The distribution f(x; 7, 0) is in the two-parameter exponential family, and the binomial distribution arises when θ = 1.
To show that the discrete distribution function f(x; 7, 0) is in the two-parameter exponential family, we need to express it in the form:
f(x; 7, 0) = h(x, 7, 0) * exp{ θT(x) - A(θ) },
where:
h(x, 7, 0) is the base measure,
θ is the natural parameter,
θT(x) is the sufficient statistic,
A(θ) is the log partition function.
Let's start by expressing f(x; 7, 0) in terms of its parameters:
f(x; 7, 0) = c(7, 0) * (7C0)^(1-θ) * (θ^x) * ((1-θ)^(n-x))
We can rewrite this as:
f(x; 7, 0) = [c(7, 0) * (7C0)^(1-θ)] * [θ^x * (1-θ)^(n-x)]
Comparing this with the form of the exponential family, we can identify:
h(x, 7, 0) = 1 (since there is no multiplicative factor dependent on x)
θ = θ (the natural parameter)
θT(x) = x (the sufficient statistic)
A(θ) = -log[c(7, 0) * (7C0)^(1-θ)] (the log partition function)
Now, let's consider the case when θ = 1. When θ = 1, the distribution function becomes:
f(x; 7, 0) = c(7, 0) * (7C0)^0 * (1^x) * (0^(n-x))
Simplifying this, we have:
f(x; 7, 0) = c(7, 0) * 1 * 1 * 0^(n-x) = c(7, 0) * 0^(n-x) = c(7, 0) * 0
In the case where θ = 1, the probability mass function collapses to a constant value (0 in this case), indicating that the binomial distribution occurs.
Hence, when θ = 1, we have:
f(x; 7, 0) = c(7, 0) * 0
This demonstrates that the binomial distribution is a special case of the discrete distribution f(x; 7, 0) when θ = 1.
Overall, the distribution f(x; 7, 0) is in the two-parameter exponential family, and the binomial distribution arises when θ = 1.
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Will mark brainliest for explanation of all parts!!!!!!
A study showed that vitamin E oil reduces pain levels in patients with lupus. 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 E oil also reduces pain in patients suffering from bulging disks in the thoracic 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 E Oil Placebo Reported Pain Reduction 52 35 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 E oil for patients with bulging disks in the thoracic region of the back? (5 points)
Answer:
Step-by-step explanation:
Part A.
An appropriate design for the new study to examine whether vitamin E oil reduces pain in patients suffering from bulging disks in the thoracic region of the back would be a randomized controlled trial (RCT). The study should include the following elements:
1.Treatments: The study should include two treatment groups, one receiving vitamin E oil injections and the other receiving a placebo (e.g. a neutral oil) injections.
2.Method of treatment assignment: Patients should be randomly assigned to either the vitamin E oil treatment group or the placebo group, to control for potential confounding variables.
3.Variables that should be measured: The study should measure the following variables:
-Pain levels: Pain should be measured using a validated self-reported pain scale (such as the Visual Analog Scale or the Numeric Rating Scale) before and after each treatment session.
-Patient's demographics: Age, sex, and medical history should be recorded to evaluate the effect of these factors on the treatment outcome.
-Number of treatments: The number of treatments should be recorded for each patient.
-Adverse effects: Any adverse effects should be recorded, such as redness or swelling at the injection site.
It is important to note that this is a simplified design and a real study would need to consider many other aspects such as sample size, statistical analysis, and ethical considerations.
Part B
If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20-40, I would likely modify the study design. One reason is that age can be a confounding variable and could affect the outcome of the study. Studies have shown that age can affect pain perception and management, older adults have been found to have more chronic pain, and different pain management strategies might be more effective for different age groups.
I would modify the study design by including an age variable in the analysis and stratifying the sample by age, creating two subgroups (young and old patients) and comparing the results separately. This would allow us to see if there is any age-related differences in the effectiveness of vitamin E oil in reducing pain in patients suffering from bulging disks in the thoracic region of the back.
