Answer:
24 vowels
Step-by-step explanation:
A B C D E F G
two out of 7 are vowels....you would expect to get 2/7 ths of 84 spins to be vowels
2/7 * 84 = 24 vowels
The monthly income of a family is Rs. 50000. The ratio of the expenditure and saving is 4:1. Find the amount of expenditure and saving.
Answer:
Step-by-step explanation:
If the ratio of expenditure and saving is 4:1, it means that for every 4 units of expenditure, there is 1 unit of saving.
Let's call the expenditure "E" and the saving "S".
We know that the monthly income is Rs. 50000 and the ratio of expenditure and saving is 4:1.
So, we can set up the following proportion:
E/S = 4/1
We know that E+S = 50000, since the income is equal to the sum of expenditure and saving.
So, we can use this equation to find the value of E and S.
We can first solve for E in terms of S:
E = (4/5)S
We can then substitute this equation into the equation E+S = 50000 to find the value of S:
(4/5)S + S = 50000
Solving for S, we get:
S = (50000/(4+1)) = 50000/5 = 10000
Now that we know the value of S, we can use the proportion E/S = 4/1 to find the value of E:
E = 4 * S = 4 * 10000 = 40000
So, the expenditure of the family is Rs. 40000 and the saving is Rs. 10000.
use quadratic reciprocity to see whether the following have solutions; each modulus is prime x^2 = 123 mod 4-1
modulus is prime x^2 = 123 mod 4-1 this implies 123 mode 3 and hence we get x^2 = 2 prime
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
therefore , modulus is prime x^2 = 123 mod 4-1 this implies 123 mode 3 and hence we get x^2 = 2
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How to multiply polynomials
Utilizing the distributive law, first multiply each term in one polynomial by each term in the other polynomial. Using the exponent rule, multiply the powers of the same variables. Then, add or remove like terms to simplify the resulting polynomial.
What is a polynomial?A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and x² + 3x + 11.In particular, a polynomial term cannot contain any square roots of variables, fractional or negative powers on the variables, or variables in any fraction's denominator.To learn more about polynomial, refer to:
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Swimming Pool a certain summer's day, 406 people the poolThe daily prices are 1.50 for and 2.00 for The receipts for How children and how many adults swam at the public pool that day
The number of children and the number of adults swam at the public pool that day are 157 and 249 respectively.
What are the numbers of children and adult?The number of children and the number of adults swam at the public pool that day is calculated as follows;
let the number of children = x
let the number of adult = y
x + y = 406 ------ ( 1)
1.5x + 2y = 733.5 ---- (2)
From equation (1), y = 406 - x
Substitute the value of y into equation ( 2)
1.5x + 2( 406 - x ) = 733.5
1.5x + 812 - 2x = 733.5
-0.5x = -78.5
x = 78.5 / 0.5
x = 157 children
y = 406 - 157
y = 249 adults
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The complete question is below:
Swimming Pool a certain summer's day, 406 people the pool, The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled $733.5. How children and how many adults swam at the public pool that day
What type of angle is x?
Answer:
reflex angle since it's greater than 180 degrees
Step-by-step explanation:
There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
If we know that there is 360 total degrees, we can figure out what number degree is x by using this equation:
360 - 50 = 310
Therefore, because 310 is more than 180 degrees, it is considered a reflex angle.
The cost of a company picnic varies directly as the number of employees attending the picnic. If a company picnic costs $487.50 for 30 employees, how much does a company picnic cost for 80 employees?
$1,300.00
I took the quiz
On making an horizontal slice through the solid, the
following two-dimensional shape is produced. Select the
solid that will yield this shape.
Answer:
Step-by-step explanation:
C
a statistics professor asked students in a class their ages. based on this information, the professor states that the average age of all the students in the university is 24 years. this is an example of a. an experiment. b. an observational study. c. statistical inference. d. descriptive statistics.\
The correct option is statistical inference (b).
The professor uses sample data from the population to determine the average age. Anytime inferential statistics or statistical inference is used to make inferences from samples.
Instead of gathering data from the entire institution, the professor took age samples from a class and used those data to draw conclusions about the entire university.
Descriptive statistics in statistics help you describe the facts, whereas inferential statistics assist you in drawing conclusions from the data.
Data from the sample are used in inferential statistics, which allows you to generalise about the population.
