Answer:
BC ≈ 20.9
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
BC² + AC² = AB²
BC² + 7² = 22²
BC² + 49 = 484 ( subtract 49 from both sides )
BC² = 435 ( take the square root of both sides )
BC = \(\sqrt{435}\) ≈ 20.9 ( to the nearest tenth )
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
17. Find an equation of the straight line that is perpendicular to x - y = 5 and passes through the point (8, -1).
18. Find the equation of the line in slope-intercept form that passes through the points (12, 4) and (4, 6)
Answer:
17.y=-x+12
18.y=-1/4x+7
Step-by-step explanation:
17.a Solve for y (y=-5+x)
17. b Reciprocal (y=-1x-5)
17. c Subsitute equation into (8,-1) (-1=-13=y=x+12)
18.a Subtract y values and x values= (6-4)/(4-12)=2/-8=-1/4, this will be your slope
18. b Plug in -1/4 into either of the two ordered pairs to find y value=(12,4)=(4=-3)=y value=7.
18. c=y=-1/4x+7
The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election. What percentage of the members voted?
The percentage of members that voted is 70%.
How to find the percentage of members that voted?The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election.
Therefore, the percentage of the members that voted can be calculated as follows;
percentage that voted = number of people that voted / total number members × 100
Therefore,
number of people that voted = 42
total number members = 60
Hence,
percentage that voted = 42 / 60 ×100
percentage that voted = 4200 / 60
Therefore,
percentage that voted = 70%
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Find the value of x.
================================
Explanation:
The two angles shown are a linear pair. They are adjacent and supplementary.
Supplementary angles add to 180
(8x+1) + (4x+11) = 180
8x+1+4x+11 = 180
(8x+4x) + (1+11) = 180
12x+12 = 180
12x+12-12 = 180-12 ... subtract 12 from both sides
12x = 168
12x/12 = 168/12 ... divide both sides by 12
x = 14
Answer:
x=14
Step-by-step explanation:
A line has 180 degrees, so add your two equations and set them equal to 180. Then all you have to do is solve for x.
\(180= 8x+1+4x+11\)
\(180= 12x+12\)
\(168=12x\)
\(14=x\)
If you want to find the answer for each angle, then just plug 14 in for x.
8(14)+1= 113
4(14)+11= 67
what numbers will you add to get 214,907,000
Answer:
I don't really understand this question. But i hope it helps.
Step-by-step explanation:
214,000,000
+ 907,000
Answer:
Answer Below
Step-by-step explanation:
Let us take the variables as x,x+1
x+x+1 = 214907000
2x+1 = 214907000
2x = 214906999
x = \(\frac{214906999}{2}\)
x = 107453499.5
1st number = x = 107453499.5
2nd number = x + 1 = 107453499.5 + 1 =107453500.5
Hence , the number that need to be added to get 214,907,000 are 107453499.5 and 107453500.5
Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.
6 x = negative 2 x minus 4.5
What errors did Emma make? Select two options.
She should have used division to represent the quotient of six and x.
She should not have included an equal sign.
She should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5).
She should have subtracted the difference (x minus 4.5) from Negative 2.
She should have used parentheses to show that Negative 2 is multiplied by (4.5 minus x).
According to the solution we have come to find that, The two errors that Emma made are: She should have used division to represent the quotient of six and x and she should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5).
What is division?Division is a mathematical operation that is the opposite of multiplication. It involves dividing a number (the dividend) by another number (the divisor) to find how many times the divisor can fit into the dividend.
The two errors that Emma made are:
She should have used division to represent the quotient of six and x.She should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5).The correct translation of the statement is:
6 ÷ x = -2(x - 4.5)
The division symbol should be used to represent the quotient of six and x, and parentheses should be used to show that negative 2 is multiplied by (x - 4.5) instead of just x.
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Answer: A and C are the two options
how many square miles of land did the railroad companies get for each mile of track they laid?
The amount of land the railroad companies received for each mile of track they laid varied depending on the specific circumstances and agreements.
However, a common benchmark used during the construction of railroads in the United States was the granting of land through the Homestead Act of 1862. Under this act, railroad companies were granted approximately 6,400 acres (10 square miles) of land for every mile of track laid. This land was typically located alongside the tracks and served as an incentive for the companies to expand and develop the rail network across the country.
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Solve for y. 4- 2y + 8 = -6 y = [?]
Answer:
y=9
Step-by-step explanation:
4-2y+8=-6
-2y=-4-8-6
-2y=-18 divide by -2 both side
y=-18/-2
y=9
A salesperson at a jewelry store earns 9% commission each week. Last week, Jarrod sold $540 worth of jewelry. How much did he make in commission? How much did the jewelry store make from his sales?
