Option A is the correct Answer. The total cost of his loan if he paid it off 4 years early is 312,423.90
We have given:
The principal amount which is 30,000
Time which is 30 year
The rate which is 5.5%
And since, we have to find 4 years early so, the time would be: 20-4=16 years.
And since, we have to find for 12 months
Hence, n=12
We have the formula to calculate compound interest:
[tex]A=P(1+\frac{r}{n})^n^t[/tex]
Where
A=compound interest
P= Orginal amount deposited.
r= rate
n=times its compounds per year monthly
t= years.
P=155000, r=5.5, t=16
On substituting the values we get:
[tex]A=155000(1+\frac{0.055}{12})^1^2^*^1^6\\\\A=155000(1+\frac{0.055}{12})^1^9^6\\\\A=155000(14884.0754)\\\\A=312,423. 90[/tex]
Therefore, the compound interest is 312,423.90
To know more about Compound interest:
https://brainly.com/question/3730172
#SPJ4
determine the indices for the directions shown in the following cubic unit cell
The direction of A for the given indices of the cubic unit cell is:
A = [3 3 -1].
What do cubic lattice system Miller indices mean?A notation used to pinpoint crystal planes is called a Miller index.
The three integers define plane-obstruction directions, forming reciprocal basis vectors. The standard notation for negative integers is an overbar.These indices [-u, -v, -w] simply indicate the opposite side of the exact direction as [uvw]. These direction indices all are integer that whenever a primitive unit cell is used, but they could be rational whenever a centred unit cell is used.For the direction of A:
Head point: [1 1 1/3]Tail point: [0 0 2/3]Direction of A = [(1 - 0) , (1 - 0), (1/3 - 2/3)]
= [ 1 1 -1/3]
Multiply each by 3.
= [3 3 -1]
Thus, the direction of A for the given indices of the cubic unit cell is:
A = [3 3 -1].
To know more about the cubic unit cell, here
https://brainly.com/question/12977980
#SPJ4
The complete question is-
Determine the indices for A, the directions shown in the following cubic unit cell.
The diagram is attached:
Answer:
Step-by-step explanation:
the value of a certain two digit number is 9 times the sum of its digits. it the digits are reversed, the resulting number is 63 less than the original number. find the original number
Answer:
Step-by-step explanation:
10x+y=9(x+y)
10y+x=10x+y-63
now put x alone and solve for x then y and add the values of x and y and you will get your answer
consider the following mixture problem and the table used to translate the problem Drink A is 20% fruit juice and drink B is 5% fruit juice. how much should be used in order to make 30 gal of a drink that is 10% fruit juice? complete the following table letting x=gallons of drink A and y=gallons of drink B.
Substance Gallons % Fruit Juice
Drink A x 20%
Drink B y 5%
Total x + y = 30 10%
To find the number of gallons of Drink A and Drink B that should be used, we can write two equations based on the percentage of fruit juice.
20% * x = 10% * (x + y)
5% * y = 10% * (x + y)
Simplifying and solving for x and y:
x = 1.5 * y
10% * (x + y) = 10% * 30
y = 15
x = 1.5 * 15 = 22.5
So, we would use 22.5 gallons of Drink A and 15 gallons of Drink B to make a 30 gallon mixture that is 10% fruit juice.
the points o(0,0,0), p(,,), and q(,,) lie at three vertices of a parallelogram. find all possible locations of the fourth vertex.
The two possible locations for the fourth vertex of the parallelogram are p and q.
The fourth vertex of a parallelogram can be obtained by adding the vector difference between two of its vertices to the third vertex. In this case, the vector difference between two vertices can be found by subtracting one vertex from the other, i.e. p-o and q-o. So, the fourth vertex can be found by adding either of these vectors to vertex o, i.e. r = p - o + o = p or r = q - o + o = q.
Therefore, the two possible locations for the fourth vertex of the parallelogram are p and q.
To learn more about parallelograms,
Visit; brainly.com/question/29147156
#SPJ4
What are the domain and range of the function represented by the set of
ordered pairs?