Inference generally refers to "guessing," which involves drawing conclusions about something.
So, drawing conclusions about the population is what is meant by statistical inference. It makes use of a number of statistical analytic tools to draw a conclusion about the population.
Therefore, the correct option is statistical inference.
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Mrs. Thakur invested Rs 8000 at an interest rate of 8% per annum. Find the total amount that he will get after 2 years, if the interest is compounded annually.
Mrs. Thakur will receive Rs 9331.2 after 2 years, with an interest rate of 8% compounded annually.
How to determine the amount after tow yearsTo find the total amount Mrs. Thakur will receive after 2 years,
We need to calculate the compound interest.
The formula for compound interest is: A = P * (1 + r/100)^n
Where A is the final amount, P is the principal (Rs 8000),
r is the interest rate (8%), and n is the number of years (2).
So,
A = 8000 * (1 + 8/100)^2
A = 8000 * (1.08)^2
A = 8000 * 1.1664
A = 9331.2
Therefore, Mrs. Thakur will receive Rs 9331.2 after 2 years
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for each matrix, consider the corresponding system of linear equations. how many free variables are there in the solution?
The number of free variables in the solution of the given matrix are as follow:
Attached matrix.
1. First matrix has one free variable x₃.
2. Second matrix has three free variable x₂ , x₃ , x₄.
3. Third matrix has one free variable x₃ , x₄ , x₅
4. Fourth matrix has two free variable x₂ , x₃.
Number of free variables for the corresponding matrix are :
1. First matrix has two pivot element at first and second column , it implies number of free variable is one that x₃.
2. Second matrix has one pivot element in the first column therefore there are three free variable in the second, third and fourth column x₂ , x₃ , x₄.
3. Third matrix has two pivot element at first and second column so
there are three free variable in the third ,fourth , and fifth column x₃ , x₄, x₅.
4. Fourth matrix has one pivot element in the first column therefore it has two free variables in the second and third column x₂ and x₃.
Therefore, the free variables present in the corresponding matrix are :
1. First matrix : one free variable.
2. Second matrix : three free variables.
3. Third matrix : one free variable.
4. Fourth matrix : two free variables.
The above question is incomplete, the complete question is:
For each matrix, consider the corresponding system of linear equations. how many free variables are there in the solution?
Matrix are attached.
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Kevin Carter Male Clothing Ltd is a chain of fashion outlets across Birmingham and the
midlands. In quarter 1 they had inflows of £540,000 across their three stores, with outflows
of £495,000. Their opening balance for the quarter was £20,000. For quarter 2 they
anticipate inflows to increase by 7.5% and outflows increase by 5%. Calculate their closing
balance for Quarter 2.
The closing balance for quarter 2 will be £230,450.
Calculation of closing balanceTo calculate the inflows and outflows for quarter 2, We se the following formula:
Inflows = inflows quarter 1 + (inflows quarter 1 x increase percentage)
Outflows = outflows quarter 1 + (outflows quarter 1 x increase percentage)
Where inflows quarter 1 and outflows quarter 1 are the inflows and outflows for quarter 1 and increase percentage is the percentage increase anticipated for quarter 2.
First, we can calculate the inflows for quarter 2:
Inflows Q1 = £540,000
Increase in inflows = 7.5%
Inflows Q2 = £540,000 x (1 + 7.5%) = £584,700
Next, we can calculate the outflows for quarter 2:
Outflows Q1 = £495,000
Increase in outflows = 5%
Outflows Q2 = £495,000 * (1 + 5%) = £519,250
Then, we can calculate the closing balance for quarter 1:
Closing balance Q1 = Opening balance + Inflows Q1 - Outflows Q1 = £20,000 + £540,000 - £495,000 = £65,000
Finally, we can calculate the closing balance for quarter 2:
Closing balance Q2 = Closing balance Q1 + Inflows Q2 - Outflows Q2 = £65,000 + £584,700 - £519,250 = £230,450
So, the closing balance for quarter 2 will be £230,450.
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Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the volume.
The volume of the cone is 615.44 cm³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
Slant height l = 14 cm.
Curved surface area of a cone = 308 cm².
