The first derivative of y with respect to x is d(y)/dx = 4t² + 10t, and the second derivative of y with respect to x is d(2y)/dx² = 8t + 10.
Differential equations are mathematical equations that describe how a function changes over time or with respect to its inputs.
Let x = t² + 3 and y = t² + 5t. We want to find the derivatives of y with respect to x, which means we need to use the chain rule.
The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by
=> d(y)/dx = d(y)/du * du/dx.
First, we will find the derivative of y with respect to t, which is given by
=> d(y)/dt = 2t + 5.
Next, we will find the derivative of x with respect to t, which is given by
=> d(x)/dt = 2t.
Finally, we will multiply these two derivatives to find the derivative of y with respect to x, which is given by
=> d(y)/dx = (2t + 5)(2t) = 4t² + 10t.
Next, we will find the second derivative of y with respect to x, which is given by
=> d(2y)/dx² = d((4t² + 10t))/dt = 8t + 10.
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steps to solve slope intercept word problems like step 1: step2:
According to the problem, if the slope is 3 and the y-intercept is 5, the equation of the line would be y = 3x + 5.
What is the equation ?The equation is an expression that shows the relationship between different variables. It is typically written with an equals sign (=) and can have constants, variables, and operators such as addition, subtraction, multiplication, and division. An equation can be used to solve for a variable, to show a relationship between different variables, or to identify a pattern. For example, the equation y = 2x + 5 can be used to calculate the value of y for any given value of x. Additionally, equations can be used to show relationships between different variables such as the equation y = ax2 + bx + c, which shows a relationship between y and x, where a, b, and c are constants.
Step 1: Identify the given information in the problem. This should include the slope and the y-intercept.
Step 2: Use the slope-intercept form of a line, y = mx + b, to express the equation of the line in terms of the given information. Here, m is the slope and b is the y-intercept.
For example, if the slope is 3 and the y-intercept is 5, the equation of the line would be y = 3x + 5.
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What is the length of each leg in the right triangle shown?
45
7sqrt2
45°
Answer:
Below
Step-by-step explanation:
It is an isosceles right triangle ( the two legs are equal length).
Use Pythagorean Theorem
(7 sqrt2)^2 = L^2 + L^2
98 = 2 L^2
49 = L^2
L = 7
a quadrilateral abcd has diagonals that are perpendicular bisectors of one another. which of the following classifications must apply to quadrilateral abcd? i. parallelogram
ii. rhombus iii. square
O I and III only
O I and II only
O I, II, and III
O II and III only
C) I, II, and III which are parallelogram,rhombus and square. These classifications must apply to quadrilateral ABCD.
ABOUT DIAGONALIn simple terms the diagonal is an oblique line. Line is one of the mediums in fine art, including diagonal lines. Apart from the diagonal lines, there are also horizontal and vertical lines.
A line is a set of points that are parallel and equal in size and aligned in such a way that a prominent longitudinal dimension has a direction. These dimensions produce a variety of shapes, ranging from long, short, smooth, thick, curved, straight and many more. The line diagonal is an oblique line.
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A 2012 Pew Research survey asked 2,373 randomly sampled registered voters their political a liation (Republican, Democrat, or Independent) and whether or not they identify as swing voters. 35% of respondents identified as Independent, 23% identified as swing voters, and 11% identified as both.58
Are being Independent and being a swing voter disjoint, i.e. mutually exclusive? #### not really, i think there’s a slight connection, a lot of independent voters are also swing voters.
Draw a Venn diagram summarizing the variables and their associated probabilities.
No, being Independent and being a swing voter is not disjoint that mutually exclusive.
As in 2012 Pew Research survey asked 2,373 randomly sampled registered voters ;
The 11% of respondents are identified as both Independent and swing voters which means that there is overlap between the two groups, i.e. they are not mutually exclusive.
Some voters may identify as Independent and also as swing voters, meaning they are not independent in terms of political affiliation, but are still considered swing voters because they are not firmly committed to one political party.
Therefore, the categories of Independent and swing voter are not disjoint and can coexist for the same individual.
The given question is incomplete , the complete question is
A 2012 Pew Research survey asked 2,373 randomly sampled registered voters their political affiliation (Republican, Democrat, or Independent) and whether or not they identify as swing voters. 35% of respondents identified as Independent, 23% identified as swing voters, and 11% identified as both.