{(-13, 9), (-7, -5), (5, 14). (11, -10))
The domain and range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is as follows:
domain = [-13, -7, 5, and 11]
range = {9, -5, 14 and -10}
How to find the domain and range of a function?The domain of a function is independent variable of a function. The domain is the input value of the function. The domain lies on the x axis of the function.
Therefore, the domain of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is [-13, -7, 5, and 11]
The range is the dependent value of the function. The range is also called the output value of the function. The range lies on the y-axis of the function.
Therefore, the range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) are {9, -5, 14 and -10}
learn more on functions here: https://brainly.com/question/28690006
#SPJ1
Answer all theses for a surprise ⬇️
Definitely not at school rn
The proportionate equation for each problems are:
constant of proportionality: 4.75; price per unitconstant of proportionality: 8.5; times per ditance or minutes per milesy = 1.5x y = 18x 10.5 cups of water15 3/4 yards of fabricLet's discuss each problem we have:
1. Liv earns $9.50 for every 2 bracelets she sells.
y = 4.75x
because y = kx, then:
y = $9.50
x = 2
4.75 --> constant of proportionality
--> price per unit of bracelet sold
2. John ran 3 miles in 25.5 minutes
y = 8.5x
y = 25.5 minutes
x = 3 miles
8.5 --> constant of proportionality
--> minuntes per miles
--> times per distance
3. Lincoln bought 3 bottles of energy drink for $4.50
y = kx
y = $4.50
x = 3
$4.50 = k (3)
k = $1.50 --> price of a bottle of energy drink
4. Total cost of 4 hours renting a cotton candy machine is $72.
y = kx
y = $72
x = 4 hours
$72 = k(4)
k = $18 --> price of renting per hour
5. 7 cups of water are used to make 4 loaves of French bread.
y = kx
y = 7
x = 4
7 = k(4)
k = 7/4
Proportionate equation: y = 7/4 x
(x = 6)
y = 7/4 (6)
y = 21/2 = 10.5 cups of water
6. 6 3/4 yards of fabrics are used to make 3 elf costumes
y = kx
y = 6 3/4
x = 3
6 3/4 = k (3)
27/4 = 3k
--------------- x 4
27 = 12k
k = 9/4
Proportionate equation: y = 9/4 x
(x = 7)
y = 9/4 (7)
y = 63/4
y = 15 3/4 yards of fabric
Learn more about Proportionate Equation here: brainly.com/question/22962960
#SPJ1
Fells had 9 boxes. Scarlett had 18 boxes but fewer than Dylan. Dylan had 2 times minus 1 boxes than Fells. How many boxes do they have in all?
You'll get 40 points.
The number of boxes with three of them are 44.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Fells had 9 boxes.
Dylan had 2 times minus 1 boxes than Fells.
2(9)-1 which is 18-1= 17 boxes.
Scarlett had 18 boxes but fewer than Dylan
The total number of boxes are 9+17+18
44 boxes
Hence, the number of boxes with three of them are 44.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
A point charge with magnitude +Q is located inside the cavity of a spherical conducting shell. The shell has an inner radius equal to a, an outer radius equal to b, and holds a net charge of -3Q, as shown in the figure. What is the magnitude of the electric field inside the conducting shell, at a radial distance r where a < r < b?
Zero is the magnitude of the electric field inside the conducting shell, at a radial distance r where a < r < b.
What is electric field?Each point in space has an electric field associated with it when there is charge existing in any form. E, often known as electric field strength, electric field intensity, or just the electric field, is a mathematical constant that expresses the strength and direction of an electric field.
The electromagnetic region which surround electrically charged particles and acts to either attract or repel all those other positive ions in the field is known as an electric field (or E-field). A systems of charged particles' physical field is also referred to in this phrase.
By applying Gauss law, to the sphere of radius r with dotted lines:
∅(E) = ∫E. dA
∅(E) = E (4πr²) = Q/∈₀
E₁ = Q/4πr²∈₀
The electric field in a conductor is zero. a < r < b has an r value in the conductor.
E₂ = 0
To know more about electric field refer to:
https://brainly.com/question/30325241
#SPJ4
Is this statement true or false? Explain.
4x(3+5)-10=4x3+5-10
Answer:
False. The two sides evaluate to different numbers.
