By using the unitary approach to answer the given question, we may conclude that total 28 + 40 = $68.
Unitary method: what is it?The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. something has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.
One package of chicken costs = $7
steaks cost = $4 per pound.
cost of 4 chicken = 4 * 7 < $28
cost of 10 steaks = 4*10 < $40
total 28 + 40 > $ 68
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In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology. All the students do at least one of the three subjects. 3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only. Find the number of numbers of students that do two subjects only exactly one subject at least two of the subjects Represent the information on a complete Venn diagram.
Number of students that do two subjects are 12.
Number of students that do only exactly one subject are;
For Art;
⇒ 14
For Chemistry;
⇒ 11
For Bio;
⇒ 8
Number of students that do at least two of the subjects are 15.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.
All the students do at least one of the three subjects.
3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.
Here,
Total students = 48
So, Number of students that do two subjects are = 4 + 3 + 5
= 12
And, Number of students that do only exactly one subject are;
For Art;
⇒ 24 - (3 + 4 + 3)
⇒ 14
For Chemistry;
⇒ 22 - (3 + 5 + 3)
⇒ 11
For Bio;
⇒ 20 - (3 + 4 + 5)
⇒ 8
Number of students that do at least two of the subjects are;
⇒ 3 + 3 + 4 + 5
⇒ 15
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prove that the value of the expression does not depend on the value of x. (x-5)(x+8)-(x+4)(x-1)
The value of the expression is -44 and thus does not depend on the value of x
What are algebraic expressions?An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.
They are also made up of mathematical or arithmetic operations, which includes;
MultiplicationSubtractionAdditionBracketParenthesesDivision, etcFrom the information given, we have that;
(x-5)(x+8)-(x+4)(x-1)
expand the bracket
x² + 8x - 5x - 40 - (x² -x + 4x - 4)
x² + 8x - 5x - 40 - x² + x - 4x + 4
collect like terms
3x - 3x - 40 - 4
add or subtract like terms
0 - 44
Hence, the expression does not depend o x
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The ratio of the four sides of a trapezoid is 2:1:1:1.$ The area of the trapezoid is 27*sqrt3. Find the length of the median of the trapezoid.
The length of the median = 6[tex]\sqrt{3}[/tex]
If we call the longer base "a" and the shorter base "b", then we know that:
a:b = 2:1
Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.
We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
We know that the area is 27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:
(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]
We also know that a:b = 2:1, so we can substitute that in:
(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]
Simplifying, we get:
3b^2 = 54 * [tex]\sqrt{3}[/tex]
So the length of the median (h) is b
= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]
= 6[tex]\sqrt{3}[/tex]
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round 3.967 to the hundredth place
Please Help me find the area of the figure round to the nearest hundredth nessary
Answer:
912 cm²
Step-by-step explanation:
Formula for area of triangle: 1/2bh
So you'll first multiply the base by the height of the triangle
48 x 38 = 1,824
Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)
1,824 ÷ 2 = 912
Answer the questions about the following polynomial.
8x³+6x-1
The expression represents a
term is
the leading term is
polynomial with
terms. The constant
, and the leading coefficient is
The expression represents a polynomial with three terms.
What is polynomial?A polynomial is an expression consisting of variables (often denoted by x, y, z, etc.) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can be used to express a wide range of algebraic equations, from simple linear equations to more complex equations. Polynomials can also be used to construct functions with properties that are useful for solving real-world problems.
The expression represents a polynomial with three terms.
The constant term is -1, and the leading coefficient is 8. The leading term is 8x³.
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In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
We have to given that;
In 2010, the population of a city was 237,000.
And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
We know that;
Where, A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
Hence, The population in 2015 is, =
A = 237,000(1 + 0.076)⁵
A = 341829.629
And, The population in 2020 =
A = P (1 - r)ⁿ
A = 341829.629 (1 - 0.047)⁵
A = 268704.047
So, Percent grow = (268704.047 - 237,000) / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
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Gcf of -28, 60, and 72
Answer:
4
Step-by-step explanation:
-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4
Answer: 12
Step-by-step explanation:
Therefore, the highest common factor of 60 and 72 is 12.
:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!
How do you know if a triangle is a 45 45 90 triangle?
The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.
