Using the given information, the height of the shorter cone is 6.81 cm
Calculating volume of a coneFrom the question, we are to determine the height of the shorter cone.
First, we will calculate the volume of the first cone
Using the formula for calculating the volume of a cone,
\(V = \frac{1}{3}\pi r^{2}h\)
Where V is the volume
r is the radius
and h is the height
From the given information,
r = 8.5 cm
h = 10 cm
Then,
\(V = \frac{1}{3}\pi \times 8.5^{2}\times 10\)
\(V = \frac{1}{3}\pi \times 72.25\times 10\)
\(V = \frac{722.5}{3}\pi\) cm³
Now, for the shorter cone
r = 10.3 cm
Since the two cones have the exact same volume, we can write that
\(\frac{722.5}{3}\pi= \frac{1}{3}\pi \times 10.3^{2} \times h\)
\(722.5= 106.09 \times h\)
\(h = \frac{722.5}{106.09}\)
h = 6.81 cm
Hence, the height of the shorter cone is 6.81 cm.
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1. If f(x) = x + 3 and g(x) = x² + 2x - 3, find [gxf](x).
The answer is g(f(x)) =(x+6)(x+2)
From the question, we have
f(x) = x + 3 and g(x) = x² + 2x - 3
g(f(x)) = g(x + 3)
=(x + 3)² + 2(x + 3) - 3
=x² + 9+6x+2x+6-3
=x² + 8x+12
=x² + 6x+2x+12
=(x+6)(x+2)
The answer is g(f(x)) =(x+6)(x+2)
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Mrs.li wants to compare her students test scores to the school average. She created a table to help her. Which list orders the students from least to highest?
Answer:
Cierra and fionna
Step-by-step explanation:
because their under 0
and 0 is the school average
Answer:
B uWu
Step-by-step explanation:
1/6 divided by 5/6 i really need help
Answer: 1/5
Step-by-step explanation:
When dividing fractions, use the strategy of KCF (keep, change, flip). Keep the first fraction (this is a must) and then flip the second fraction.
In this case it would be 6/5. Then multiply both fractions, this would be 1 by 6 and 6 by 5. (6/30) in simplest form is 1/5, in the end to get the simplest form you would have to divide both the numerator and denominator by their common factor.
Hope this helped!
[7th Grader]
A firm utilizes a strategy of capital rationing, which is currently $375,000 and is considering the following two projects: Project A has a cost of $335,000 and the following cash flows: year 1 $140,000; year 2 $150,000; and year 3 $100,000. Project B has a cost of $365,000 and the following cash flows: year 1 $220,000; year 2 $110,000; and year 3 $150,000. Using a 6% cost of capital, which decision should the financial manager make?
Select project A.
Select project B.
Do not select either project.
Select both projects.
The financial manager should select Project A.
What is Capital Rationing?Capital rationing refers to a situation in which a corporation decides to restrict the amount of new investment projects it will pursue so that it can maintain its current level of indebtedness. It is a state of constraint on the amount of investment that a company can make.
Capital rationing is also one of the financial management's most critical investment decisions.
Project A and Project B are two potential investment proposals.
Both projects' cash inflows are given over a three-year term. A cost of 6% is used to discount cash flows in both proposals.
Following that, the net present value of each project is determined.
Given that Project A has a favorable net present value compared to Project B, the financial manager should select Project A since it will yield a greater return on investment.
As a result, the answer is to select project A.
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Determine if the table how a proportional relationhip. X 25. 6 72. 8 77. 2 y 6. 4 18. 2 19. 3 Ye, it i proportional becaue all y over x ratio are equivalent to one fourth. Ye, it i proportional becaue all y over x ratio are equivalent to one third. No, it i not proportional becaue 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8. No, it i not proportional becaue 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Proportional relationship for the given table is true and is define as
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
As given in the question,
Value of x and y in the given table are :
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.
y / x for all the values of x and y:
First values:
y /x = 6.4 / 25.6
= 0.25
Second values:
y/x = 18.2/ 72.8
= 0.25
Third values :
y /x = 19.3/ 77.2
= 0.25
0.25 is equivalent to One fourth ( 1/4).
Constant of proportionality exist = 0.25 or One fourth.
Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.
The complete question is:
Determine if the table how a proportional relationship.
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
Yes, it is proportional because all y over x ratio are equivalent to one third.
No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.
No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
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Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Answer:
B - The correct answer is graph B
Step-by-step explanation:
Answer:
the correct choice is graph B. (see attachment below)
If i buy a disc which costs $16,30, there's a 10% discount. how much i'm i going to pay?
The price we have to pay for the disc after 10% discount is 1467 dollars.
What is percentage ?Percentage is the value per hundredth.
According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.
10% of 1630 dollars will be
= (10/100) × 1630 dollars.
= 16300/100 dollars.
= 163 dollars.
So, the price we have to pay for the disc after 10% discount is
= (Total amount - Discount amount)
= ( 1630 - 163 ) dollars.
= 1467 dollars.
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Find the gradient vector for the function f(x,y,z)=x 2
ln(x+y)+z 2
cos(xy)−e xyz
. Suppose f(x,y,z)=xyz−e x+y+z
, and u
is the unit vector in the direction of ⟨1,2,3⟩. Find the directional derivative D u
(f). Find an equation for the plane tangent to the surface x 2
+y 2
−z 2
=1 at the point (1,2,2). 3 Suppose f(x,y)=x 2
−y 2
, where (x,y) lies on the curve r
(t)=⟨cos(t),sin(t)⟩. Find dt
df
.
The the derivative of f along the curve is:df/dt = lim_{h → 0} [cos^2(t + h) - sin^2(t + h) - (cos^2(t) - sin^2(t))] / h = 2sin(2t)of f along the curve is: df/dt = lim_{h → 0} [cos^2(t + h) - sin^2(t + h) - (cos^2(t) - sin^2(t))] / h = 2sin(2t) , Gradient vector for f(x,y,z)=x^2ln(x+y)+z^2cos(xy)−exyz.
The gradient vector for a scalar field f is a vector that points in the direction of the greatest rate of increase of f. The components of the gradient vector are the partial derivatives of f.
In this case, the gradient vector for f(x,y,z) is: ∇f = (2x ln(x + y) + 2z cos(xy) - exyz, 2x ln(x + y) - exyz, z^2 sin(xy) - exyz)
Directional derivative of f(x,y,z)=xyz−e x+y+z in the direction of ⟨1,2,3⟩
The directional derivative of a function f in the direction of a unit vector u is the rate of change of f in the direction of u. It is calculated using the following formula: Duf = ∇f • u
In this case, the unit vector u is ⟨1,2,3⟩. The gradient vector for f is given above. Therefore, the directional derivative of f in the direction of u is: Duf = (2ln(2) + 6 - 3e) ≈ 11.34
Equation for the plane tangent to the surface x^2+y^2−z^2=1 at the point (1,2,2)
The equation for a tangent plane to a surface f(x,y,z) = 0 at the point (a,b,c) is: f(a,b,c) + ∇f • (x - a, y - b, z - c) = 0
In this case, the surface is x^2+y^2−z^2=1 and the point is (1,2,2). The gradient vector for f is given above. Therefore, the equation for the tangent plane is: 1 + 2ln(3) - 3e + (2x - 2, 4y - 4, -2z + 4) • (x - 1, y - 2, z - 2) = 0
Derivative of f(x,y)=x^2−y^2 along the curve r(t)=⟨cos(t),sin(t)⟩
The derivative of a function f along a curve C is the limit of the difference quotient as the secant approaches the curve. It is calculated using the following formula df/dt = lim_{h → 0} [f(r(t + h)) - f(r(t))] / h
In this case, the function is f(x,y)=x^2−y^2 and the curve is r(t)=⟨cos(t),sin(t)⟩. Therefore, the derivative of f along the curve is: df/dt = lim_{h → 0} [cos^2(t + h) - sin^2(t + h) - (cos^2(t) - sin^2(t))] / h = 2sin(2t)
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\( log_{9 }( {1}^{x} ) \)what's the answer :
the options
1
0
9
x
The value of the logarithmic expression is (b) 0
How to evaluate the logarithmic expressionFrom the question, we have the following parameters that can be used in our computation:
log₉(1ˣ)
The logarithmic rule log(1^b) = 0 can be used to evaluate log(1^x) base 9:
log₉(1ˣ)
This is true because
Since 1^x = 1, no matter what the value of x is,
Then log(1^x) base 9 = x = 0.