Are being Independent and being a swing voter disjoint, i.e. mutually exclusive ?
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A poll asked 15 men in two age groups, 30 and younger and older than 30 whether they had facial hair (mustache, beard, sideburns, etc.). The results are recorded in the table.
(a) Create a two-way table of the data. Of the men surveyed, how many were 30 and younger? How many men did not have facial hair?
(b) create a two-way relative frequency table that displays the relative frequency of the men 30 and younger and of the men older than 30 who did or did not have facial hair. Express your answers as decimals written to three decimal places.
(c) What percentage of men older than 30 had facial hair?
Answer: look below
Step-by-step explanation:
You need to count the persons and classify them into four groups.
1) 30 and younger with facial hair: 4 people
2) older than 30 with facial hair: 5 people
3) 30 and younger without facial hair: 3
4) older than 30 without facial hair: 4
(a)
Create a two-way table of the data. Of the men surveyed, how many were
30 and younger? How many men did not have facial hair?
This is the table using the data classified:
--------------------------------------------------------------
|with facial hair | without facial hair | total |
-------------------------------------------------------------------------------------
30 & younger | 4 | 3 | 7 |
-------------------------------------------------------------------------------------
older than 30 | 5 | 3 | 8 |
-------------------------------------------------------------------------------------
Total | 9 | 6 | 15 |
-------------------------------------------------------------------------------------
7 men were 30 and younger.
6 men did not have facial hair.
(b) Create a two-way relative frequency table that displays the relative
frequency of the men 30 and younger and of the men older than 30 who
had or did not have facial hair.
Express your answers as decimals
written to three decimal places.
This is the table:
---------------------------------------------------------------
|with facial hair | without facial hair | total |
-------------------------------------------------------------------------------------
30 & younger | 4/15 | 3/15 = 1/5 | 7/15 |
-------------------------------------------------------------------------------------
older than 30 | 5 /15 = 1/3 | 3/15 = 1/5 | 8/15 |
-------------------------------------------------------------------------------------
Total | 9/15 = 3/5 | 6/15 = 2/5 | 1 |
-------------------------------------------------------------------------------------
This is the answer showing three decimal digits:
---------------------------------------------------------------
|with facial hair | without facial hair | total |
-------------------------------------------------------------------------------------
30 & younger | 0.267 | 0.200 |0.467 |
-------------------------------------------------------------------------------------
older than 30 | 0.333 | 0.200 |0.533 |
-------------------------------------------------------------------------------------
Total | 0.600 | 0.400 | 1 |
-------------------------------------------------------------------------------------
(c) What percentage of men older than 30 had facial hair?
Percentage = relative frequency * 100 % = (1/3)*100 % = 33.33%
ACTIVITY 1.13 Indicate the GAAP concepts that relate to the following statements: 1. Land and buildings are shown in the Statement of Financial h R250 000, even though the municipal valuation indicates 2. When merchandise is sold, the selling price and cost price is the same time. 3. The owner of the business wins R1 000 in a competition. This not recorded in the books of the business. 4. Petrol costs and servicing of vehicles recorded "Motor expense Controll
The purpose of GAAP standards is to guarantee the reliability, accuracy, and consistency of the financial data presented to investors and regulators.
Where Are Generally Accepted Accounting Principles (GAAP) Used?Companies prepare their financial statements and other accounting disclosures in accordance with the GAAP, which is a set of procedures and rules.
The Financial Accounting Standards Board (FASB), a separate non-profit organization, is responsible for creating the standards. The objective of GAAP standards is to ensure that the financial data presented to investors and regulators is accurate, dependable, and consistent with other sources of financial data.
The universally accepted methods of capturing and reporting accounting information are combined with authoritative standards (established by policy bodies) to construct GAAP. The goal of GAAP is to make financial information more understandable, reliable, and comparable.
GAAP is crucial because it keeps investors' confidence in the financial system. Without GAAP, investors would be less inclined to believe that the information corporations give to them is accurate because they would have less faith in its veracity.
In the absence of that trust, there might be fewer transactions, which could result in greater transaction costs and a weaker economy. By facilitating "apples to apples" comparisons across different companies, GAAP also aids in the corporate analysis process for investors.
