The estimated difference of 3 1/2 and 1 1/3 is 2 1/6.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Are two fractions 3 1/2 and 1 1/3.
Now, The difference between 3 1/2 and 1 1/3 would be,
1/2 - 1/3 is 1/6 and 3 - 1 is 2,
So, The estimated 3 1/2 -1 1/3 is 2 1/6.
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In Exercises 21 and 22 , determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 21. [ 2 4 3 6 h 7]
22. [ 1 5 −3 h −2 −7]
The original matrix [ 1 5 −3 h −2 −7] and [ 2 4 3 6 h 7] is the augmented matrix of a consistent linear system, regardless of the value of h.
The augmented matrix of a consistent linear system, we need to perform row operations and transform it into an echelon form or a reduced row echelon form. In this form, we can easily read the system of linear equations and determine its consistency.
Let's apply some row operations to the given matrix. We can start by dividing the first row by 2 to obtain a leading 1 in the first column:
[ 1 2 3/2 3 h/2 7/2]
Next, we can subtract twice the first row from the second row to get a zero in the first column of the second row:
[ 1 2 3/2 3 h/2 7/2]
[ 0 1 -3/2 0 h/2 -5/2]
Now, we can subtract 3/2 times the second row from the third row to get a zero in the first column of the third row:
[ 1 2 3/2 3 h/2 7/2]
[ 0 1 -3/2 0 h/2 -5/2]
[ 0 0 9/2 3 -3h/4 13/4]
At this point, the matrix is in echelon form, and we can read the system of linear equations:
x + 2y + (3/2)z = 3
y - (3/2)z + (h/2)w = -5/2
(9/2)z + 3w - (3h/4)v = 13/4
Therefore, the original matrix [ 2 4 3 6 h 7] is the augmented matrix of a consistent linear system, regardless of the value of h.
Exercise 22 follows a similar procedure. The matrix is [ 1 5 −3 h −2 −7], and we can apply row operations to transform it into echelon form:
[ 1 5 -3 h -2 -7]
[ 0 1 -1/5 h/5 4/5 -3/5]
[ 0 0 -6/5 (h²)/5 -38/25 22/25]
The resulting system of linear equations is:
x + 5y - 3z + hw - 2v = -7
y - (1/5)z + (h/5)w + (4/5)v = -3/5
(-6/5)z + (h²)/5w - (38/25)v = 22/25
We see that the last row has no zeros, except for the rightmost column, so the system is consistent for any value of h
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find the number of ordered triples (a,b,c) where a , b , and c are positive integers, a is a factor of b , a is a factor of c , and a b c
The number of ordered triples (a, b, c) where a, b, and c are positive integers and a is a factor of b, a is a factor of c, and abc=N, is 64.
To find the ordered triplets, Firstly Factorize N into its prime factors.For each prime factor. we can choose its exponent as the value of a, b, and c. The total number of ordered triples (a, b, c) is (number of exponents + 1)^3.
let N = 24. The prime factorization of 24 is 2^3 * 3^1.
The number of possible values of a is 4 (from 0 to 3), so the number of possible values of b and c is also 4.
The number of ordered triples is 4^3 = 64.
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According to the Quotient Remainder Theorem, for every integer n and positive integer d, there exist integers q and r such that n=dq+r, 0≤r
Let n be your 8-digit student identification number (ID) and let d
be the leftmost three digits of your student ID. For example, if your student ID was 12034567 , then n=12,034,567 and d=120. Find q and r as required by the Quotient Remainder Theorem using n and d constructed from your student ID.
Divide the 8-digit student ID by the leftmost 3 digits to find q and r using the Quotient Remainder Theorem. If your 8-digit student ID is 12345678, then d = 123, n = 45,678, q = 371, and r = 45.
Suppose your 8-digit understudy ID is 12345678. Then, at that point, we can take the furthest left three digits to get d = 123. Also, we can take the excess 5 digits to get n = 45,678.
To find q and r, we can utilize the condition n = dq + r and address for q and r.