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A function is shown f(x)=-(13)/(5)x+k if f(30)=-1 what is the vallue of k?
The value of the variable , k is -385/13
What is a function?A function can be described an expression, equation, law or rule explaining the relationship between two variables.
These variables are known as;
Dependent variableIndependent variableFrom the information given, we have the function;
f(x)=-(13)/(5)x+k
Also, for the value of f(30), the function is equivalent to -1
Now, substitute the value of x as 30 and equate the function to -1. we have;
-1 = -13/(5)30 + k
Divide both sides by the cofficient of 30 + k
30 + k = -1 × -5/13
Multiply the values
30 + k = 5/13
Now, collect like terms
k = 5/13 - 30
k = -385 /13
Thus, the value is -385/13
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In the coordinate plane, the point A (-2,0) is translated to the point A prime (-6,-3) . Under the same translation B(2, 4) the points and C (1,-4) are translated to B prime and C prime , respectively. What are the coordinates of B prime and C prime ?
Under the given translation, the point B(2, 4) is translated to B'(-2, 1), and the point C(1, -4) is translated to C'(-3, -7).
To find the coordinates of B' and C' after the translation, we need to determine the change in x and y coordinates for each point.
For point B, the x-coordinate changes by -2 and the y-coordinate changes by -3. Therefore, the coordinates of B' are (-2 + 2, 4 + (-3)), which simplifies to (-2, 1).
Similarly, for point C, the x-coordinate changes by -2 and the y-coordinate changes by -3. Thus, the coordinates of C' are (1 + (-2), -4 + (-3)), which simplifies to (-3, -7).
In conclusion, the coordinates of B' are (-2, 1) and the coordinates of C' are (-3, -7) under the given translation.
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Please help me.
2. Use three digits to write a number equal to 3 hundreds, 4 tens, and 8 ones.
Answer:
348
Step-by-step explanation:
If we are asking for 3 digits, we are looking for hundreds, tens, and ones. The hundreds go first, so we have 3*100=300. Then the tens, so 4*10=40. Last the ones. 8*1=8. Finally, we add everything together. 300+40+8=34+8=348
Hello:) how to do question 6? :) I’m not sure which property to use :/
Answer:
which grade are you in so that i can tell you according to that
i, vì AD//BC nên góc A +góc B =180°
ii, góc A=góc B nên góc C=góc D -> ABCD là hình bình hành
And AB=BC=> ABCD là hình thoi
If it is true that z2 - 6 = 19, then z2 + 6 = ?
Edward deposited $10,000 into a savings account 2 years ago. The simple interest rate is 2%. How much money did Edward earn in interest?
Step-by-step explanation:
Simple interest = PRT/100
S I = $10000 x 2 x 2
_____________
100
SI = $400
Answer:
$ 10,400
Step-by-step explanation:
Interest = P( 1 + rt)
10000 { 1 + ( 0.02 x 2 )
= 10000 * 1.04
= 10, 400
The probability distribution for the number of defective items in a random sample is as follows: x: 0 1 2 3 4 p(x) : 1 0.15 13 07 0.55
calculate:
expected value of X = ____
From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.
To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.
The expected value of X, denoted as E(X) or μ, is calculated using the formula:
E(X) = ∑ (x * p(x))
where x represents each possible value of X and p(x) represents the corresponding probability.
In this case, the probability distribution for X is given as follows:
x: 0 1 2 3 4
p(x): 0.1 0.15 0.13 0.07 0.55
To calculate the expected value, we perform the following calculations:
E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)
E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2
E(X) = 2.82
The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.
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a reciprocal is a number that
Answer:
The reciprocal of a number is 1 divided by the number. The reciprocal of a number is also called its multiplicative inverse. The reciprocal of a fraction is found by flipping its numerator and denominator.
The reciprocal of a number is this fraction flipped upside down. In other words, the reciprocal has the original fraction's bottom number—or denominator—on top and the top number—or numerator—on the bottom. So the reciprocal of 6 is 1/6 because 6 = 6/1 and 1/6 is the inverse of 6/1. Below, you can see more reciprocals.
