it is as large as possible. Previous sales figures of the cheese are shown in the following table. Use the sales figures for the prices S3 and $5 per pound to construct a demand function of the form q = Ae^-bp, where A and b are constants you must determine. (Round A and b to two significant digits.) q = Use your demand function to find the price elasticity of demand at each of the prices listed. (Round your answers to two decimal places.) P = $3, E = P = $4, E = P = $5, E = At what price should you sell the cheese in order to maximize monthly revenue (Round your answer to the nearest cent.) $ If your total Inventory of cheese amounts to only 200 pounds, and It win spoil one month from now, how should you price it in order to receive the greatest revenue? (Round your answer to the nearest cent.) $ Is this the same answer you got In part (c)? If not, give a brief explanation. It is a higher price than in part (c) because at a lower price you cannot satisfy the demand. It is the same price. It is a lower price than in part (c) because at a higher price the demand is not high enough.
a) The demand function is 134.33e^-0.693p
b) At P = $3, we have elasticity is 0.83, at P = $4, we have elasticity is 1.05, at P = $5, we have elasticity is 1.34.
c) We should sell the cheese at a price of $3.84 per pound to maximize monthly revenue.
d) We should sell the cheese at a price of $4.22 per pound to generate the highest revenue within the timeframe of one month.
a) To construct a demand function of the form q = Ae^-bp, we can use the sales figures for the prices $3 and $5 per pound. First, we calculate the values of A and b:
A = q/p = 403/3 ≈ 134.33
b = ln(q/Ap) / p = ln(403/134.33) / (3-5) ≈ 0.693
Using these values, the demand function becomes:
q = 134.33e^-0.693p
b) To find the price elasticity of demand at each of the prices listed, we can use the formula:
E = (dq/dp) * (p/q)
At P = $3, we have:
E = (dq/dp) * (p/q) = (-134.33 * -0.693 * 3) / 403 ≈ 0.83
At P = $4, we have:
E = (dq/dp) * (p/q) = (-134.33 * -0.693 * 4) / 284 ≈ 1.05
At P = $5, we have:
E = (dq/dp) * (p/q) = (-134.33 * -0.693 * 5) / 225 ≈ 1.34
c) To find the price that will maximize monthly revenue, we can use the formula:
p = (1/b) * ln(A/b)
Plugging in the values of A and b that we calculated earlier, we get:
p = (1/0.693) * ln(134.33/0.693) ≈ $3.84
d) If we only have 200 pounds of cheese and it will spoil in one month, we need to sell it at a price that will generate the highest revenue within that timeframe. To do this, we can use the formula:
R = pq
where R is the revenue, p is the price per pound, and q is the quantity sold. We can express q in terms of p using our demand function:
q = 134.33e^-0.693p
Substituting this into the revenue equation, we get:
R = p * 134.33e^-0.693p
To find the price that will maximize revenue, we can take the derivative of R with respect to p and set it equal to zero:
dR/dp = 134.33e^-0.693p - 93.13pe^-0.693p = 0
Solving this equation numerically, we get:
p ≈ $4.22
This price is different from the price calculated in part (c) because we have a limited quantity of cheese that will spoil, so we need to balance the price and quantity sold to maximize revenue within the given timeframe.
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Which expressions are equivalent to b2c52b−2c12? Select all that apply
The "equivalent-expression" for the given expression "b²c⁵b¹ - 2c¹b²" is b²c(bc⁴ - 2).
An "Equivalent-Expression" is an expression which has the same-value as the original expression, but may look different. The two expressions are equivalent if they simplify to the same result.
We have to solve the expression : "b²c⁵b¹ - 2c¹b²",
To simplify this expression, we first combine the "like-terms" by adding the exponents of b and c;
= b²c⁵b¹ - 2c¹b²,
Now we add the exponents having the same-base;
= b²⁺¹c⁵ - 2b²c¹;
= b³c⁵ - 2b²c
= b²c(bc⁴ - 2).
Therefore, the required "equivalent-expression" is b²c(bc⁴ - 2).
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The given question is incomplete, the complete question is
Write an equivalent expression for the given expression "b²c⁵b¹ - 2c¹b²".
Dans une boite il ya 12 boules vertes et 6 boules bleues quelle est la proportion de boules vertes dans cette boite
La proportion de boules vertes dans cette boîte est de 2/3.
How to calculate the proportion of green balls in the box?Pour déterminer la proportion de boules vertes dans cette boîte, nous devons comparer le nombre de boules vertes au nombre total de boules dans la boîte.
Le nombre total de boules dans la boîte est la somme des boules vertes et des boules bleues, soit 12 + 6 = 18 boules.
Maintenant, pour calculer la proportion de boules vertes, nous divisons le nombre de boules vertes par le nombre total de boules.
Proportion de boules vertes = Nombre de boules vertes / Nombre total de boules
Proportion de boules vertes = 12 / 18
Simplifiant cette fraction, nous obtenons :
Proportion de boules vertes = 2/3
La proportion de boules vertes dans cette boîte est donc de 2/3 ou environ 66.67%.
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Solve the problem.
Find the area bounded by y = 3 / (√36-9x^2) • X = 0, y = 0, and x = 3. Give your answer in exact form.
To solve the problem, we first need to graph the equation y = 3 / (√36-9x^2) and find the points where it intersects the x-axis and y-axis.
To find the x-intercept, we set y = 0 and solve for x:
0 = 3 / (√36-9x^2)
0 = 3
This has no solution, which means that the graph does not intersect the x-axis.