Step-by-step explanation:
Let's evaluate each side:
4 × (3 + 5) - 10 = 4 × 8 - 10 = 32 - 10 = 22
4 × 3 + 5 - 10 = 12 + 5 - 10 = 17 - 10 = 7
Fabian harvests 10 pounds of tomatoes from his garden. He needs
2 2/5
pounds to make a batch of soup. If he sets aside 2.8 pounds of tomatoes to make spaghetti sauce, how many batches of soup can Fabian make? Drag numbers to write and solve an equation. Numbers may be used once, more than once, or not at all.
2.8 returned to choices list.
2.2 2.4 2.5 2.6 2.8 3 5 6 8 10
x + =
x =
PLEASE HELP ME
The number of batches of soup that Fabian can make is given as follows:
3 batches.
How to obtain the number of batches of soup?The number of batches of soup is obtained applying the proportions in the context of the problem.
He has 10 pounds, and sets aside 2.8 pounds of tomatoes to make spaghetti sauce, hence the amount remaining for soup is given as follows:
10 - 2.8 = 7.2 pounds.
He needs 2 and 2/5 = 2 + 0.4 = 2.4 pounds for each batch, hence the number of batches is obtained as follows:
7.2/2.4 = 3.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim x → 8 12−x − 2 24−x − 4
The limit does not exist as x approaches 8 for (√(12−x) − 2)/ (√(24−x) − 4).
Therefore the answer is dne.
The square root of 12 - x approaches 2 as x approaches 8 and the square root of 24 - x approaches 4 as x approaches 8.
The limit fails to exist because both the numerator and the denominator approach 0 as x approaches 8, but the ratio of the two approaches positive infinity. This shows that the limit is undefined or "dne".
As both the numerator and denominator approach 0, the fraction they form can approach any real number or it can oscillate between two values, leading to an undefined limit. In such cases, the limit fails to exist.
--The question is not readable, answering to the question below--
"evaluate the limit, if it exists. (if an answer does not exist, enter dne.)
lim x → 8 (√(12−x) − 2)/ (√(24−x) − 4)"
To know more on limit
https://brainly.com/question/28975075
#SPJ4
what is the probability that the digit 7 doesn’t appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely?
The probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.
The probability that the digit 7 doesn't appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely is given by the probability that all 100 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 8, 9}. There are 10 choices for each digit, so there are 10^100 possible sequences of 100 digits. The number of sequences that don't contain the digit 7 is 9^100. Therefore, the probability that the digit 7 doesn't appear among 100 digits is: P(7 doesn't appear) = (9^100) / (10^100) = 9 / 10
Therefore, the probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.
To learn more about probability,
Visit; brainly.com/question/30034780
#SPJ4
suppose f ( x ) = 3 x 2 − 4 x − 5 . compute the following: a.) f ( − 4 ) f ( 3 ) = b.) f ( − 4 ) − f ( 3 ) =
To find f ( -4 ) - f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. Now that we have both values we can subtract them to get the answer of -67.
a.) f ( -4 ) = 3 ( -4 )2 - 4 ( -4 ) - 5 = -47 f ( 3 ) = 3 ( 3 )2 - 4 ( 3 ) - 5 = 20 f ( -4 ) f ( 3 ) = -47 ( 20 ) = -940
b.) f ( -4 ) - f ( 3 ) = -47 - 20 = -67
a.) To find f ( -4 ) f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. This gives us -47. To evaluate f ( 3 ) we plug 3 into the function and simplify. This gives us 20. Now that we have both values we can multiply them together to get the answer of -940.
b.) To find f ( -4 ) - f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. This gives us -47. To evaluate f ( 3 ) we plug 3 into the function and simplify. This gives us 20. Now that we have both values we can subtract them to get the answer of -67.
learn more about function here
https://brainly.com/question/12431044
#SPJ4
John make two clay pot. Each pot i fired independently. The probability that a pot crack while being fired i 0. 03 Calculate the probability that only one of John’ pot crack while being fired
The Probability that only one of John's pot crack while being fired is 0.06.