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in 250 explain the power of substitutes from porters 5
forces
The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.
The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.
The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.
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A train travels 600 km in one hour .what is the trains Velocity in meters /seconds?
Answer:
166.6666 metres/second
Step-by-step explanation:
1 km/hr = 5m/18s
600*5/18
Find GM. A 10 B. 11 C. 12 D. 13 L 156 G 108 M H9 N
Answer:
b.11
Step-by-step explanation:
b is the answer
Using the weighted average approach to process costing, floridyne would use what number of equivalent units in 2019 to calculate the cost per equivalent unit for direct labor?
Floridyne would use an equivalent unit labor of 166,340 unit to calculate the cost per equivalent unit for direct labor.
How do we get the equivalent unit labor?Under weighted average, we do not make distinction between started and finished and just finished. Thus we work with finished and ending WIP only:
Finished 162,000
Ending - WIP 6,200 ending at 70% complete
Equivalent units for labor = Finished + Percentage of completion ending units
= 162,000 + 6,200 x 70%
= 166,340
Therefore, he would use an equivalent unit labor of 166,340 unit to calculate the cost per equivalent unit for direct labor.
Missing word "Floridyne, Inc. manufactures mouthwash. They had no finished goods inventory at the beginning of 2019. They have only one processing department for this product. A review of the company’s inventory records shows the following: At the beginning of January 2019, Floridyne has 4,500 gallons of mouthwash in process. (costs $8,410 for materials, 1,663 for labor and 4,990 for overhead) During 2019, Floridyne finishes/transfers 162,000 gallons of mouthwash. On December 31, 2019, Floridyne has 6,200 gallons of mouthwash that is 70% complete. Direct materials are added half at the beginning of the process and half after the process is 60% complete. During 2019 $349,000 of direct materials and $92,500 of direct labor were added. Using the weighted average approach to process costing,"
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For a normal distribution, the probability of a value being between a positive z-value and its population mean is the same as that of a value being between a negative z-value and its population mean.
For a normal distribution, the probability of a value being between a positive z-value and its population mean is indeed the same as that of a value being between a negative z-value and its population mean.
This is due to the symmetric nature of the normal distribution curve, where probabilities are mirrored around the mean.
The normal distribution is characterized by its bell-shaped curve, which is symmetric around the mean. The mean is also the midpoint of the curve, and the curve approaches but never touches the horizontal axis. The standard deviation of the distribution controls the spread of the curve.
In a normal distribution, the probability of a value being between a positive z-value and its population mean is indeed the same as that of a value being between a negative z-value and its population mean.
This is due to the symmetric nature of the normal distribution curve, where probabilities are mirrored around the mean.
This means that if we have a normal distribution with a mean of μ and a standard deviation of σ, the probability of a value falling between μ+zσ and μ is the same as the probability of a value falling between μ-zσ and μ.
This property of the normal distribution makes it easy to compute probabilities for any range of values, by transforming them into standard units using the z-score formula.
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You frop a ball off a 50-foot roof to see how long it will bounce. Wach bounce looses 10% of the height of its previous bounce. How high will the 8th bounce be in feet?
Answer:
\(50( {.9}^{8} ) = 21.52\)
The 8th bounce will be about 21.52 feet high.
What's the area of this figure
Answer:
137.6 un^2
Step-by-step explanation:
A = b * h
A = 16 * 8.6
A = 137.6
Hope this helps :)
Answer:
Area = 137.6 units
Step-by-step explanation:
The equation for the area of a parallelogram is A = bh, where b = the base and h = the height. On this parallelogram, the base is 16 and the height is 8.6. Their product is 137.6.
a positively skewed distribution is due to: an extremely small number. an extremely large number. the fact that all data is equal. none of these choices are correct.
A positively skewed distribution is due to an extremely large number.
What is positively skewed distribution?A positively skewed distribution is a type of distribution in which the majority of the data values are clustered towards the left side of the distribution, with a tail extending to the right. This means that there are relatively more smaller values in the dataset than larger values. In a positively skewed distribution, the mean of the dataset is typically larger than the median, and the mode may not be a good representation of the central tendency of the data. This is because the presence of a long tail on the right-hand side of the distribution pulls the mean towards the higher values, while the median remains closer to the center of the dataset. Some common examples of positively skewed distributions include income distributions, where there are a few extremely high earners that skew the data towards the right, and test scores, where there may be a few students who perform extremely well and pull the average higher than the median.