To find the y-intercept, we set x = 0 and solve for y:
y = 3 / (√36-9(0)^2)
y = 3 / 6
y = 1/2
So the graph intersects the y-axis at (0, 1/2).
Next, we need to find the point where the graph intersects the vertical line x = 3. To do this, we substitute x = 3 into the equation y = 3 / (√36-9x^2):
y = 3 / (√36-9(3)^2)
y = 3 / (√-243)
This is undefined, which means that the graph does not intersect the line x = 3.
Now we can draw a rough sketch of the graph and the region bounded by the x-axis, the line x = 0, and the curve y = 3 / (√36-9x^2):
|
_______|
/ |
/ |
/ |
/_________|
| |
The area we want to find is the shaded region, which is bounded by the x-axis, the line x = 0, and the curve y = 3 / (√36-9x^2). To find the area, we need to integrate the equation y = 3 / (√36-9x^2) with respect to x from x = 0 to x = 3:
A = ∫(0 to 3) 3 / (√36-9x^2) dx
We can simplify this integral by using the substitution u = 3x, du/dx = 3, dx = du/3:
A = ∫(0 to 9) 1 / (u^2 - 36) du/3
Next, we use partial fractions to break up the integrand into simpler terms:
1 / (u^2 - 36) = 1 / (6(u - 3)) - 1 / (6(u + 3))
So we have:
A = ∫(0 to 9) (1 / (6(u - 3))) - (1 / (6(u + 3))) du/3
A = (1/6) [ln|u - 3| - ln|u + 3|] from 0 to 9
A = (1/6) [ln(6) - ln(12) - ln(6) + ln(6)]
A = (1/6) [ln(1/2)]
A = (-1/6) ln(2)
Therefore, the exact area bounded by y = 3 / (√36-9x^2), x = 0, y = 0, and x = 3 is (-1/6) ln(2).
To find the area bounded by y = 3 / (√36-9x^2), x = 0, y = 0, and x = 3, we can set up an integral to compute the definite integral of the function over the given interval [0, 3]. The integral will represent the area under the curve:
Area = ∫[0, 3] (3 / (√(36-9x^2))) dx
To solve the integral, perform a substitution:
Let u = 36 - 9x^2
Then, du = -18x dx
Now, we can rewrite the integral:
Area = ∫[-√36, 0] (-1/6) (3/u) du
Solve the integral:
Area = -1/2 [ln|u|] evaluated from -√36 to 0
Area = -1/2 [ln|0| - ln|-√36|]
Area = -1/2 [ln|-√36|]
Since the natural logarithm of a negative number is undefined, there's an error in the original problem. Check the problem's constraints and the given function to ensure accuracy before proceeding.
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A home buyer is financing a house for $135,950. The buyer has to pay $450 plus 1.15% for a brokerage fee. How much are the mortgage brokerage fees?
$2,489.25
$2,013.43
$2,018.60
$2,031.43
Answer: $2,013.43
Step-by-step explanation:
$135,950 x 1.15% = 1,563.425
Round to $1,563.43
Add in $450
$1,563.43 + $450 = $2,013.43
Antonio and lizeth have a combined income of $83,366. they have 1099
forms which report $1,200 in interest. they also have $4,922 income from
rental property. they can reduce their income by $3,500. what is their
adjusted gross income?
Antonio and lizeth's adjusted gross income is $85,988.
To find their adjusted gross income, we need to start with their total income and subtract any adjustments.
Total income:
Combined income: $83,366
Interest income: $1,200
Rental income: $4,922
Total income before adjustments: $89,488
Adjustments:
Reduce income by $3,500
Adjusted gross income:
$89,488 - $3,500 = $85,988
Therefore, their adjusted gross income is $85,988.
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QUESTION 2 2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6 marks) Shape No. of match- sticks Rule 1 4 2 7 3 10 4 13 6 10 43 [24] 82 [6]
The completed table based on the given pattern is as follows: Shape 1: 4 matchsticks, Shape 2: 7 matchsticks, Shape 3: 10 matchsticks, Shape 4: 13 matchsticks, Shape 5: 24 matchsticks, Shape 6: 82 matchsticks.
To complete the table based on the given pattern, we need to identify the rule that determines the number of matchsticks for each shape.
Looking at the provided information, we can observe that the first four shapes follow a consistent rule, while the last two shapes seem to deviate from that rule.
For the first four shapes:
Shape 1: 4 matchsticks
Shape 2: 7 matchsticks (Shape 1 + 3 matchsticks)
Shape 3: 10 matchsticks (Shape 2 + 3 matchsticks)
Shape 4: 13 matchsticks (Shape 3 + 3 matchsticks)
Based on this pattern, it appears that each shape adds three additional matchsticks compared to the previous shape.
Now, let's analyze the last two shapes:
Shape 6: 43 matchsticks
Shape 7: 82 matchsticks
From Shape 4 to Shape 6, there is an increase of 3 matchsticks as expected.
However, from Shape 6 to Shape 7, there is an unexpected increase of 39 matchsticks.
Since the given information does not provide a clear pattern or rule for the last two shapes, we cannot accurately determine the number of matchsticks for those shapes.
Therefore, we can complete the table as follows:
Shape 1: 4 matchsticks
Shape 2: 7 matchsticks
Shape 3: 10 matchsticks
Shape 4: 13 matchsticks
Shape 5: (Unknown)
Shape 6: (Unknown).
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