Another modification would be to include a larger sample size to ensure that there are enough patients in each subgroup to detect any potential differences in the effect of vitamin E oil on pain reduction between young and old patients.
It is important to note that this is a simplified design and a real study would need to consider many other aspects such as sample size, statistical analysis, and ethical considerations.
Part C
To construct 90% confidence intervals for the proportion of pain reduction for each treatment group, we can use the following steps:
1.Calculate the sample proportion of pain reduction for each treatment group:
For the Vitamin E oil group, the proportion of pain reduction = (52 / 100) = 0.52
For the Placebo group, the proportion of pain reduction = (35 / 100) = 0.35
2.Calculate the standard error (SE) for each proportion:
SE = sqrt( (p * (1-p)) / n )
Where p is the sample proportion and n is the sample size.
For the Vitamin E oil group, SE = sqrt( (0.52 * (1-0.52)) / 100) = 0.049
For the Placebo group, SE = sqrt( (0.35 * (1-0.35)) / 100) = 0.045
3.Calculate the margin of error (ME) for each proportion:
ME = z * SE
Where z is the critical value for a 90% confidence level, which is approximately 1.645.
For the Vitamin E oil group, ME = 1.645 * 0.049 = 0.0806
For the Placebo group, ME = 1.645 * 0.045 = 0.0743
4. Calculate the lower and upper bounds of the 90% confidence intervals for each proportion:
Lower bound = p - ME
Upper bound = p + ME
For the Vitamin E oil group, the 90% confidence interval is:
0.52 - 0.0806 = 0.4394 and 0.52 + 0.0806 = 0.6006
For the Placebo group, the 90% confidence interval is:
0.35 - 0.0743 = 0.2757 and 0.35 + 0.0743 = 0.4243
Therefore, the 90% confidence interval for the proportion of pain reduction for the Vitamin E oil group is (0.4394, 0.6006) and the 90% confidence interval for the proportion of pain reduction for the Placebo group is (0.2757, 0.4243)
What is the value of x? responses x = 4. 8 cm x, = 4. 8 cm x = 30 cm x, = 30 cm x = 93 cm x, = 93 cm x = 187. 5 cm x , = 187. 5 cm two segments c d and segment a b intersect at point e to form two triangles c a e and d b e. Angle c is congruent to angle d. B e is 30 centimeters. D e is 12 centimeters. A e is 75 centimeters. C e is x.
Therefore, when two segments c, d, and a, b, cross at point e to form two triangles, the value of x is 30 cm.
what is triangle ?Triangles are shapes with three sides and three vertices, making them polygons. It is one of geometry's fundamental forms. A triangle containing vertices A, B, and C is known as a triangle ABC. In Euclidean geometry, a singular plane and triangle are discovered when the three points are not collinear. A polygon with three sides and three corners is called a triangle. The corners of the triangle are the points where the three sides meet one another end to end. The sum of the angles in a triangle is 180 degrees.
given
From the diagram shown, the following equation is true:
x/75 = 12/30
Cross multiply
30x = 12 * 75
30x = 900
Divide both sides by 30
30x/30 = 900/30
x = 30
Therefore, when two segments c, d, and a, b, cross at point e to form two triangles, the value of x is 30 cm.
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a package of 6 pairs of insulated costs $40.74 . What is the unit price of the pairs of ?
Answer: 6.79
Step-by-step explanation: divide them
determine if the triangles are similar
1. yes by AA
2. yes by SAS
3. yes by SSS
4. no not similar
The triangles Illustrated are not similar. The correct option is 4. no not similar
How to illustrate the information?If two pairs of corresponding angles in two triangles are congruent, then the triangles are similar. All three corresponding sides of the acronym SSS (side-side-side) are congruent. SAS (side-angle-side) (side-angle-side) Congruence exists between two sides and their angle.
The triangles are congruent if all three sets of corresponding sides are present. The side-side-side shortcut is a congruence technique (SSS). Side-angle-side (SAS), which uses two pairs of sides and an angle between them that is known to be congruent, is another shortcut.
In this case, they aren't similar. The correct option is 4.