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what is y=7x + 4 in standard form
Answer:
the answer to this would be 7x - y = -4
Step-by-step explanation:
you move the 7x in front of the y which causes the 4 to become negative which then causes the 7x to be subtracted from y
hope this helped
The sum of two numbers is -40. The difference of the two numbers is -12. What are the two numbers?
Answer:
-26 and -14
Step-by-step explanation:
Let x = one number
Let y = the other number
x + y = -40
x - y = -12 Add the two equations together.
2x = -52 Divide both sides by 2
x = -26
Substitute -26 for x to find y
x + y = -40
-26 + y = -40 Add 26 to both sides
-26 + 26 + y = -40 + 26
y = -14
Check:
x + y = -40
-26 + -14 = -40
-40 = -40 Checks
x - y = -12
-26 - (-14) = -12
-26 + 14 = -12
-12 = -12 Checks
The difference of -1/5 of a number and 1 is 12. PLEASE HELP!!!! DUE IN 30 MINUTES!!!!
Find the curve of best fit for the data. Round to 2 decimals.
The curve of best fit is discussed below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the curve of best fit.
The curve of best fit is the curve the best approximates the trend on a scatter plot.The line of best fit estimates a straight line that minimizes the distance between itself and where observations fall in some data set. The line of best fit is used to show a trend or correlation between the dependent variable and independent variable(s). It can be depicted visually, or as a mathematical expression.Therefore, the curve of best fit is discussed above.
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Plot the image of point of B under a dilation about point P with a scale factor of 1/2
Point B is a point on a two-dimensional plane.
What is scale factor?Scale factor is a numerical value used to represent the proportional change between two similar objects. This value is often used to compare the size of objects in different measurements, such as inches to millimeters or feet to meters. Furthermore, the scale factor can be used to find the area, volume, or surface area of an object, as the measurements are proportional to the scale factor. This is especially useful when objects are enlarged or reduced, as it allows for the accurate calculation of the changed measurements.
When plotting the image of point B under a dilation about point P with a scale factor of 1/2, it is necessary to first plot the given point P, which serves as the center of the dilation. The next step is to draw a line from point B to point P, which will be the radius of the dilation. After this, draw a circle with a radius of half the length of the original line and centered at point P. The image of point B will be the point on the circle directly opposite of the original point B. This point is the dilated image of point B.
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Question 32
Small Box Unit Rates:
^
Question Help:
Using Unit Rates for Comparison
A small box of cereal is 14.3 ounces for $4.86.
A large box is 27 ounces for $9.99
Dollars per Ounce
>
Round your answers to the nearest hundredth as needed.
Large Box Unit Rates:
Ounces per Dollar
Video
Dollars per Ounce
The Select an answer is a better buy because it costs Select an answer dollars per ounce.
Ounces per Dollar
The Select an answer is a better buy because you receive Select an answer ounces per dollar.
Options for select an answer are:
-small box
-large box
-more
-less
The numbers that complete the table are Small box: 2.94 and 0.33/ Big box: 3.73 and 0.35.
What are the rates?By using the information provided let's calculate the rates:
Small Box rates:
14.3 ounces for $4.86
14.3/ 4.86 = 2.94 ounces per dollar
4.86 / 14.3 = 0.33 dollars per ounce
Big Box rates:
27 ounces for $9.99
27/ 9.9. = 3.73 ounces per dollar
9.9/ 27= 0.35 dollars per ounce
Based on this, it can be concluded
The small box is better because it cost less dollars per ounce.
The big box is better because you receive more ounces per dollar.
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The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 8. What proportion of children have MDI of at least 80? Choose one answer. A- .3446 B- .6554 C- .0062 D- .9938
The proportion of children with an MDI of at least 80 is approximately 0.0062.
Hence, option (c) is the correct answer.
The proportion of children who have an MDI of at least 80 can be found by using a standard normal table.
Now we will find the z-score for 80, and then find the corresponding cumulative probability.
With mean = 100 and
standard deviation = 8,
we have z = (80 - 100) / 8
=> z = -2.5.
Using a standard normal table,
we find that the cumulative probability for z = -2.5 is approximately 0.0062.