This means,
πrl = 308
πr x 14 = 308
πr = 308/14
r = 308/(14π)
r = 7 cm
Now,
Volume = (1/3)πr²h.
l² = r² + h²
l² - r² = h²
h = √(l² - r²)
h = √(196 - 49)
h = √(147)
h = 12 cm
Now,
Volume.
= (1/3)πr²h
= (1/3) x π x r² x h
= (1/3) x 3.14 x 49 x 12
= 615.44 cm³
Thus,
615.44 cm³ is the volume of the cone.
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I DONT EVEN UNDERSTAND WHAT IT'S ASKING T^T!!! I will give you 80 points.
1. Diamond - A four-sided figure with two equal, parallel sides, and two equal, opposite angles.
2. Rectangle - A four-sided figure with four right angles.
3. Hexagon - A six-sided figure with six equal sides and six equal angles.
Find the three different quadrilaterals in this Navajo eye-candy pattern, and then give them all the proper names.1. To identify a diamond in the eye-dazzler design, look for a four-sided figure with two equal, parallel sides and two equal, opposite angles.
The diamond shape in the eye-dazzler design should be easy to spot as it is outlined in black or a darker color.
2. To identify a rectangle in the eye-dazzler design, look for a four-sided figure with four right angles.
The rectangle shape in the eye-dazzler design should be easy to spot as it is outlined in black or a darker color.
3. To identify a hexagon in the eye-dazzler design, look for a six-sided figure with six equal sides and six equal angles.
The hexagon shape in the eye-dazzler design should be easy to spot as it is outlined in black or a darker color.
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A shop has a sale of 1/5
off all items in stock.
If the original price of a dress is £45, what would be its sale price?
Answer:
36
Step-by-step explanation:
4/5(45) = 36.00
if you are taking 1/5 off, you are leaving 4/5 on.
If uare pro solve this for 40 points
Show that the line joining the points (0, 2) and (-5,-4) divides the line segment joining the point (6, 3) and (-2, 1) in the ratio 2:1.
The line joining the points (0, 2) and (-5,-4) divides the line segment joining the point (6, 3) and (-2, 1) in the ratio 2:1.
How can we show the intersection?Let the point of intersection of the two lines be (x, y). Using point-slope form, the equation of the line joining the points (0, 2) and (-5,-4) is y-2 = -3/5(x-0), and the equation of the line segment joining the points (6, 3) and (-2, 1) is y-3 = -2/8(x-6).
Solving for x and y, we get x = 8/5 and y = 4/5.
So, the distance from (x, y) to (0, 2) is 2/5 and the distance from (x, y) to (6, 3) is 6/5.
Hence, the ratio of the distances is 2/5 : 6/5 = 2 : 1.
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Help me please. I don't get it
Sorry..Bro the pic isn't clear...I can't help you..
I am so sorry bro
Salut/Hello!
Step-by-step explanation:
You can use the explanation it has above (in the screenshot) to calculate.
The area of the rectangle or square is the length x width
For a square, all sides are equal so it's enough to just know one.
If you observe you can see how the area of the triangle is exactly half of the area of the square/rectangle. So if you struggle to find it using the formula 1/2 x base x height then you can simply divide the area of the rectangle with 2
Answer:
a. square 12 x 12 = 144 cm
triangle 1/2 x 144 = 72
and we know 1/2 is equal to 0.5
b. rectangle 11 ft x 5ft = 55 ft
triangle 1/2 x 55 = 27.5
... The rest aren't clear but with that example you can definitely do it on your own!
I hope it was useful! :]
The two polygons shown are similar. Calculate the value of OK.
The required value of OK is 8.5 units for the given polygon.
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
The two polygons shown are similar.
As we know that two similar polygons with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
So AT/OK = MH/RS
⇒ 2/OK = 4/17
⇒ OK = 34/4
⇒ OK = 8.5 units
Thus, the required value of OK is 8.5 units.
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Marco order 7 copie of a book online. He pay $3 for hipping. Which expreion repreent hi total cot? a. 7b3. B. 7-3b. C. 7b-3. D. 73
The expression that allows us to know the total cost Marco's seven books is
C. 7b-3What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
If the order is for 7 books, then the cost of only 7 books is expressed as:
TC = 7b
Where "b" is the unit cost for each book.