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Is △pmr similar to △smn? if so, which postulate or theorem proves these two triangles are similar? responses △pmr is similar to △smn by the ssa similarity theorem. , triangle p m r, , , , , is similar to , , , , triangle s m n, , , , , , by the , , , , , , , s s a similarity theorem, , , . △pmr is similar to △smn by the sas similarity theorem. , , triangle p m r, , , , , is similar to , , , , triangle s m n, , , , , by the , , , , , , s a s theorem, , . △pmr is similar to △smn by the sss similarity theorem. , triangle p m r, , , , , is similar to , , , , , , triangle s m n, , , , , by the, , , , , , s s s similarity theorem, , , . △pmr is not similar to△smn. , , triangle p m r, , , , , is not similar to, , , , triangle s m n, , , , . a triangle with vertices p m r. segment s n is inside the triangle. point s is on side p m. point n is on side m r. p s is equal to 8 feet. s m is equal to 14 feet. m n is equal to 21 feet. n r is equal to 12 feet.
Right angles, isosceles triangles, acute angles, obtuse triangles, scalene triangles, and equilateral triangles are some of the several types of triangles.
Describe the triangles.The term "trigon" is frequently (though not usually) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, of which some might be the same. Three points and three sides make up a triangle, which is a polygon. The three angles of the triangle sum up to 180 degrees. With three sides & three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.
Here ,
are a number of triangles.
Triangular Scalene. a triangle that doesn't have adjacent sides.
a triangle where each of a three angles is far less than 90° degrees is referred to as a sharp triangle.
Straight triangle a triangular including one angle that extends beyond 90 degrees.
Isosceles, right, and equilateral triangles are examples of triangles.
Right angles, isosceles triangles, acute triangular, obtuse triangles, scalene triangles, and equilateral triangles are some of the several types of triangles.
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Malik learned to sing a total of 36 pieces over the course of 18 weeks of voice lessons. How many weeks of lessons will Malik need before he will be able to sing a total of 48 pieces? Solve using unit rates.
The number of weeks it would take is 24 weeks.
How many weeks would it take?The first step is to determine how many weeks it would take to learn one piece. In order to determine his value, divide 18 by 36.
Number of weeks = 18 / 36 = 0.50
Now, multiply the answers gotten in thee previous step by 48
Number of weeks it would take to learn 48 songs = 0.50 x 48 = 24
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A car producer stocks three types of tires: a, b, and c. Let p(a) = 0. 40, p(b) = 0. 15 and p(c) = 0. 45. The percentage of defective tires is 2%, 1% and 5%, respectively. Someone picks a tire off the shelf at random and it is brand a. If you want to know the probability that it is a defective tire (event d), which formula would you use?.
The formula which we would use to know the probability that it is a defective tire of brand A is P(A|D) = P(D|A)P(A) / P(D). P(D) is the probability that a tire produced is defective.
What is probability?Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.
A car producer stocks three types of tires. They are A, B, and C.
P(A) = 0.40P(B) = 0.15P(C) = 0.45The percentage of defective tires is 2%, 1% and 5%, respectively. Someone picks a tire randomly and he gets brand A.
Find the formula to know the probability that it is a defective tire!
The options are
a) P(A|D) = P(D|A)P(A) / P(D)
b) P(D|A) = P(A|D)P(D) / P(A)
c) P(A|D)= P(D/A)P(D) / P(A)
d) P(D|A)= P(A|D)P(A) / P(D)
From the information, we get:
P(D|A) = 2% = 0.02P(D|B) = 1% = 0.01P(D|C) = 5% = 0.05The probability that it is a defective tire of brand A = P(A|D). The formula is
P(A|D) = P(A∩D) / P(D)
P(A|D) = P(D|A)P(A) / P(D)
Hence, if we want to know the probability that it is a defective tire, the formula would be P(A|D)= P(D|A)P(A) / P(D).
The answer is (a).
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Write in radical form. Do not simplify.
11x^1/4
The radical form of the given exponential form of a number 11x^(1/4) is written as ( 11 ) × [tex]\sqrt[4]{x}[/tex].