The standard normal distribution table is a collection of regions from the standard normal distribution, sometimes referred to as a bell curve, and it shows the size of the region under the bell curve and to the left of a particular z-score to illustrate probabilities of occurrence in a specific population.
The required standard normal table is attached below:
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46+ (-2k) for k = 3, 23, -2
Answer:
Step-by-step explanation:
for K=3
3.46+(-2K) = 3.46+(-6)= 3.46-6 = 2.54
K=23
3.46+(-2K) = 3.46+(-46)=3.46-46=42.54
k= -2
3.46+(-2K) = 3.46+(4)=7.46
For k = 3: 40.
For k = 23: 0.
For k = -2: 50.
Step-by-step explanation:1. Write the expression.[tex]46+(-2k)\\k=3[/tex]
2. Substitute "k" by the given values and calculate.For k = 3:
[tex]46+(-2(3))=\\ \\46+(-6)=\\ \\46-6=\\ \\40[/tex]
For k = 23:
[tex]46+(-2(23))=\\ \\46+(-46)=\\ \\46-46=\\ \\0[/tex]
For k = -2:
[tex]46+(-2(-2))=\\ \\46+(4)=\\\\50[/tex]
3. Conclude.For k = 3: 40.
For k = 23: 0.
For k = -2: 50.
-------------------------------------------------------------------------------------------------------
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The Leona Vicario school cooperative will deliver to its 96 members this year's profits, which were $5,616. How much will each receive if the division is equitable?
Answer:
$58.50
Step-by-step explanation:
You can solve this problem by dividing the total amount of profits ($5,616), with the amount of members (96), as they are receiving equitable shares.
Divide:
[tex]5616/96 = 58.50[/tex]
Each member will receive $58.50 for their share.
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Answer: Each will receive 58.5 $.
Step by step explanation:
Data :
Partners = 96Earnings = $5616Each one receives = ?We solve: in this problem we have to divide the number of partners with the earnings of that year:
[tex]\bf \: \cfrac{5615}{96} = 58.5[/tex]
Rpt : Each will receive 58.5 $.
assume x and y are two independent binary random variables, and p (x) and p (y ) are given as the followings: X P(X)
0 0.3
1 0.7
Y P(X)
0 0.6
1 0.4
calculated the mutual information
Mutual information=I(x, y)=0
By definition,
Mutual information=I(I(x, y)=
Σ^(X, Y) p( x, y) x log (p(x, y)/p(x)P(y))
due to independence, we can write
:
for all (x ,y) : p(x, y)=p(x) x p(y), plugging this in above, we get
:
Mutual information=I(X ,Y)= Σ^(X, Y) p( x, y) x log (p(x, y)/p(x)P(y))
=Σ^(x ,y)P(x, y)x log(1)=0
so, Mutual Information = I(X,Y) = 0
A binary variable is one with only two possible outcomes. A binary categorical variable is something like sex (male/female) or having a tattoo (yes/no).
By defining a "success" and a "failure," a random variable can be transformed into a binary variable.
For instance, divide age into two categories: less than 35 and 35 or more.
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6 cm
Give your answer in cm².
16 cm
8 cm
יש
11 cm
For instance, to calculate the value in square centimeters for an object with a rectangle shape, multiply the length and width measurements. The formula is 15cm*10cm, which equals 150 cm2 for a measurement of 15cm in length and 10cm in width.
How to convert cm to cm2?A measurement unit known as the square centimeter is best suited for measuring small areas, such as those on drawings. A square with one centimeter on each side is used to define it. The area is measured using this unit. It is abbreviated as sq.cm or cm2.
Here,
To compute the area of a shape in square centimeters, the shape must first be measured before using the proper equation. The form of the object is measured using a metric measuring stick or measuring tape.
For instance, to calculate the value in square centimeters for an object with a rectangle shape, multiply the length and width measurements. The formula is 15cm*10cm, which equals 150 cm2 for a measurement of 15cm in length and 10cm in width.
A square centimeter's dimensions
100 square millimeters make to one square centimeter.
1 square centimeter is 0.15500031 square inches. 10 micrometers square
1 sq cm 0.00107639 square feet.
1 sq cm is 0.00000002 acres.
1 square centimeter is 0.00000001 acre.