The probability that only one of John's pots cracks while being fired can be calculated using the formula for the binomial distribution:
P(X = 1) = C(2, 1) * (0.03)^1 * (1 - 0.03)^(2 - 1)
= 2 * 0.03 * 0.97
= 0.0582
Where C(2, 1) is the number of combinations of 2 items taken 1 at a time, and (0.03)^1 and (1 - 0.03)^(2 - 1) are the probabilities of the first pot cracking and the second pot not cracking, respectively.
So, the probability that only one of John's pots cracks while being fired is approximately 0.06.
To learn more about Probability.
https://brainly.com/question/13032389
#SPJ4
when using a graduated pipet, at which point do you measure the volume?
The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.
1. Place the graduated pipet on a flat surface and make sure it is level
2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume
3. Make sure the liquid is not touching the etched line above it
4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines
The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.
Learn more about volume here
https://brainly.com/question/16134180
#SPJ4
The Wildgrove library has 15 pop CDs and 59 other CDs.
If a library patron randomly selects one of the CDs, what is the probability that it will be a pop CD?
Write your answer as a fraction or whole number.
The probability of randomly selecting a pop CD is 15/74.
What is probability?Probability is a measure of the likelihood of a certain event occurring, expressed as a number between 0 and 1.
An event with a probability of 1 is considered certain to occur, while an event with a probability of 0 is considered impossible. Events with probabilities between 0 and 1 are considered uncertain, with higher probabilities indicating greater likelihood of occurrence.
Probability is a mathematical concept that represents the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur. The calculation of probability involves using rules of probability theory and statistical analysis to determine the chance of a specific outcome or set of outcomes.
There are various methods for calculating probability, including classical probability, empirical probability, and subjective probability.
Learn more on probability here https://brainly.com/question/24756209
#SPJ1
The first term of an A.Pis -1 and the common difference is 0.5. Find the 6th term.
Answer:
Step-by-step explanation:
-4
Work Shown:
[tex]a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\[/tex]
Move 1 1/4 units in the negative direction from 3/4, and then plot a point at this location.
Answer:
The point you would plot would be at -1/2
Explanation:
3/4 - 1 1/4 = -1/2
The perimeter of a rectangle is 34 units. Its width is 6.5 units.
Write an equation to determine the length (t) of the rectangle.
Find the length of the rectangle.
On solving the provided question, we can say that the equation foe the rectangle will be = 34 = 12 + 2W
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Perimeter of rectangle is = 2(L+W)
the equation foe the rectangle will be =
34 = 2(6.5 + W)
34 = 12 + 2W
To know more about rectangle visit:
https://brainly.com/question/29123947
#SPJ1
when two dice are thrown, what is the probability that their numbers are different? round to the nearest hundredth.
The probability for getting the different numbers when two dice are thrown is: 5/6.
Explain the term sample space?The catalog of all potential outcomes of such an experiment is referred to as the sample space. Regardless of the number many ways an event could occur, each potential result is symbolized by a single point with in sample space. For instance, the results of the experiment using a simple fair dice throw are used to create the sample space.The sample space formed by rolling two dice are: 6*6 = 36.
Total number of pairs having same number = (1,1), (2,2),(3,3),(4,4),(5,5),(6,6) = 6 samples.
Thus,
Number of outcomes having different numbers:
36 - 6 = 30
Probability (different numbers) = total number of different number / total outcomes.
Probability (different numbers) = 30 / 36
Probability (different numbers) = 5/6
Thus, the probability for getting the different numbers when two dice are thrown is: 5/6.
To know more about the sample space, here
https://brainly.com/question/15659544
#SPJ4
I need help with ‘classifying polynomials; adding & subtracting polynomials’
Classifying polynomials refers to categorizing polynomials based on the degree of the polynomial and the number of terms in the polynomial.
The degree of a polynomial is the highest exponent in the polynomial. Polynomials can be classified into several types, including constant polynomials (degree 0), linear polynomials (degree 1), quadratic polynomials (degree 2), and so on. Adding and subtracting polynomials is the process of combining two or more polynomials by combining like terms. Like terms are terms with the same variable and exponent. To add or subtract polynomials, simply line up the terms with the same variable and exponent and add or subtract the coefficients. The result will be a new polynomial with the combined terms.