To begin with, we really want to see as the biggest various of d that is not exactly or equivalent to n. We can do this by separating n by d and taking the floor of the outcome:
q = ⌊n/d⌋ = ⌊45,678/123⌋ = 371
Then, we can track down the rest of taking away the result of d and q from n:
r = n - dq = 45,678 - 123 × 371 = 45,678 - 45,633 = 45
Along these lines, in the event that your 8-digit understudy ID is 12345678, d = 123, n = 45,678, q = 371, and r = 45.
The Remainder Leftover portion Hypothesis expresses that for any whole number n and positive whole number d, there exist whole numbers q and r with the end goal that n=dq+r, where q is the remainder and r is the rest of. We can track down q and r by separating n by d and taking the floor of the outcome for q, and deducting the result of d and q from n for r.
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Country Day's scholarship fund receives a gift of $ 165000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 5.2 % interest, and stocks pay 7 % interest. Country day invests $ 75000 more in bonds than in CDs. If the annual income from the investments is $ 9442.5 , how much was invested in each vehicle?
Invested in each vehicle is $40,000 if the annual investment income is $944.25.
What is meant by interest?The sum that must be repaid for a loan or the sum that is collected in exchange for a loan is known as interest. Principal is the term used to describe borrowed or lent funds. The total of the principal plus interest is referred to as the Amount. Rate of Interest refers to the amount at which interest is calculated on the principal. A percentage of the principle is how interest is most commonly computed. For instance, if you agreed to borrow $100 from a friend with 5% interest and repay it over time, the interest you would have to pay would simply be 5% of $100, or $5.Let
CD's = x
Bonds = x + 60000
Stocks = y
x + x + 60000 + y = 140000 ----> 2x + y = 80000 .......(1)
Using I = Prt; t = 1; I = Pr
2x + 3.7(x + 60000) + 11.1y = 7800(100× ) × Since I used an exact proportion, the opposite side needs to be multiplied by 100.
5.7x + 11.1y = 558000 .......(2)
Either elimination or substitution;
x = 20000 y = 40000
So CD's = 20000, Bonds = 80000, Stocks = 40000
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if PQRS is a parallelogram find the value for x and y
3y
7x+5
x+29
8y-35
Diagonals of a parallelogram bisect each other.
[tex]x+29=7x+5 \implies x=4 \\ \\ 3y=8y-35 \implies y=7[/tex]
True or false? It's possible to create a regular tessellation with a regular heptagon
.
Answer:
False.
Step-by-step explanation:
It is not possible to create a regular tessellation with a regular heptagon. A regular tessellation refers to a pattern of repeating shapes that completely covers a flat surface without any gaps or overlaps. The only regular polygon shapes that can form regular tessellations are the equilateral triangle, square, and hexagon. Regular heptagons do not have the symmetry necessary to form a repeating pattern that covers a flat surface without gaps or overlaps.
Determine the values of c so that the following functions represent joint probability distributions of the random variables X and Y : f(x, y) = c|x − y|, for x = −2, 0, 2; y = −2, 3.
The value of c is 1/15
What is a joint probability distribution in statistics?Joint probability is a statistical measure that calculates the likelihood of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs.
To be valid probability functions, the sum of changes across the entire range of x and y variables must equal one
b) In this case, the joint probability could be represented as follows:
x = -2 x = 0 x = 2
y = -2 0 2c 4c
y = 3 5c 3c c
As a consequence, the total likelihood in this case is:
=> c(2 + 4 + 5 + 3 + 1) = 15c
=> 15c = 1
c = 1/15
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Laura deposits $3000 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 5 years?
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The amount of interest that Laura will be paid in the first 5 years is $600.
How much interest will Laura be paid in the first 5 years?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that;
Principal P = $3,000Interest rate r = 4% = 4/100 = 0.04Elapsed time t = 5 yearsInterest I = ?Plug the given values into the above formula and solve for interest I.
I = P × r × t
I = $3,000 × 0.04 × 5
I = $3,000 × 0.2
I = $600
Therefore, the amount of interest payable is $600.