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The complete question is "What is the area of below given figure having dimension as 16cm ,11,cm ,6cm and 8 cm ? "
Given the sequence: 7; 1; 7; 3; 7; 5;...
11.1 Determine the value of T17
11.2 Determine the sum of the sum of the sequence from T9 up to and including T13
The sum of the sum of the sequence from T9 up to and including T13 is 504
How can determine a sequence's sum?The sum of an arithmetic sequence is calculated using the formula Sn=n2[2a+(n1)d], where n is the total number of elements to be added. A stands for the first term in the series. The interterm constant is denoted by d.
1. The value of T17
The number series is 7; 1; 7; 3; 7; 5;...
Common deviation (d) = 3 - 1 = 2
A=1 is the first phrase.
Therefore, the nth term is given by t
n =a+(n-1)d
=1 +( 17 -1) 2
=1 + 16 *2
n = 32 +1 = 33
The value of T17 =33.
2. Sn=n2[2a+(n−1)d],
Sn = 13 * 2[2*1+(9−1)2],
26 * 2 + 8 * 2
26 * 18 = 504
The sum of the sum of the sequence from T9 up to and including T13 is 504
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what to put in the 3 boxes and graph also what to write to the question please be literal
If all of the ratios of the variables are equal, then there is a proportional link between the two variables.
Explain the Proportional relationship ?An equation of the type y=kx can be used to model any proportional connection.
Where k is the constant of proportionality.
Given,
Here, there are some missing values in the table of x and y values.
Now that we know that x and y have a proportional connection, we must determine the values that are missing.
Now that we know that x and y have a proportional connection, we must determine the values that are missing.
Therefore, x and y can be expressed as,
y = k x
We must discover the constant k in this case.
When x = 3 and y = 4.5 are applied, the value of k is,
4.5 = k (3) (3)
k= 4.5/3
k = 1.5
Therefore, if we assume that x is 6 then the value of y is,
y = 1.5 x 6
y = 9
Therefore, if we assume that y equals 22.5, the value of x is,
22.5 = 1.5x
22.5/1.5 = x
y = 15.
Hence, the complete table that shows the proportional relationship between x and y is
x y
3 4.5
6 9
15 22.5
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pls help !
A study showed that vitamin A oil reduces pain levels in patients with Lyme disease. During each session, the oil was injected into the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether vitamin A oil also reduces pain in patients suffering from pinched nerves in the cervical region of the back. Two hundred patients aged 20–40 years are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (5 points)
Part B: If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20–40, would you change the study design? If so, how would you modify your design? If not, why not? (5 points)
Part C: Suppose the data in the following table was collected at the end of the study you described in part A.
Vitamin A Oil Placebo
Reported Pain Reduction 37 21
Total Treated 100 100
Construct 90% confidence intervals for the proportion of pain reduction for each treatment group. Show all work. (5 points)
Part D: What can you conclude about the use of vitamin A oil for patients with pinched nerves in the cervical region of the back? (5 points)
The solution is, given below.
What is Treatment?A treatment is something that health care providers do for their patients to control a health problem, lessen its symptoms, or clear it up. Treatments can include medicine, therapy, surgery, or other approaches.
here, we have,
Part A: The appropriate design for the study includes;
Treatment used; Chamomile oil treatment
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
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Read the quotation from Theodore Rhodie, a former Pullman employee. “I do not like to walk up there and hand up my membership in the American Railway Union because when a man asks me to give up my principles, my rights as an American citizen, he might just as well ask for my life.” To which result of the Pullman strike is Theodore Rhodie referring? the loss of money by the Pullman Company the imprisonment of Eugene V. Debs the rehiring of workers who resigned from Debs’s union the increase in anti-union court decisions
In the quotation, Theodore Rhodie is expressing his resistance to the idea of giving up his membership in the ARU, as doing so would mean giving up his principles and rights as an American citizen.
What is Quotation?Using someone else's precise words or statements as part of your writing is known as a direct quotation.
Theodore Rhodie, a former Pullman employee, is referring to the imprisonment of Eugene V. Debs in his quotation. Debs was the leader of the American Railway Union (ARU) and was a prominent figure in the Pullman Strike of 1894. The strike resulted in the shutdown of the nation's rail system, causing widespread economic disruption. In response, the federal government intervened, sending in troops to restore order. Debs was arrested and convicted of violating a federal court injunction against the strike, leading to his imprisonment.