For example, to add the polynomials [tex]2x^2 + 3x + 4[/tex] and [tex]-x^2 + 5x - 6[/tex], we line up the terms with the same variable and exponent and add the coefficients:
[tex](2x^2 + 3x + 4) + (-x^2 + 5x - 6) = (2x^2 - x^2) + (3x + 5x) + (4 - 6) \\[/tex]
[tex]= x^2 + 8x - 2.[/tex]
Learn more about exponent :
https://brainly.com/question/5497425
#SPJ4
SALARY The average salary for an entry-level mechanical engineer position in Texas ranges from $63,000 to $73,500
a year.
Write a compound inequality to represent the possible monthly salary m of an entry-level mechanical engineer in Texas.
Answer:
$5,250 ≤ m ≤ $6,125
Step-by-step explanation:
A compound inequality is a mathematical statement that combines two inequality statements using "and" or "or". In this case, the compound inequality represents the range of possible monthly salary for an entry-level mechanical engineer in Texas.
The average salary for this position ranges from $63,000 to $73,500 per year. To find the monthly salary, we need to divide these amounts by 12 months, which gives us the minimum and maximum monthly salary:
$63,000/12 = $5,250
$73,500/12 = $6,125
Therefore, the compound inequality is:
$5,250 ≤ m ≤ $6,125
This means that the monthly salary of an entry-level mechanical engineer in Texas could be anywhere between $5,250 and $6,125.
the national and nutrition survey reported that 30% of adults in the u. s have hypertension (high blood pressure). let x be the number of adults in the u. s with hypertension. a sample of 25 adults is studied: calculate the following probabilities using rguroo and then fill in the blanks with your answers. a) the probability that 12 or fewer adults in the sample have hypertension is . round your answers to three decimal places. b) the probability that more than 10 adults in the sample have hypertension is . round your answers to three decimal places. c) calculate the
Probability that more than 10 adults in the sample have hypertension is 0.768
Var(X) = 5.25
The probability that more than 10 adults in the sample have hypertension is 0.6086
The National and Nutrition survey reported that 30% of adults in the U. S have hypertension (high blood pressure). Let X be the number of adults in the U. S with hypertension.
A sample of 25 adults is studied:
Calculate the following probabilities using R guro and then fill in the blanks with your answers.
a) The probability that 12 or fewer adults in the sample have hypertension is . Round your answers to three decimal places.
b) The probability that more than 10 adults in the sample have hypertension is . Round your answers to three decimal places.
c) Calculate the Var(X)=n ∗p∗(1−p) = . Round the answer to the nearest whole number.
The National and Nutrition survey reported that 30% of adults in the U. S have hypertension
A sample of 25 adults is studied
therefore X = 25
adults in the U. S have hypertension = 30% of 25
= 7.5
a) the probability that 12 or fewer adults in the sample have hypertension is
Let X: Number of adults that were told they have hypertension.
The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.
X~ Binomial(n=12, p =0.30)
Required probability,
P(X≥2)=1−P(X=0)−P(X=1)
=1−( 12 ( 12
0 )0.30^ 0(1−0.30) ^(12−0) − 1)0.30^ 1(1−0.30) ^(12−1)
=1−0.1660−0.0652
=0.768
b) the probability that more than 10 adults in the sample have hypertension is
Let X: Number of adults that were told they have hypertension.
The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.
X~ Binomial(n=10, p =0.30)
Required probability,
P(X≥2)=1−P(X=0)−P(X=1)
=1−( 10 ( 10
0 )0.30^ 0(1−0.30) ^(10−0) − 1)0.30^ 1(1−0.30) ^(10−1)
=1−0.2824−0.1089
=0.6086
c) Calculate the Var(X)=n ∗p∗(1−p)
n= 25
p=0.30
Var(X)=n ∗p∗(1−p)
= 25*0.30*(1-0.30)
=5.25
Probability that more than 10 adults in the sample have hypertension is 0.768
Var(X) = 5.25
The probability that more than 10 adults in the sample have hypertension is 0.6086
To know more about Probability visit brainly.com/question/30034780
#SPJ4
Probability that more than 10 adults in the sample have hypertension is 0.768
Var(X) = 5.25
The probability that more than 10 adults in the sample have hypertension is 0.6086
The National and Nutrition survey reported that 30% of adults in the U. S have hypertension (high blood pressure). Let X be the number of adults in the U. S with hypertension.