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Newjet, Inc. manufactures inkjet printers and laser printers. The company has the capacity to make 70 printers per day, and it has 120 hours of labor per day available. It takes 1 hour to make an inkjet printer and 3 hours to make a laser printer. The profits are $50 per inkjet printer and $80 per laser printer. Find the number of each type of printer that should be made to give maximum profit, and find the maximum profit.
inkjet-
laser printers-
Maximum profit
A drum of oil contains 55 gal and costs $164.80. What is the cost per quart?
The solution is, $1.33, is the cost per quart.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
A drum of oil contains 55 gal and costs $164.80.
now, we know , 1 gal = 4 quart
so, 55 gal =55 * 4
= 220 quart
now, the cost per quart= 220/164.80
=$1.33
Hence, The solution is, $1.33, is the cost per quart.
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Which of the following is the best definition of a unit rate? * 1 point A.) A ratio of something in comparison to another. B.) A ratio of something per the total amount. C.) How much something goes up or down by. D.) How much of something per 1 unit of something else.
The best definition of the unit rate is how much of something per 1 unit of something else. Hence option D is the correct answer
Unit rate is basically a ratio and it compares something with 1 unit of some other quantity. So they are used for comparing two different things and if we talk about unit rate then the denominator is always 1 or the other value is always 1
So if we talk about an example of unit rate and if we specifically talk about speed, then we say kilometer per hour
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Evaluate xy + 2x if x = 7 and y =5
Answer:
Step-by-step explanation:
35 + 2x
Answer:
xy+2x
x=7
y=5
input the value of x and y in the equation.
7×5+(2×7)
=35+14
=49
Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution using Class Boundaries. Use 5 classes and the minimum data value for the lowest class limit. Then create a histogram and describe the shape of the distribution. 92 92 93 90 92 99 97 90 93 91 82 85 87 83 89 82 89 87 75 70 73 76 60 61 55 X quantitatve variable(s), the correct graph to make a) Since data were collected for 2 v is a histogram b) The class width is: class width = 9 Complete the frequency/relative frequency table using the given class width. Round relative frequencies to 3 decimal places. Class Boundaries Frequency Relative Frequency 54.5 - 63.5 72.5 olan 81.5 90.5
The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.
The class width, also known as the class interval, is the difference between the upper and lower boundaries of a class. In this frequency distribution, the class width is 9 since the lower boundary of the first class is 54.5 and the upper boundary of the last class is 90.5. We can calculate the frequency of each class by counting how many numbers fall within the class boundaries. For example, the first class has 72 observations since there are 72 numbers that fall between 54.5 and 63.5. To calculate the relative frequency of each class, we divide the frequency of each class by the total frequency. For example, the relative frequency of the first class is 0.312 since 72/231 = 0.312. Once the frequencies and relative frequencies have been calculated, a histogram can be made to represent the data. The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.
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after a long series of calls to fib(k1), fib(k2),. . . fib(km), with k1, k2, . . . km being random values between 0 and maxmemo, what will be the big-o for the expected work performed by a call to fib(n) (where n < maxmemo)?
The big-o for the expected work performed by a call to fib(n) (where n < maxmemo) will be constant.
If the function is implemented with memoization, i.e., storing the results of previously calculated Fibonacci numbers to avoid redundant calculations, the expected work performed by a call to fib(n) would be O(1) for n < maxmemo, regardless of the number of previous calls made to fib.
This is because if the function has already calculated fib(n) earlier, it can simply look up the result in the memoized dictionary and return the stored value without performing any additional calculations. Otherwise, it would calculate fib(n) once and store the result in the memoized dictionary for future lookups.
Therefore, the expected work performed by a call to fib(n) is constant, O(1), as long as the previously calculated Fibonacci numbers are stored in memory using memoization. The number of previous calls made to fib has no impact on the expected work performed by a call to fib(n) as long as n is less than maxmemo.
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Suppose that $2000 is invested at a rate of 5.3%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 9 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
Rounding to the nearest cent, the total amount after 9 years is $3182.67.