In the quotation, Theodore Rhodie is expressing his resistance to the idea of giving up his membership in the ARU, as doing so would mean giving up his principles and rights as an American citizen. This reflects the sentiment of many workers during the Pullman Strike who felt that their rights were being violated and were willing to stand up for their principles, even if it meant facing consequences such as imprisonment.
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Answer:b
Step-by-step explanation:
m is a random variable that is normally distributed with a mean of 3.05 and a standard deviation of 1.72.
M is a random variable that is normally distributed with a mean of 3.05 and a standard deviation of 1.72, then the probability P(x ≤ 8.5) is 0.99923.
A random variable that is normally distributed with a mean = 3.05
A random variable that is normally distributed with a standard deviation (SD) = 1.72
Now determining the probability
P(x ≤ 8.5) = P[(M - Mean)/SD ≤ (8.5 - 3.05)/1.72
P(x ≤ 8.5) = P(Z ≤ 5.45/1.72)
P(x ≤ 8.5) = P(Z ≤ 3.17)
From the Z-table
P(x ≤ 8.5) = 0.99923
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The complete question is:
M is a random variable that is normally distributed with a mean of 3.05 and a standard deviation of 1.72. Find the probability P(x ≤ 8.5)
What is a disadvantage of using credit cards compared to other forms of
payment?
OA. They cannot be used to build credit.
B. They offer protection from fraud or loss.
C. They may encourage overspending and debt.
D. They don't provide a way to pay for large purchases over time.
SUBMIT
Answer:
C
Step-by-step explanation:
Credit cards can be used even without the money in hand. This can lead to continually swiping your credit card and over time gaining debt due to being unable to pay the monthly payments on the items.
Answer:
Credit Card Disadvantages-Debt

What is a disadvantage of using credit cards compared to other forms of payment?
A disadvantage of using credit cards compared to other forms of payment is that it can lead to high levels of debt if not used responsibly. The ease of spending with a credit card can make it easy to overspend and rack up large balances that can be difficult to pay off. Additionally, credit cards often have higher interest rates than other forms of credit, such as personal loans, so carrying a balance can be costly.
find the equation of a sphere if one of its diameters has endpoints: (-18, -17, 2) and (-2, -1, 18).
The equation of the sphere using the endpoints of the diameter is equal to x² + 20x + y² + 18y + z² - 20z + 269 =0.
Let us consider coordinates of the endpoints of the diameter of a sphere are :
( x₁ , y₁ , z₁ ) = (-18, -17, 2)
( x₂ , y₂ , z₂ ) = (-2, -1, 18)
Let 'd' , 'r' , 'c' represents the diameter , radius , and center of the sphere
d² = ( x₂ - x₁ )² + ( y₂ - y₁ )² + ( z₂ - z₁ )²
⇒ d² = ( -2 + 18 )² + ( -1 + 17 )² + ( 18 - 2 )²
⇒ d² = 256 + 256 + 256
⇒d² = 768
⇒ d = 4√3
Radius 'r' = d/2
= 4√3 /2
= 2√3
center coordinates of the sphere
= [ ( x₁ + x₂) /2 , ( x₁ + x₂) /2 , ( x₁ + x₂) /2]
= [ ( -2 - 18) /2 , (-1 -17 )/2 , ( 18 + 2 )/2 ]
= ( -10 , -9 , 10 )
Equation of the sphere is :
( x -(-10))² + ( y - (-9))² + ( z - 10 )² = r²
⇒( x+ 10 )² + ( y + 9)² + ( z- 10 )² = ( 2√3)²
⇒ x² + 20x + 100 + y² + 18y + 81 + z² - 20z + 100 = 12
⇒ x² + 20x + y² + 18y + z² - 20z +281 - 12 =0
⇒ x² + 20x + y² + 18y + z² - 20z + 269 =0
Therefore, the equation of the sphere with endpoints of the diameter (-18, -17, 2) and (-2, -1, 18) is given by :
x² + 20x + y² + 18y + z² - 20z + 269 =0
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Alexis has 2/3 pounds of grain. If the grain is used to feed 12 chickens, how much grain is there for each chicken? Write an expression to model the problem, and then solve the problem. Show your work.