Now the shipment of these is $3, then the final expression that will give us the cost is given by:
7b - 3 option C
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Jaime Reparte su fortuna de la siguiente manera a Rosa le da el 28% de la fortuna,a Maria el 32% y a Fidel los 160 soles restantes ¿ de cuanto fue la Fortuna?
Jaime's total fortune was 4. Rosa received 28% of the fortune which is 4 x 28% = 1.12, Maria received 32% of the fortune which is 4 x 32% = 1.28 and Fidel received the remaining 160 soles.
The fortune of Jaime can be calculated with the following formula:
F = 28% x F + 32% x F + 160
Where F is the total fortune.
Therefore, to find the total fortune we need to solve the equation and we do this by multiplying both sides of the equation by F:
F = 28% x F + 32% x F + 160
F x 100% = 28% x F x 100% + 32% x F x 100% + 160
F x 100% = 28F + 32F + 160
100F = 28F + 32F + 160
100F - 60F = 160
40F = 160
F = 160 ÷ 40
F = 4
Therefore, Jaime's total fortune was 4. Rosa received 28% of the fortune which is 4 x 28% = 1.12, Maria received 32% of the fortune which is 4 x 32% = 1.28 and Fidel received the remaining 160 soles.
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Describe the translation needed to obtain the graph
Answer:
Shift down 4 units
Step-by-step explanation:
As you can see in the photo, the blue graph, 9^x -4, is 4 units down from the red graph, 9^x.
(a) how many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? (note: 062 is not a legit three-digit number)
There are 720 possible three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once. Thus, 6 x 5 x 4 = 120, and 120 x 6 = 720.
There are 720 possible three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once. This is because you can have 6 different choices for the first digit, 5 choices for the second digit, and 4 choices for the third digit. This means that for each of the 6 choices for the first digit, you can have 5 choices for the second digit, and for each of those 5 choices, you can have 4 choices for the third digit. This results in 6 x 5 x 4 = 120 possible combinations for each of the 6 choices for the first digit. Since there are 6 choices for the first digit, 120 x 6 = 720 possible three-digit numbers in total.
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Can someone help me with this
2. Divide 20xy^4 z^12 by 4x^3 yz^24
A) 5x^-2 y^3 z^12
B) 5x^-3 y^4 z^12
C) 5y^3/ x^2 z^12
D) 5x^3 y^4/ z^12
Answer:
C.
Step-by-step explanation:
When dividing, you can simplify the fraction by eliminating like terms. This is what the question is asking.
You have 4 types of terms. You have the constants, the x term, the y term, and the z term.
This equation can be rewritten as:
(20/4)*(x/x^2)*(y^4/y)*(z^12/z^24)
First, simplify the constants.
20/4=5
Next, do the same for the x term. Dividing variables with exponents can be tricky, but if you think about it as just taking the top exponent minus the bottom one, you should come out with a negative in this case. Whenever an exponent is negative, you can move that variable into the denominator, as shown below.
x/x^2 = x^(-1) = 1/x
Third, you would repeat the last step, except with the y term.
y^4/y = y^3
Then, repeat the same thing with the z term.
z^12/z^24 = z^(-12) = 1/z^12
Finally, we plug all that into our rewritten equation.
5*(1/x)*(y^3)*(1/z^12)
Simplify
(5*y^3)/(x*z^12)
Therefore the answer is C.
Madeline went to the store to buy some cherries. The price per pound of the cherries is $6.50 per pound and she has a coupon for $1 off the final amount. With the coupon, how much would Madeline have to pay to buy 2 pounds of cherries? Also, write an expression for the cost to buy
p
p pounds of cherries, assuming at least one pound is purchased.
Madeline have to pay to buy 2 pounds of cherries 5.50.
How much would Madeline have to pay ?To get some cherries, Madeline headed to the supermarket. The cherries cost $6.50 a pound, but she has a coupon that will take $1 off the final price.
Madeline have to pay to buy 2 pounds of cherries is;
The total cost of 5 pounds is:
2 * 6.50 - 1.00 = 5.50
Unit price times quantity equals total cost.
P pounds' total cost:
If Zoey purchases p pounds
She must pay 6.50 pts. = 6.50 pts.
She has a voucher for $44.75 off the total, therefore she will ultimately pay 6.50p - 1.00$ = 5.50
Madeline have to pay to buy 2 pounds of cherries 5.50.