Step-by-step explanation:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, P = 2000, r = 0.053, n = 2 (compounded semiannually), and t = 9.
Plugging in these values, we get:
A = 2000(1 + 0.053/2)^(2*9)
= 2000(1.0265)^18
≈ 3182.67
Rounding to the nearest cent, the total amount after 9 years is $3182.67.
samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. the result is120 grams 15% sugar syrup. how many grams of 25% sugar syrup did samantha use?
Answer:
Final mixture is 120 gm
x = 10% then (120-x) = 25%
.25(120-x) + .1 (x) = .15 (120) solve for x= 10% amount
then 25% amount = 120-x
Step-by-step explanation:
Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.) x = 22 - ++ 9, y = t3 - 3 Horizontal tangents (x,) - (L smaller x-value (x,y) - ( larger x-value Vertical tangent (x, y) - (O .) Need Help? Read it Watch it Talk to a Tutor
Looking at the derivative, we see that it is defined for all values of t, so there are no vertical tangents.
The critical spots where the slope of the curve is zero or undefinable must be located in order to identify the points of horizontal tangency.
Our first step is to determine y's derivative with regard to x:
dy/dx = 3t^2 - 0
In the event that the derivative is set to zero, we obtain:
3t^2 = 0
t = 0
We gain one crucial insight from this at (22, 0).
The places where the derivative is undefinable must be located in order to determine the vertical tangent. There are no perpendicular tangents when looking at the derivative because it is defined for all values of t.
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The state population for the year was 20 million live births in the same year total of 324,600 deaths were as follows fetal deaths 3244 neonatal death 2200 Post neonatal doves 2700 and infant deaths 4900 calculate the post neonatal mortality rate for the year
The post-neonatal mortality rate for the year is 1.1×10⁻⁷.
What is the post-neonatal mortality rate?The post-neonatal mortality rate in a year is applicable when the death day lies between 28 and 364. First, divide the number of post-neonatal deaths by the number of live births. Then multiply the obtained value by 1000 to get the post-neonatal mortality rate.
It is known that 1 billion units = 10⁹ units. So, 20 billion live births will be 20×10⁹ live births. Also, the number of post-neonatal deaths is 2200.
So, use the formula, post-neonatal mortality rate = (the number of post-neonatal deaths)/(the number of live births).
post-neonatal mortality rate = 2200/(20×10⁹)
= 110×10⁻⁹
= 1.1×10⁻⁷
Therefore, the obtained answer is 1.1×10⁻⁷.
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can someone please help me? ill give brainlist
The true statement is: The difference in height between the whale and the plane is 11,835 feet.
How to find the true statementWe can calculate this difference by subtracting the height of the whale from the height of the plane:
= Height of plane - Height of whale
= 10,300 feet - (-1,535 feet)
= 11,765 feet
Therefore, the difference in height between the whale and the plane is 11,765 feet.
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Please help me with this question
In the figure, angles ∠5 and ∠1 are complementary angle.
What is Complementary angle?The sum of two or more angle is 90 degree then the angle is called the complementary angle.
Given that;
Angles are shown in figure.
Now, By the figure we have;
⇒ ∠ 1 and ∠ 4 are vertically opposite angles, hence both are equal.
Here, ∠4 and ∠5 are complementary angles.
⇒ ∠4 + ∠5 = 90°
⇒ ∠1 + ∠5 = 90°
Hence, Angles ∠5 and ∠1 are complementary angle.
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What is the solution of |2x| = -4?
The solution of the modulus equation is -
x = 2
x = - 2
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 a function as -
|2x| = - 4
We can write -
For {x < 0} → {|x| = - x}. We can write the function as -
- 2x = - 4
x = 2
For {x > 0} → {|x| = x}. We can write the function as -
2x = - 4
x = - 2
Therefore, the solution of the modulus equation is -
x = 2
x = - 2
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What is the most important thing to know when working with circle
theorems?
a) identifying the theorem by looking at the information provided
b) identify the angles
c) identifying arcs
d) B and C Only
Identifying the theorem is the most important step while working with circle theorems.