Pls help I’m struggling
Answer:
Jarrod made $48.60 in commission and the store made $491.40.
Step-by-step explanation:
540 x .09 = 48.60
540 - 48.60 = 491.40
Answer:15.90
Step-by-step explanation:
Reuben jogs 2.25 miles every weekday.Every Saturday and Sunday ,he jogs 1.8 times as far. To the nearest hundredth , how many miles does Reuben jog in 2 full calendar weeks?
Answer:
38.70 miles
Step-by-step explanation:
Each week, Reuben jogs ...
(2.25 mi)(1 +1 +1 +1 +1 +1.8 +1.8) = (2.25 mi)(8.6)
Then in 2 weeks, he jogs ...
2(2.25)(8.6) mi = 38.70 mi
Reuben jogs 38.70 miles in 2 full weeks.
The order of the differential equation d 2 y dx2 4x dy dx = d 3 (cos 2x) dx3 is:_________
The order of the differential equation d²y/dx² + 4x(dy/dx) = d³(cos(2x))/dx³ is 3.
The order of a differential equation is determined by the highest derivative present in the equation. In the given differential equation, the highest derivative is the third derivative, d³(cos(2x))/dx³. Since this is the highest derivative and there are no higher-order derivatives present, the order of the differential equation is 3. This means that the equation involves up to the third derivative of the dependent variable y with respect to the independent variable x.
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please help me and explain it
Answer:
Divide both sides by -3.
Step-by-step explanation:
This question is asking you how to get from step 1: \(-3(p-7) = -15\) to step 2: \(p - 7 = 5\).
We can see that the expression inside of the parentheses (p - 7) didn't go away from step 1 to step 2, and the term that was being multiplied by (p-7) had gone away. The only way you can "get rid" of a multiplied term is by doing the inverse of multiplication, which is division. Thus, you have to divide both sides by -3 to get to step 2.
Verify that each given function u is harmonic (in the region where it is defined) and then find a harmonic conjugate of u. (c)! = xy -x + y (e) 11 = In Izl for Rez>0
The function u is harmonic and the harmonic conjugate of u is
v(x,y) = -ln|x| + ln|y| + C.
(c) Let's verify if the given function u = xy -x + y is harmonic:
The Laplacian of a function u is defined as the sum of the second partial derivatives with respect to the x and y variables. For the function u = xy - x + y, the Laplacian can be calculated as follows:
∇^2 u = ∂^2 u/∂x^2 + ∂^2 u/∂y^2 =
∇^2 u = 2 + 1 = 3
Since the Laplacian of u is a constant (3), it follows that u is a harmonic function in the region where it is defined.
Now let's find the harmonic conjugate of u:
A harmonic conjugate of a harmonic function u is a function v such that u + iv is analytic (complex differentiable), where i is the imaginary unit. To find the harmonic conjugate of u, we integrate the partial derivative of u with respect to x with respect to x and the partial derivative of u with respect to y with respect to y.
The partial derivative of u with respect to x is y - 1, and the partial derivative of u with respect to y is x. Thus, the harmonic conjugate of u is given by:
v(x,y) = ∫ (y - 1) dx + ∫ x dy
v(x,y) = xy - x + ∫ x dy
v(x,y) = xy - x + (1/2) y^2 + C,
where C is an arbitrary constant of integration.
(e) Let's verify if the given function u = In Izl for Rez > 0 is harmonic:
The Laplacian of the function u = In Izl for Rez > 0 can be calculated as follows:
∇^2 u = ∂^2 u/∂x^2 + ∂^2 u/∂y^2
∇^2 u = (1/z^2) ∂^2 u/∂z^2
∇^2 u = 0, for Rez > 0
Since the Laplacian of u is 0, it follows that u is a harmonic function in the region where it is defined.
Now let's find the harmonic conjugate of u:
A harmonic conjugate of u is a function v such that u + iv is analytic. To find the harmonic conjugate of u, we integrate the partial derivative of u with respect to x with respect to x and the partial derivative of u with respect to y with respect to y.
The partial derivative of u with respect to x is -y/x, and the partial derivative of u with respect to y is x/y. Thus, the harmonic conjugate of u is given by:
v(x,y) = -∫ (y/x) dx + ∫ (x/y) dy
v(x,y) = -ln|x| + ln|y| + C, where C is an arbitrary constant of integration.
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suppose a survey is given at the university to randomly selected students. there are 30 classes in session at 1:00 pm on tuesdays. the survey is given to every student in 5 randomly selected classes. what sampling technique is being used?