As given in the question ,
Given exponential form is equal to :
11x^(1/4)
Using th formula to convert exponential form into radical form in standard form we have :
( y )^ ( a / b ) = [tex]\sqrt[b]{y^{a} }[/tex]
Here y is equal to x
a is equal to 1
b is equal to 4
Substitute the value of the given expressions in the formula we have,
11x^(1/4)
= ( 11 ) × [x^(1/4) ]
= ( 11 ) × [tex]\sqrt[4]{x^{1} }[/tex]
Any thing raise to one is the number or variable itself the required radical form is equal to:
= ( 11 ) × [tex]\sqrt[4]{x}[/tex]
Therefore, the radical form of the given expression 11x^(1/4) is given by :
( 11 ) × [tex]\sqrt[4]{x}[/tex].
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Evaluate $\frac 23+\frac 34+\frac 42$. If a fraction appears in your answer, it should be in simplified form.
When evaluated [tex]\frac 23+\frac 34+\frac 42$[/tex] into simplified form we get [tex]3\frac{5}{12}[/tex] as the answer.
What is simplified form?If the top and bottom have no common factors other than one, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and remain whole numbers.
You may also hear "lowest terms" when referring to the simplest form.
The fraction 4/5, for example, is in its simplest form. Except for 1, there is no number that divides both 4 and 5.
To evaluate in simplified form
[tex]$\frac 23+\frac 34+\frac 42$[/tex]
Lets simplify!
[tex]$ \Rightarrow \frac 23+\frac 34+\frac 42$[/tex]
[tex]$ \Rightarrow \frac{8}{12} + \frac{9}{12} +\frac{24}{12}[/tex]
[tex]$ \Rightarrow \frac{8+9+24}{12}[/tex]
[tex]$ \Rightarrow \frac{41}{12} = 3\frac{5}{12}[/tex]
Thus, when evaluated [tex]\frac 23+\frac 34+\frac 42$[/tex] into simplified form we get [tex]3\frac{5}{12}[/tex] as the answer.
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enge A family wants to rent a car to go on vacation. Company A charges $45.50 and 10¢ per mile. Company B es $55.50 and 12¢ per mile. How much more does Company B charge for x miles than Company A?
Answer: company B charges $10 and 2 cents more
Step-by-step explanation:
What is equation simple?
An equation in algebra is a mathematical statement that proves the equality of two mathematical expressions.
what is equations ?An equation in algebra is a mathematical statement that proves the equality of two mathematical expressions. Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations. In a mathematical expression known as an equation, the equals sign appears. Algebra is used in a variety of equations. When you don't know how much to compute in math, you use algebra to approximate the answer.
given
Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal."
The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations.
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If f(x)=3x, g(x)=x+4 , and h(x)=x2−1 , find g[h(−3)]
On solving the provided question, we can say that value for the function g[h(−3)] is 12.
What is a function?A mathematical function is a rule that determines the value of the dependent variable based on the values of the independent variables. A table, a formula, or a graph are just a few examples of how a function might be expressed.
In mathematics, a function is an expression, rule, or law that establishes the relationship between independent and dependent variables.
For equation h(x)
x = -3
then h(-3) = x²-1
h(-3) = (-3)² -1
h(-3) = 9-1 = 8 now using this value in g(x)
g(x) = x+ 4
g(8) = 8+ 4 = 12
Hence the value for the function is g[h(−3)] = 12
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What is the solution to the system of equations y 1.5 x 4 y =- 4?
The solution to the given equations y = 1.5x - 4, y = -4 is (0, -4).
We can solve the given system of equations by the substitution method.
The substitution method is the algebraic approach to solving simultaneous linear equations. As the word tells, in this method, the value of one variable from one equation is substituted in the other equation and gets the value of the one variable.
y = 1.5x - 4 eqn(1)
y = -4 eqn(2)
Put the value of y in eqn(2)
- 4 = 1.5x - 4
Solve the above equation for x, by transferring the terms,
1.5x = - 4 + 4
1.5x = 0
x = 0
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In an aquarium, there are large fish and small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
The probability that it is a large, blue fish is 21%.