Input Field 1 of 1
The expression to model the problem is [tex]\frac{2}{3}[/tex] ÷ 12, and the solution is 1/18.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Total fraction of grains Alexis has = 2/3 pounds
Grains used to feed 12 chickens = 2/3
Grains used to feed 1 chicken = (2/3) / 12
= [tex]\frac{2}{3}[/tex] ÷ 12
Using the reciprocal rule,
Grains used to feed 1 chicken = [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{12}[/tex]
= 1/18
Hence the amount of grains for 1 chicken is 1/18.
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> thank you cure 4. Higher Order Thinking Jeff finds some bugs. He finds 10 fewer grasshoppers than crickets. He finds 5 fewer crickets than ladybugs. If Jeff finds 5 grasshoppers, how many ladybugs does Jeff find? How many crickets does he find? Write two equations to solve the problem.23 thank you cards 4. Higher Order Thinking Jeff finds some bugs. He finds 10 fewer grasshoppers than crickets. He finds 5 fewer crickets than ladybugs. If Jeff finds 5 grasshoppers, how many ladybugs does Jeff find? How many crickets does he find? Write two equations to solve the problem.
Answer:
15 crickets
10 ladybugs
Step-by-step explanation:
Let [tex]g[/tex] be the number of grasshoppers Jeff finds.
Let [tex]c[/tex] be the number of crickets Jeff finds.
Let [tex]l[/tex] be the number of ladybugs Jeff finds.
[tex]c=g+10\\c=l-5\\[/tex]
if [tex]g=5[/tex] then sub that into the first equation.
[tex]c=(5)+10\\\\c=15[/tex]
Jeff finds 15 crickets.
[tex]15=l-5\\15-5=l\\l=10[/tex]
Jeff finds 10 crickets.
I need help with a geometry problem
solve this equation 1/3y-12=2/9y.
Answer:
y=108
Step-by-step explanation:
[tex]\frac{1}{3} y-12=\frac{2}{9} y[/tex]
=-12=-1/9y
y=-12times -9=108
PLEASE HELP 20 points
In the blueprint, each square is 1/4 inch.
a. What is actual area of bedroom suite?
b. What is the actual area of the bathroom?
c. It costs $12 per square foot of carpet. How much would it cost to carpet the bedroom and closet?
a. To find the area of the bedroom suite, we need to add the area of the main bedroom and the area of the two square inches. The main bedroom has a length of 7/8 inches and a width of 1/2 + 2(1/4) inches. To find the area, we multiply the length and width:
What does a math area mean?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
(7/8 inches) * (1/2 + 2(1/4) inches) = (7/8 inches) * (1/2 inches + 1/2 inches) = (7/8 inches) * 1 inches = 7/8 square inches
The two square inches have a length and width of 1/4 inches each, so their combined area is:
2 * (1/4 inches)^2 = 2 * 1/16 square inches
Adding the area of the main bedroom and the area of the two square inches, we get:
7/8 square inches + 2 * 1/16 square inches = 7/8 square inches + 1/8 square inches = 15/8 square inches
b. To find the area of the bathroom, we multiply the length and width:
(1/2 inches) * (3/8 inches) = 3/16 square inches
c. To find the cost of carpeting the bedroom and closet, we need to find the combined area of both in square feet, and then multiply by the cost per square foot.
First, we need to convert the measurements of the bedroom and closet from inches to feet. We can do this by dividing each measurement by 12:
Bedroom: (15/8 inches) / 12 = 5/32 feet
Closet: (3/8 inches) / 12 = 1/32 feet
Then we add the area of both:
(5/32 feet) + ( 1/32 feet) = 6/32 square feet
Finally, we multiply by the cost per square foot:
6/32 square feet * $12/square foot = $9/4
So it would cost $9/4 to carpet the bedroom and closet.
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Select the correct answer.
The vertex of a parabola is at (8,-1), and its y-intercept is -17. Which function represents this parabola?
Step-by-step explanation:
simplify the ffratio of 3kota 1to7and 11to4
Answer:
Step-by-step explanation:
f(x)= -1/4(x-8)^2 - 1