What is a circle?Circle is a round plane figure whose boundary (circumference) consists of points equidistant from a fixed point (centre). The general equation of the circle is -x² + y² = r²
Given are the points about circle theorems.
While working with circle theorems, identifying the theorem by looking at the information provided is the most important step.
Therefore, identifying the theorem is the most important step while working with circle theorems.
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What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 9.4 yd 18.6 yd square yards
The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.
What is the surface area of this cylinder?The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 9.4 cm and the height of the cylinder is 18.6 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 9.4)18.6
= (59.06)18.6
= 1098.56
Thus, The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.
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National results for the SAT test show that for college-bound seniors the average combined SAT Writing, Math and Verbal score is 1500 with a standard deviation of 250. National results for the ACT test show that for college-bound seniors the average composite ACT score is 20.4 with a standard deviation of 4.8.
Sean took both the SAT and the ACT college entrance exams. His SAT score was 1700 and his ACT score was 24. He wants to know on which test he performed better.
Find the z-scores for his result on each exam.
Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.
How to find Z-score value?To find the z-score for Sean's SAT score, we use the formula:
z = (x - μ) / σ
where x is Sean's SAT score, μ is the population mean (1500), and σ is the population standard deviation (250). Substituting the values, we get:
z = (1700 - 1500) / 250 = 0.8
Therefore, Sean's z-score on the SAT is 0.8.
To find the z-score for Sean's ACT score, we use the formula:
z = (x - μ) / σ
where x is Sean's ACT score, μ is the population mean (20.4), and σ is the population standard deviation (4.8). Substituting the values, we get:
z = (24 - 20.4) / 4.8 = 0.75
Therefore, Sean's z-score on the ACT is 0.75.
Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.
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Suppose Kala places $9500 in an account that pays 15% interest compounded each year. Assume that no withdrawals are made from the account. find the ampunt for one year
given: cn perpendicular to ab; h is the geomtric mean between d and e. prove abc is a right triangle
Pythagorean theorem and its converse to prove that triangle ABC is a right triangle.
The converse of Pythagorean theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
Let's begin by visualizing the given triangle ABC and the line CN that is perpendicular to side AB. Since CN is perpendicular to AB, we can say that triangle ACN and triangle BCN are right triangles (as the angle at C is 90 degrees).
Now, let's focus on the point H that is the geometric mean of points D and E. This means that DH multiplied by HE is equal to CH squared (as per the definition of geometric mean).
We can represent this relationship using the Pythagorean theorem as well. Since triangle CDH and triangle CEH are right triangles (as angle C is 90 degrees), we can say that:
CD² + DH² = CH² (using Pythagorean theorem for triangle CDH)
CE² + EH² = CH² (using Pythagorean theorem for triangle CEH)
From the given relationship of geometric mean, we can substitute CH² in the above equations and get:
CD² + DH² = HE*DH
CE² + EH² = HE*EH
Adding these two equations, we get:
CD² + CE² + DH² + EH² = HE*(DH + EH)
AB² = 4HE² (using the fact that DH + EH = DE = 2HE)
This equation gives us an important insight about the triangle ABC. It tells us that the sum of the squares of the sides (AB²) is equal to four times the square of the length HE (4HE²).
Now, we can use the converse of Pythagorean theorem to prove that triangle ABC is a right triangle.
In our case, we have AB² = 4HE², which satisfies the converse of Pythagorean theorem. Therefore, we can conclude that triangle ABC is a right triangle.
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A recipe for oatmeal cookies calls for 5 cups of flour for every 6 cups of oatmeal. How much flour is needed
for a big batch of cookies that uses 24 cups of oatmeal?
cups
The flour is needed for a big batch of cookies that uses 24 cups of oatmeal would be 20 cups.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
In order to find out how many groups of 6 cups of oatmeal there are.
So, For every 6 cups of oatmeal = 24 / 6 = 4
Now,
For 5 cups of flour = 4 x 5 = 20
The flour is needed for a big batch of cookies that uses 24 cups of oatmeal would be 20 cups.