What is probability?Probability is the mathematical study of outcomes in uncertain situation. It is used to describe the likhood of an event occurring and it can be expressed as a number between 0 to 1. Probability is used to quantify the uncertainty associated with any given event it helps us understand how likely it is that something will happen and it can be used to make prediction about futures even probability theory is it cornerstone of modern statistic and is widely used in field such as finance economics and science.
Here we have to use the definition of a simple probability, wherever all fishes has the same Probability to be chose.
So, we have to divided the possible of outcomes with the total of outcomes. The possible outcomes refer to the number of large-blue fishes, and the totals numbers of outcomes represent the total number of fishes. So
Therfore, there's 21% of chances to selected one fish randomly and be a large, blue fish.
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13 Y 5 Raj is the finance manager for the tea company. He produces the table below to show the different costs of running the company for the last year. Type of spend Wages Premises Materials Miscellaneous Total Amount (£) 331 560 10600 15400 10840 368400 The company owner asks Raj for more information about the proportion spent on wages. What fraction of the total amount was spent on wages last year? Raj needs the answer in its simplest form
The operational costs a business bears in order to make money are referred to as expenses.
What Is an Expense?Simply put, it is the amount of money necessary to acquire anything. "It costs money to make money," as the saying goes.Paying suppliers, paying employees' wages, leasing factories, and depreciating equipment are all common costs. The Internal Revenue Service (IRS) maintains rigorous guidelines on which expenses firms are allowed to claim as a deduction. Businesses are permitted to deduct tax-deductible expenses on their income tax returns to reduce their taxable income and hence their tax burden.The operating costs incurred by a business in order to produce revenue are referred to as expenses.As long as a business complies with IRS regulations, it is allowed to deduct certain expenses from its taxable income.Using either the cash basis or the accrual basis, accountants keep track of their spending.The two primary types of business expenses in accounting are operating expenses and non-operating expenses.Compared to the majority of other business expenses, capital expenses are treated differently by the IRS.The Complete Question is expenses.
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How do you write 4 exponents?
The four main types of Exponents that can be written are Positive Exponents , Negative Exponents , Zero Exponents and Rational Exponents .
What are Exponents ?
The Exponents are defined as a method to express large numbers in terms of powers which means, that exponent refers to how many times the number is multiplied by itself.
The Four Main types of Exponents are listed below :
(i) Positive Exponents : The Positive exponents tell us about how many times we multiply the base by itself. The result of the positive exponent is generally a very large number. For Example : [tex]x^{82} , x^{9}[/tex] .
(ii) Negative Exponent : The Negative exponents tell us about how many times to divide the base by itself. The result of the negative exponent is generally a very small number. For Example : [tex]x^{-82} , x^{-9}[/tex] .
(iii) Zero Exponent : The Zero Exponent is the expression in which the power is 0 , and the result of the zero exponent is always 1 . For Example : [tex]x^{0}=1[/tex] .
(iv) Rational Exponent : The Rational Exponent means that there is a fraction present in the exponent. For Example : [tex]x^{\frac{1}{2} } ,y^{\frac{2}{3} }[/tex] .
The given question is incomplete , the complete question is
How do you write the 4 types of Exponents ?
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235.20= 7(0.06m +25.80 +0.10(25.80))
By solving the given expression we get the value of M is 87.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
7(0.06m+ 25.80 +0.10 (25.80))
7(0.06m+ 25.80 + 2.58)
7(0.06m+ 28.38)
7(0.06m+ 28.38)
7 0.06m+ 7·28.38
0.42m+ 198.66
In this case, we need to get the value for m
235.20=0.42m+ 198.66
If we place the m value of 87,
=0.42×87+198.66
= 235.20
When an equation is solved symbolically, expressions can be employed to represent the solutions.
For example, the phrase x = y + 1 solves the equation x + y = 2x – 1 for the unknown x, since substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, which is a true assertion.
Therefore, the value of M is 87.