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Which expression can be used to find the total amount in an account after three years, if the initial deposit is $2,000, and the annual simple interest rate is 2%?
A. 2,000 x 0.02 x 3
B. 2,000 x (2,000 x 0.02 x 3)
C. 2,000 x (2,000 x 2 x 3)
D. 2,000(1 x 0.02)^3
Answer:
Below
Step-by-step explanation:
Actually....NONE of those answers would show the total amount after 3 years
the correct option would be 2000 + (2000*.02 *3) a PLUS sign rather than a multiplication sign ....so the answer MIGHT be B if you transcribed it incorrectly
the probability that a student likes math is 0.7 and the probability that a student likes history is 0.2 . if only 10% of students like both math and history, what is the probability that a student chosen at random dislikes at least one of them?
The probability that a student chosen at random dislikes at least one of them is 0.2. Probability is the likelihood of occurrence of an event.
Probability a student likes math's = 0.7
Probability a student dislikes maths = 1 - 0.7 = 0.3
Probability a student likes history = 0.2
Probability a student dislikes history = 1 - 0.2= 0.8
Probability a student likes maths and history = 0.1
Probability a student dislikes maths = 1 - 0.1= 0.9
Probability a student dislikes at least one of them = probability he dislikes math's + Probability a student dislikes history- Probability a student dislikes math's and history = 0.3+0.8-0.9 = 0.2
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A plane travelled 1200 miles to its destination and then made the same return trip. The outbound trip was with a tailwind and took 3.5 hours. The return trip was into the same wind and took 4.5 hours. What was the speed of the plane in still air and the speed of the wind?
The speed of the plane in still air is 304.76 mph and the speed of the wind is 38.09 mph.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, a plane travelled 1200 miles to its destination and then made the same return trip.
Let x be the speed of the plane and y be the speed of the wind, both in miles per hour.
On its way to the destination, the plane takes 3.5 hours to travel 1200 miles. So the speed of the plane along with the tailwind is
1200/3.5
= 342.85 mph
Then, x+y =342.85 -------(I)
While flying back, it takes 4.5 hours to cover the same distance. So the speed of the plane against the headwind is
1200/4.5
= 266.67
So, x-y = 266.67-------(II)
Add equation (I) and (II), we get
2x=342.85+266.67
2x=609.52
x=304.76 mph
Substitute x=304.76 in equation (I), we get
y=38.09 mph
Therefore, the speed of the plane in still air is 304.76 mph and the speed of the wind is 38.09 mph.
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Three angles in triangle T have the ratio 1: 2: 3. What type of triangle is T
Answer: A scalene triangle
Step-by-step explanation: Since the angles in the triangle are not equal, then the sides aren't also equal. This makes it a scalene triangle (a triangle with unequal sides)
b) If 2 tan^2thita. cos^2thita =1 find value of thita
Answer:
The value of θ can be found by solving the equation 2tan2θcos2θ = 1. Using the identities tan2θ = (1 - cos2θ)/(1 + cos2θ) and cos2θ = (1 - tan2θ)/(1 + tan2θ), we get 1 = 2/(1 + cos2θ). Solving for cos2θ gives cos2θ = -1, which implies that tan2θ = 1. Thus, the value of θ is 45°.
Write five linear equations based on the directed graph below.
Given x5 = 15, determine the values of x1, x2, x3 and x4.
The solution is,
x1 = 5
x2 = -1
x3 = 3
x4 = 2
x5 = 1
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
x1 + x2 − 2x3 + 3x4 + 2x5 = 6
3x1 + 3x2 − x3 + x4 + x5 = 12
2x1 + 2x2 − x3 + x4 − 2x5 = 5
4x1 + 4x2 + x3 +0x4 − 3x5 = 16
8x1 + 5x2 − 2x3 − x4 + 2x5 = 29;
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A family wants to rent a car to go on vacation. Company A charges $75.50 and 14 cents per mile. Company B charges $45.50 and 8 cents per miles. How much more does Company B charge for x miles than Company A?
Answer:
Company A
Step-by-step explanation:
Company A charges $75.50 + $0.14x per mile.
Company B charges $45.50 + $0.08x per mile.
The difference in charges is:
($75.50 + $0.14x) - ($45.50 + $0.08x) = $30 + $0.06x.
Therefore, for x miles, Company B charges $30 + $0.06x more than Company A.