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Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 3
The Triangle ABC has been dilated through point p and scale factor 3 to produce this finished picture.
What exactly is a triangle?Having three sides, three angles, and three points, a triangle is indeed a closed, two-dimensional object. A hexagon also includes a triangular. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signals, clothes hooks, and billiards racks.
Assume point P as origin then.
P has coordinate (0,0).
And point A has coordinate (-4,0).
point B has coordinate (0,-3).
point C has coordinate (-4,-3).
P(0,0), A(-4,0) B(0,-3) C(-4,-3).
Since the triangle goes an dilation with center at P and scale factor 3.
Then k=scale factor =3.
Now the new coordinate of Triangle is given by A',B' and C', whose coordinate in (x, y) plane is calculated as.
[tex](\mathrm{x}, \mathrm{y}) \rightarrow(\mathrm{kx}, \mathrm{ky})[/tex]
Now calculating the Coordinates on dilated triangle
A'=3(-4,0)=(-12,0)
B'=3(0,-3)=(0,-9)
C'=3(-4,-3)=(-12,-9).
We will calculate the coordinates of dilated triangle assuming the point P as origin
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Please help me answer this problem!
The linear function relationship between the change in the median home value and the year, indicates that we get;
a) The home values increased at a higher rate in Connecticut
b) The median home value in West Virginia in 2010 is $80,721
c) The home values in both states are equal in 1915
What is a linear function relationship?A linear function relationship can be expressed in the form; y = m·x + c. Where, m is the slope of the graph of the function and c is the y-intercept.
a) The rate of increase of the home value, where the values of the house change linearly can be found as follows;
Rate of change of home value for West Virginia = [tex]\frac{72800-33200}{200-1950} = 792[/tex]
The home values in West Virginia increases by about $792 per year
Rate of change of home values for Connecticut = [tex]\frac{166900-71900}{2000-1950} =1900[/tex]
The home values in Connecticut increases by $1900 each year
Therefore;
The state that have home values increase at higher rate is Connecticutb) The increase in the home value in West Virginia per year is $792, therefore, the home value in 2010 can be found as follows;
The number of years between 2010 and 2000 = 2010 - 2000 = 10
Home value in 2010 = Home value in 2000 + 792 × 10
Home value in 2010 = $72800 + $792 × 10 = $80720
Home value in 2010 in West Virginia = $80720c) The equation for the median home value for West Virginia can be presented as follows;
y - 33200 = 792×(x - 1950)
y = 792×(x - 1950) + 33200
The equation for the median home value for Connecticut can be presented as follows;
y - 71900 = 1900×(x - 1950)
y = 1900×(x - 1950) + 71900
When the home values in West Virginia is equal to the home value in Connecticut, we get;
792 × (x - 1950) + 33200 = 1900 × (x - 1950) + 71900
1900·x - 792·x = 1900 × 1950 - 792 × 1950 + 33200 - 71900 = 2121900
1108·x = 2121900
x = 2121900/1108 ≈ 1915.07
The year the median value will be the same in both states is about 1915
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Zeke and Erin were playing a game with a number cube and a spinner divided into equal ports red.
yellow, and blue. Zeke wins if the number cube is a factor of and the spinner lands on red Erin
wins if she rolls a 5 or 6 and the spinner lands on yellow or blue.
1 Create a probability table or free to show all outcomes of rolling a number cube and spinning the
spinner,
R₁
≤18
y₁
B3
2. What is the probability of Zeke winning? What is the probability of Erin winning?
The solution is, the required probability is p= 1/10.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given information we get,
We have 5 possible parts colored red, green, blue, purple and yellow
The cube for this case have 6 possible numbers 1,2,3,4,5,6
We have the following even numbers: 2,4,6
Then the probability of obtain an even number is:
p1= 3/6= 1/2
Then the probability of obtain a blue color on the spinner is:
p2= 1/5
Then we want this probability:
Obtain an even number AND sppining a blue on the spinner
Then since the events are independent we can do this:
p = 1/2 * 1/5= 1/10
Hence, The solution is, the required probability is p= 1/10.
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