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HELP ME I DONT UNDERSTAND
In the system of linear equations given, only option b have exactly one solution
What is System of Linear EquationA system of linear equations is a collection of two or more linear equations that are solved simultaneously. A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are real numbers and a is not equal to 0.
In this given problem, we have four system of linear equations and we need to determine which has exactly one solution.
a)
2x - 4y = 8 ...eq(i)
x + y = 7 ...eq(ii)
Solving both equations
x = 6, y = 1
b)
3x + y = - 1 ..eq(i)
8x + 2y = -2 ..eq(ii)
Solving both equations
x = 0, y = - 1
c)
3x + 3y = 3 ...eq(i)
-6x - 6y = 3 ...eq(ii)
Solving both equations;
There's no solution to this problem.
d)
3x - 2y = 4 ..eq(i)
-3x + 2y = 4 ..eq(ii)
Solving for both equations;
There's no solution to this problem
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What are the main types of inequalities Class 6?
Some types of inequalities that are commonly discussed include economic inequality, educational inequality, social inequality and, racial and ethnic inequality.
Economic inequality: This refers to the unequal distribution of wealth, income, and resources among individuals or groups within a society. It often results in a small group of individuals or families owning a disproportionate amount of wealth and controlling the majority of resources.
Educational inequality: This refers to the unequal access to quality education among individuals or groups within a society. It can result in a lack of educational opportunities for those from lower socio-economic backgrounds, which can limit their chances for higher-paying jobs and career advancement.
Healthcare inequality: This refers to the unequal access to quality healthcare among individuals or groups within a society. It can result in poorer health outcomes and increased health disparities for those from lower socio-economic backgrounds.
Social inequality: This refers to the unequal distribution of social status, power, and privilege among individuals or groups within a society. It can result in discrimination, prejudice and bias against certain groups, leading to reduced opportunities and access to resources.
Racial and Ethnic inequality: This refers to the unequal distribution of resources and opportunities among individuals or groups based on their race or ethnicity. It can result in discrimination and racism, leading to reduced opportunities and access to resources.
It's important to note that these types of inequalities often overlap and interact with one another, creating complex and interconnected forms of disadvantage.
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The prism below has dimensions of 2 feet (ft.), 3 feet (ft.), and 8 inches (in.).
What is the volume of the prism in cubic inches?
The volume of the prism in cubic inches is 6912 inch³.
What is Volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Volume of Cuboid = length x width x height
Given:
length = 3 feet = 36 inch
width = 8 inch
height = 2 feet = 24 inch
So, Volume of cubic prism
= length x width x height
= 36 x 8 x 24
= 6912 inch³
Hence, the volume is 6912 inch³
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{y = -4x - 6
{-4x - y - 6 = 0
y = -4x - 6 and -4x - y - 6 = 0 are both representations of the same linear equation.
The first equation, y = -4x - 6, is in slope-intercept form, where y is the dependent variable, x is the independent variable, -4 is the slope and -6 is the y-intercept. This means that when you graph this equation, the slope of the line will be -4 and the y-intercept will be -6.
The second equation, -4x - y - 6 = 0, is in standard form, where the variables are on one side of the equation and the constants are on the other side. To get this equation, you can move the y term to the other side by adding y to both sides, and then move the constants to the other side by adding 6 to both sides.
Both equations represent the same line. They are just in different forms, one is in slope-intercept form and the other is in standard form.
Answer:
infinite number of solutions
Step-by-step explanation:
y = - 4x - 6 → (1)
- 4x - y - 6 = 0 → (2)
substitute y = - 4x - 6 into (2)
- 4x - (- 4x - 6) - 6 = 0 ← distribute parenthesis and simplify left side
- 4x + 4x + 6 - 6 = 0
0 = 0 ← true statement
when both sides have the same numeric value
this indicates the system has an infinite number of solutions.
The principal wants to share 1,869 pencils equally between 4 fourth grade classrooms and 3 third grade classrooms. how many pencils will each classroom get?
Kala is driving on the highway. She begins the trip with 16 gallons of gas in her car. The car uses up one gallon of gas every 20 miles.