The sampling technique being used in this scenario is known as Cluster Sampling.
Cluster Sampling involves dividing a population into clusters or groups and selecting entire clusters at random. In this case, the 30 classes at the university that are in session at 1:00 pm on Tuesdays represent the clusters. The survey is administered to every student in five randomly selected classes, which means that the classes are the clusters being sampled.
By randomly selecting five classes and surveying all the students within those classes, the researchers are using Cluster Sampling. It is important to note that Cluster Sampling is different from Simple Random Sampling, where individual elements are selected randomly from the population without grouping them into clusters.
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(−2,−3) after a translation right 2 units and up 4 units?
Answer:
(0,1)
Step-by-step explanation:
moving right 2 units makes it (0,-3)
moving up 4 units makes it (0,1)
A continuous variable _____ (does/does not) allow fractional amounts. a discrete variable _____ (does/does not) allow fractional amounts.
A continuous variable does allow fractional amounts. a discrete variable does not allow fractional amounts.
Which variables require boundaries, also known as real limits, in their measurement scales?
A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.
What distinguishes a ratio scale from an ordinal scale?
Ordinal: The information is classifiable and rankable. The data can be equally spaced, categorized, and rated. Ratio: The data is evenly spaced, categorizable, rankable, and has a natural zero.For continuous data, what kind of data would you use?
Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.
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Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches
Answer:
V = πr²(h/3)
Step-by-step explanation:
83.74 = πr²(5/3)
R = 4.00 in
Diamater = 2r = 2 x 4.00 = 8 inches
PLEASE HELP ME!
A population grows according to an exponential growth model. The initial population is 9, and the grows by 8% each year.
Find an explicit formula for the population growth. Use that formula to evaluate the population after 9 years.
Round your answer to two decimal places
The explicit formula for the population growth is P(t) = 9 * (1 + 0.08)^t, where P(t) represents the population at time t, P0 is the initial population of 9, r is the growth rate of 8% or 0.08, and t is the time in years. Using this formula, we can calculate the population after 9 years which is approximately 16.03
To find the explicit formula for the population growth, we use the exponential growth model formula P(t) = P0 * (1 + r)^t. In this case, P0 is given as 9, and the growth rate r is 8%, or 0.08 when expressed as a decimal. Plugging these values into the formula, we get P(t) = 9 * (1 + 0.08)^t.
To evaluate the population after 9 years, we substitute t = 9 into the formula and calculate: P(9) = 9 * (1 + 0.08)^9. Using a calculator or performing the calculation manually, the population after 9 years is approximately 16.03 (rounded to two decimal places).
Therefore, the population after 9 years, based on the exponential growth model with an initial population of 9 and a growth rate of 8%, is approximately 16.03
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Brandi completed 7 out of her 9 chores. What percent does she have left to finish?
A. 22%
B. 33%
C. 78%
D. 82%
Answer: C. 78%
Step-by-step explanation:
simply divide 7 by 9 and move the decimal two places to the right and round!
Please HELP ME PLEASE PLEASE ASAP ASAP please ASAP help please please !!
Answer:
1) 360
2) 360
Step-by-step explanation:
here is the answer
A line has a slope of 8 and a y-intercept of 5. What is its equation in slope -intercept form?
Answer:
y = 8x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 8 and c = 5
y = 8x + 5 ← equation of line
helppp please enough points
Answer:
Step-by-step explanation:
i cant quite see pls put more clear
Identify which equations have one solution, infinitely many solutions, or no solution. 3u +40+2u = 6u- 30 u 2.2z+32 4.5-3.2 2.3y +3.2-y= 2.1 + 1.3y + 1.1 No Solution One Solution Infinitely Many Solutions 20+4r 32-2r
a) The equation 3u + 40 + 2u = 6u - 30 - u has no solution.
b) The equation 2.2z + 3z = 4.5 - 3.2 has one solution.
c) The equation 2.3y + 3.2 - y = 2.1 + 1.3y + 1.1 has infinitely many solutions.
d) The equation 20 + 4r = 32 - 2r has one solution.
What is an equation with infinitely many solutions ?
The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept.
Let's check which of the given equations have one solution , infinitely many solutions or no solution.
a)
3u + 40 + 2u = 6u - 30 - u
reordering the terms :
5u + 40 = 5u - 30
or subtract 5u from both sides.