A sample of 25 adults is studied:
Calculate the following probabilities using R guro and then fill in the blanks with your answers.
a) The probability that 12 or fewer adults in the sample have hypertension is . Round your answers to three decimal places.
b) The probability that more than 10 adults in the sample have hypertension is . Round your answers to three decimal places.
c) Calculate the Var(X)=n ∗p∗(1−p) = . Round the answer to the nearest whole number.
The National and Nutrition survey reported that 30% of adults in the U. S have hypertension
A sample of 25 adults is studied
therefore X = 25
adults in the U. S have hypertension = 30% of 25
= 7.5
a) the probability that 12 or fewer adults in the sample have hypertension is
Let X: Number of adults that were told they have hypertension.
The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.
X~ Binomial(n=12, p =0.30)
Required probability,
P(X≥2)=1−P(X=0)−P(X=1)
=1−( 12 ( 12
0 )0.30^ 0(1−0.30) ^(12−0) − 1)0.30^ 1(1−0.30) ^(12−1)
=1−0.1660−0.0652
=0.768
b) the probability that more than 10 adults in the sample have hypertension is
Let X: Number of adults that were told they have hypertension.
The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.
X~ Binomial(n=10, p =0.30)
Required probability,
P(X≥2)=1−P(X=0)−P(X=1)
=1−( 10 ( 10
0 )0.30^ 0(1−0.30) ^(10−0) − 1)0.30^ 1(1−0.30) ^(10−1)
=1−0.2824−0.1089
=0.6086
c) Calculate the Var(X)=n ∗p∗(1−p)
n= 25
p=0.30
Var(X)=n ∗p∗(1−p)
= 25*0.30*(1-0.30)
=5.25
Probability that more than 10 adults in the sample have hypertension is 0.768
Var(X) = 5.25
The probability that more than 10 adults in the sample have hypertension is 0.6086
To know more about Probability visit
brainly.com/question/30034780
#SPJ4
using separation of variables, solve the differential equation, use c to represent the arbitrary constant. 10 x^8
Since C is any arbitrary constant, [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.
The equation given to us is:
[tex](3 + x^{10})\frac{dy}{dx} = \frac{x^{9}}{y}[/tex]
We can re-write the above equation:
[tex]y dy = \frac{x^9}{3 + x^{10}} dx[/tex]
This is separation of variables.
A separable differential equation is any equation that can be written in the form y′=f(x)g(y). The method of separation of variables is used to find the general solution to a separable differential equation.
Now, if we differentiate the denominator,
[tex]\frac{d}{dx} (3 + x^{10} ) = 10x^9[/tex]
Integrating both sides,
[tex]\frac{y^2}{2} = \frac{1}{10} ln (3 + x^{10})[/tex] + C
⇒ [tex]y^{2} = \frac{1}{5} ln (3 + x^{10})[/tex] + 2C
Since C is any arbitrary constant, [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.
To learn more about differential equations, visit the link:
brainly.com/question/2273154
#SPJ4
Mrs. Newman's famous peanut butter cookies call for 1 cup of peanut butter for every
1
2
of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?
In a case whereby Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil the amount of peanut butter she should use can be expressed as 2 cups of peanut butter.
How can the amount of peanut butter be calculated?The concept that will be used is simplification. Base on the provided information from the question,
(1/2 cup of oil )= (1 cup of peanut butter)
we can represent (1 cup of oil) as (x)
The if we perfor a Cross Multipliplication we have:
(1/2x) =( 1 × 1)
x = (1 × 2/1)
x = 2 cups of peanut butter.
Learn more about simplification at:
https://brainly.com/question/30170850
#SPJ1
Bill reflects the point (-3, 5) over the x-axis. What is the coordinate of the new point after the reflection?.
Answer:
(-3, -5)
Step-by-step explanation:
When reflected over the x-axis, the x remains the same, and the y change to their opposite sign.
So, the answer is (-3, -5)
consider the sequence {12, 5, -2, -9, -16 ... } select all the items that define the sequence
Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.
What is arithmetic sequence ?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.
The sequence {12, 5, -2, -9, -16 ... } can be defined by the following items:
The first term: 12
The common difference: -7
The pattern of adding the common difference to find the next term.