Here,
A positively skewed distribution occurs when the tail of the distribution extends to the right, and the majority of the data is clustered towards the left side of the graph. This means that there are relatively more smaller values in the dataset than larger values. One common cause of positive skewness is the presence of extremely large values, also called outliers, in the dataset. These large values pull the mean of the dataset towards the right, resulting in the tail of the distribution stretching in that direction.
Therefore, out of the options provided, the correct answer is "an extremely large number."
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Here's a new question!
Which ray is the terminal side of a 6 radian angle in standard position?
a) positive x axis
b) positive y axis
c) negative x axis
d) negative y axis
Answer:
negative y axis
Step-by-step explanation:
6 radians is between 3pi/2 and 2pi radians, so it lies in tje fourth quadrant.
So, a terminal side is the negative y axis.
x + 16 = 9z
Help please
Answer:x=9z + 16
z= x/9 + 16/9
Step-by-step explanation: dont know if i solve for x or z so i did both subtract 16 from both sides for x
Isolate the variable by dividing each side by factors that don't contain the variable. for z let me know if u need help
Answer:
Hallooooooo
Step-by-step explanation:
Guess my number when i tripple my number snd add five,i get 26 what is my number
PLEASE HELP
What is the middle term of the product of (x - 4)(x - 3)?
A. x
B. -7 x
C. - x
Answer:
x^2−7x+12 so -7x
Step-by-step explanation:
Perform the indicated operation, if possible.
\(\ \textless \ br /\ \textgreater \
\left[\(\(\(\begin{array}{rrrr}\ \textless \ br /\ \textgreater \
2 & 8 & 13 & 0 \\\ \textless \ br /\ \textgreater \
7 & 4 & -2 & 5 \\\ \textless \ br /\ \textgreater \
1 & 2 & 1 & 10\ \textless \ br /\ \textgreater \
\end{array}\right]-\left[\begin{array}{rrrr}\ \textless \ br /\ \textgreater \
2 & 3 & 6 & 10 \\\ \textless \ br /\ \textgreater \
3 & -4 & -4 & 4 \\\ \textless \ br /\ \textgreater \
9 & 0 & -2 & 17\ \textless \ br /\ \textgreater \
\end{array}\right]\)\)\)
\)
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The resulting matrix is (Simplify your answer.)
B. The matrices cannot be subtracted.
The correct choice is A. The resulting matrix is
\(\[\begin{array}{rrrr}0 & 5 & 7 & -10 \\4 & 8 & 2 & 1 \\-8 & 2 & 3 & -7 \\\end{array}\]\)
To perform the indicated operation, we need to subtract the second matrix from the first matrix. The matrices must have the same dimensions to be subtracted.
Given matrices:
\(\[ \begin{array}{rrrr}2 & 8 & 13 & 0 \\7 & 4 & -2 & 5 \\1 & 2 & 1 & 10 \\\end{array}\]\)
and
\(\[ \begin{array}{rrrr}2 & 3 & 6 & 10 \\3 & -4 & -4 & 4 \\9 & 0 & -2 & 17 \\\end{array}\]\)
These matrices have the same dimensions, so we can subtract them element by element.
Subtracting the corresponding elements, we get:
\(\[ \begin{array}{rrrr}2-2 & 8-3 & 13-6 & 0-10 \\7-3 & 4-(-4) & -2-(-4) & 5-4 \\1-9 & 2-0 & 1-(-2) & 10-17 \\\end{array}\]\)
Simplifying the subtraction, we have:
\(\[ \begin{array}{rrrr}0 & 5 & 7 & -10 \\4 & 8 & 2 & 1 \\-8 & 2 & 3 & -7 \\\end{array}\]\)
Therefore, the resulting matrix is:
\(\[ \begin{array}{rrrr}0 & 5 & 7 & -10 \\4 & 8 & 2 & 1 \\-8 & 2 & 3 & -7 \\\end{array}\]\)
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