5u - 5u + 40 = 5u - 5u - 30
40 = - 30
which is not possible , that meant this equation has no solution.
b)
2.2z + 3z = 4.5 - 3.2
2.2z + 3z = 4.5 - 3.2
5.2z = 1.3
z = 1.3/5.2
or
z = 13/52
This equation has one solution.
c)
2.3y + 3.2 - y = 2.1 + 1.3y + 1.1
Reordering the terms :
1.3y + 3.2 = 1.3y + 3.2
0 = 0
This equation has infinitely many solutions.
d)
20 + 4r = 32 - 2r
Reordering the terms :
6r = 12
r = 2
This equation has one solution.
Therefore , the answers are :
a) The equation 3u + 40 + 2u = 6u - 30 - u has no solution.
b) The equation 2.2z + 3z = 4.5 - 3.2 has one solution.
c) The equation 2.3y + 3.2 - y = 2.1 + 1.3y + 1.1 has infinitely many solutions.
d) The equation 20 + 4r = 32 - 2r has one solution.
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what is the difference between the points (-3,4) and (-3,-5)?
The difference between the points (-3, 4) and (-3, -5) is (0, 9)
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Marble Inc. makes countertops from a variety of high-end materials. To monitor the quality of its production processes the company randomly selects one countertop and counts the number of blemishes. The results for ten samples are shown below: Sample No. No. of Blemishes 2 3 4567 89 10 17 19 15 18 16 14 15 16 15 15 Given the sample information above, the UCL using sigma = 3 for this process would be O 28 036 O 32 O 30
The UCL (Upper Control Limit) using sigma = 3 for this process would be 30. The UCL utilizing sigma=3 for this process would be 28.036.
In statistical process control, the upper control limit (UCL) is utilized as a device to identify when to stop a process due to a high variation.
A process that exceeds its UCL will result in defective or inconsistent items, which should be avoided.
Marble Inc. produces high-end countertops from a variety of materials. The company employs the process of randomly selecting one countertop to count the number of blemishes as a means of monitoring the quality of its production processes.
The formula for calculating UCL is as follows: UCL = average of blemishes + 3 × standard deviation For ten samples with a different number of blemishes in each sample, the UCL is determined.
Using the given formula for UCL using sigma= 3: UCL = (2+3+4+5+6+7+8+9+10+17)/10 + 3 × √[(2-9.1)² + (3-9.1)² + (4-9.1)² + (5-9.1)² + (6-9.1)² + (7-9.1)² + (8-9.1)² + (9-9.1)² + (10-9.1)² + (17-9.1)²]/10UCL = 28.036
From the above calculations, the UCL utilizing sigma=3 for this process would be 28.036.
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Why do we want homogeneity of variance?
a. to satisfy an assumption
b. it's considered politically correct.
c. we can't get a significant effect unless we do.
d. statement is false > we do not want homogeneity of variance.
Find m<1 and m<2. Justify your answer.
Answer:
M<1 80 by the corresponding angles postulate
Step-by-step explanation:
You walk into a tall building and take the elevator up an appointment you have on the 7th floor they send you down two floors to the 5th floor to pay your bill After paying your bill you take the stairs back to the main floor and exit the building
Answer:
The answer would be A because the person would go up 7 floors, go down 2, and go down five more.
Step-by-step explanation:
if the two firms do not cooperate, which of the following represents the payoff north springs and south springs receive in the dominant-strategy equilibrium and the nash equilibrium?
If the two firms do not cooperate, the payoff that North Springs and South Springs receive in the dominant-strategy equilibrium and the Nash equilibrium would depend on the specific game or scenario being played. Without more information about the specific game being played and the strategies of the two firms, it is impossible to provide a definitive answer.
However, in general, the dominant-strategy equilibrium refers to the situation where each player chooses their best strategy, regardless of what the other player does. The Nash equilibrium refers to the situation where each player chooses their best strategy given what the other player is doing. In some cases, the dominant-strategy equilibrium and the Nash equilibrium may be the same, but in other cases, they may differ.
So, in order to determine the payoff that North Springs and South Springs receive in these equilibria, more information about the game being played and the strategies of the two firms would be needed.
Based on the information given, we can analyze the payoff for both North Springs and South Springs firms in the dominant-strategy equilibrium and the Nash equilibrium.
Dominant-Strategy Equilibrium:
1. Identify each firm's dominant strategy (the best response regardless of the other firm's action).
2. Combine the dominant strategies for both firms to find the outcome.
Nash Equilibrium:
1. Identify each firm's best response given the other firm's action.
2. Find the outcome where both firms are simultaneously choosing their best responses.
Without specific numerical payoffs, I cannot provide the exact payoff amounts. However, once you have the payoff matrix, you can follow the steps mentioned above to find the payoffs for North Springs and South Springs in the dominant-strategy equilibrium and the Nash equilibrium.
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Please help me with edge question .
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)