Therefore, all the items that define the sequence are:
The first term: 12
The common difference: -7
This sequence is an arithmetic sequence.
Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.
To learn more about arithmetic sequence visit :
brainly.com/question/15412619
#SPJ4
PLS HELP ITS URGENT ILL GIVE YOU POINTS
The life of a Goldline auto battery is normally distributed with a mean of 42. 5 months and a
standard deviation of 6. 5. The battery warranty is 36 months. What is the probability that a
battery will last for 52 months?
A)92. 8%
B)73. 8%
C)87. 3%
D)37. 4%
The probability that the battery will last for 52 months is approximately 0.928, or 92.8%.
To calculate the probability that a battery will last for 52 months, we need to find the z-score of 52 months, using the formula:
z = (x - μ) / σ
Plugging in the values, we get:
z = (52 - 42.5) / 6.5 = 1.384615
Next, we can use a z-table to find the probability that a battery will last more than 52 months.
In this case, the z-score is positive, so we look up the area to the right of 1.384615 in the z-table. The area to the right of 1.384615 is approximately 0.928.
Therefore, the probability that a battery will last for 52 months or more is approximately 0.928, or 92.8%.
So the answer to the question is: A) 92.8%
Learn more about Probability here: https://brainly.com/question/30034780
#SPJ4
consider the following data: −11,−5,−5,−11,13,−11,−5 step 1 of 3 : calculate the value of the sample variance. round your answer to one decimal place.
The value of the sample variance rounded to one decimal place is 76.0.
What is the Mean?
The mean is a measure of the central tendency of a set of data, calculated as the sum of the values divided by the number of values in the set.
The sample variance of a set of data is a measure of the spread or dispersion of the data around the mean. To calculate the sample variance, you can follow these steps:
Calculate the mean of the data: First, find the sum of all the data points and divide by the number of data points (n).
For the given data, the mean is: (-11 + -5 + -5 + -11 + 13 + -11 + -5) / 7 = -7
Subtract the mean from each data point: Next, subtract the mean from each data point to get the deviations from the mean.
For the given data, the deviations are: (-11 - -7) = -4, (-5 - -7) = 2, (-5 - -7) = 2, (-11 - -7) = -4, (13 - -7) = 20, (-11 - -7) = -4, (-5 - -7) = 2
Square the deviations: Square each deviation to get rid of negative values.
For the given data, the squared deviations are: (-4)^2 = 16, (2)^2 = 4, (2)^2 = 4, (-4)^2 = 16, (20)^2 = 400, (-4)^2 = 16, (2)^2 = 4
Sum the squared deviations: Sum all the squared deviations.
For the given data, the sum of the squared deviations is: 16 + 4 + 4 + 16 + 400 + 16 + 4 = 456
Divide the sum by n - 1: Finally, divide the sum of the squared deviations by the number of data points minus 1 (n - 1). This gives us the sample variance.
For the given data, the sample variance is: 456 / (7 - 1) = 456 / 6 = 76
Hence, the value of the sample variance rounded to one decimal place is 76.0.
To learn more about Mean, Visit
https://brainly.com/question/14532771
#SPJ4
Which fraction have a leat common denominator of 36?
A ) 3/4 and 5 18 B ) 5/6 and 7/9 C ) 7/8 and 1/12
3/4 and 5 18 is fraction have a leat common denominator of 36.
How do you determine a fraction's least common denominator?There are several possible pairs of two whole numbers whose Least Common Denominator is 36: 36 and 36 comes first, followed by 1 and 36, 2 and 36, 3 and 36, 4 and 18 and 9, 6 and 36, 9 and 12, 12 and 36, 18 and 36, and finally 4 and 9 and 36.I would choose 4/5 and 9/13 if you want fractions in their simplest form, with several denominators, and an LCD of 36.These, in my opinion, work because 5, 13, and 36 are all pairwise relatively prime (meaning that the product of any two of them is the LCD of the other), and because the LCD of 4 and 9 is pairwise relatively prime.3/4 and 5 18 is fraction have a leat common denominator of 36.
To learn more about least common denominator refer to:
https://brainly.com/question/3188706
#SPJ4