Let G represent the number of gallons of gas she has left in her tank, and let D represent the total distance (in miles) she has traveled. Write an equation relating G to D, and then graph your equation using the axes below.
Answer: G = 15-D/20
Step-by-step explanation:
Using the variables given,
G = 15 - D/20
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
The following equations will have the same value of x as the one provided: 18x - 9 = 72.= 4.5
What are Equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
A statement is not an equation if it has no "equal to" sign.
According to our question-
3/5(30x-15)=72
18x - 9 = 72
4.5
Hence, The following equations will have the same value of x as the one provided: 18x - 9 = 72.= 4.5
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How do you find the area of a triangle with 3 unequal sides?
To find the area of a triangle with 3 unequal sides, you can use Heron's Formula.
This formula states that the area of a triangle (A) is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.
1. Calculate the perimeter of the triangle by adding together the lengths of all three sides.
2. Divide the perimeter by two to find s.
3. Plug in the lengths of the three sides and the value of s into Heron's Formula to calculate the area of the triangle.
A = √s(s-a)(s-b)(s-c)
To find the area of a triangle with 3 unequal sides, you can use Heron's Formula which states that the area of a triangle (A) is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.
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hi everyone help my math show your complete solutions
Step-by-step explanation:
what is the area of the whole circle ?
pi×r²
what is the segment length of the whole circle ?
right, that is the circumference :
2×pi×r
and a whole circle stand for 360°.
if we have only a part of these 360°, then all the attributes of the circle apply only to the corresponding fraction of 360°.
the "segment area" is (I assume) the shaded area.
that is the area of the whole segment XZY minus the triangle area.
let's start with the arc length (the easier part) :
again, for 360° it is
2×pi×r
for 135° it is
2×pi×r × 135/360 = 2×pi×8 × 135/360 =
= 18.84955592... cm
for the segment area :
the area of the full segment is
pi×r² = pi×8² = 64pi
for 135° it is
64pi × 135/360 = 75.39822369... cm²
the inner triangle is an isoceles triangle (both legs are equally long : 8 cm).
when we have the 2 legs and the encoded angle, the area of the triangle is
area= (a x b x sin(c))/2, where a, b are the two legs, and c is the angle between them.
area of the triangle = 8×8×sin(135)/2 = 22.627417... cm²
the shaded area is then
75.39822369... - 22.627417... = 52.77080669... cm²
Sarah dilutes grape juice for her two-year-old sister. She uses 1/4 cup of grape juice for every 2/3 cup of water.
How much grape juice does Sarah use for each cup of water?
A 1/6 cup
B 3/4 cup
C 3/8 cup
D 1 1/2 cup
Answer:
3/8 cup
Step-by-step explanation:
1 cup water = 2/3 cup water * 3/2
x = 1/4 cup grape juice * 3/2
1/4 * 3/2 = 3/8
find a positive and a negative co-terminal of each angle 111 degrees
The Positive co-terminal angle is 471° and negative co-terminal angle is -249°.
What is co-terminal angle?Co-terminal angles have different degrees, but they all have their initial side on the positive x -axis (it goes this way →) and share the same terminal side hence the term "co-terminal." Co-terminal angles differ by 360°. Therefore, we only need to add/subtract 360° to get our positive/negative co-terminal angle measures.
Here the given angle is ,
=> 111°
Positive co-terminal angle:
=> 111°+360°=471°
Now negative co-terminal angle is ,
=> -(360°-111°)
=> - 249°
Hence the Positive co-terminal angle is 471° and negative co-terminal angle is -249°.
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Find the median, Q1, Q3, interquartile range (IQR), and list any outliers. 1. 72, 32, 74, 66, 71, 45, 38, 49, 66, 69, 75, 34, 102 Median: Q3: QI: IQR:
Answer:
Step-by-step explanation:
Idl
What is an expression that can be use to multiply 6 x 198 mentally?
Answer:
paper and pencil
Step-by-step explanation:
get a paper then a pencil and solve it
-6 × 2 + 6 × 200.
Hope this helps! :D - your friendly neighborhood Jxro!