A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
properties of 45°-45°-90°:
It's the only possible right triangle that is also an isosceles triangle, and it has the smallest ratio of the hypotenuse to the sum of the legs.It has the greatest ratio of the altitude from the hypotenuse to the sum of the legs.To know more about 45° 45° 90° triangle:
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Explain how finding the area of a
rectangle with whole-number side lengths compares to finding the are
of a rectangle with fractional side lengths.
The area of rectangle with side whole number = ab sq. units,
and area of rectangle with fraction side = ac/bd sq. units.
What is rectangle?A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.
Given to find the area of rectangle,
Area of rectangle is given by product of length and width.
A = l x b
Let the dimensions of a rectangle are all whole numbers, a by b
Area = a x b
A = ab sq. units
another rectangle with dimensions all fractions say, a/b by c/d .
Area = a/b x c/d
A = ac/bd sq. units
In all situations, the area of the rectangle must be calculated by multiplying its length and breadth.
Hence the area of rectangle is product of length to width in both cases.
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One year ago, Farid spent $16,600 on a new pizza oven for his restaurant, The Dough Zone.
He checked the value of his oven online and discovered it is worth $15,770 today. The
website also predicts that the oven's value will continue to decrease each year.
Write an exponential equation in the form y = a(b)* that can model the value of the pizza
oven, y, x years after purchase.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Exponential equation in the form y = a(b)* that can model the value of the pizza oven, y, x years after purchase is y = 16000(0.985625)ˣ.
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The exponential equation is y = a(b)ˣ
The value of y = 15770, a = 16000 and x = 1
b = 0.985625
y = 16000(0.985625)ˣ
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Ben wants to buy a binder and some penicals from the school store.binders coast 2.25 each of the pencials coast 0.75 each.how much will it coasg ben to buy 1 binder and P penicals
The total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Cost of a binder = 2.25
Cost of a pencil = 0.75
We have to find the total cost for Ben to buy 1 binder and P pencils.
Cost of 1 binder = 2.25
Cost of P pencils = 0.75 × P = 0.75 P
Total cost of 1 binder and P pencils = 2.25 + 0.75 P
Hence the total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.
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Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio
The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.
Now, According to the question:
What is meant by ratio?
When expressed in numbers or amounts, a ratio is a relationship between two things. For example, if a room contains ten boys and thirty girls, the boy-to-girl ratio is 1:3, or one to three.A ratio, or getting rationed, on the occurs when replies to a tweet vastly outnumber likes or retweets. This means that people are reacting negatively to the tweet's content.It usually means that your comment has received more replies than likes. This implies that there are more people who disagree with your comment than agree with it.Therefore, simplifying the equation then we get,
if you take the ranges (y) and subtract one from the other you get 0.42.
(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42
(23.26 - 22.84)/(3 - 2) = 0.42
(23.68 - 23.26)/(4 - 3) = 0.42
Hence, The common difference is 0.42
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The perimeter of a square is 48. If the perimeter is 4 times than before then find the number of times the area becomes of what it was before.
Answer:
12?
Step-by-step explanation:
Lowkey don't understand the last part of your q but if it's 4 times then if the original was 12 48 is four times bigger
Use the quadratic formula to find the solutions to the equation y = 5x² - 9x + 3.
What are the zeros of the equation?
On solving the provided question, we can say that the quadratic equation is y = 5x² - 9x + 3 this quadratic equation can not factorized further
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is
y = 5x² - 9x + 3
this quadratic equation can not factorized further
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Help me pls I’m struggling and I can’t solve it
The perimeter of the rectangle is 4y + 6 (cm).
How can the perimeter equation be found?All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.
The diagram shows a rectangle. All measurements are in centimetres an expression in terms of y, for the perimeter of the rectangle.
The perimeter of the rectangle is
2(y+3)+24
=2y + 6 + 2y = 4y + 6 (cm)
{ the perimeter:
2 * width + 2 * Length}
The perimeter of the rectangle is 4y + 6 (cm).
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Use algebra tiles to solve 2x + 1 = 9 on IXL
Answer: 4
Step-by-step explanation:
1. Question: 2x+1=9
2. Subtract 1 from the 9
Answer to step 2: 2x=8
3. Divide 8/2 (4x2)
4. Answer: x=4
Answer: X= 4; look below for the explanation of algebra tiles
Step-by-step explanation: First, we need to determine the value of x. We can use the rule of inverse operations. So, the opposite of addition is subtraction, and the opposite of multiplication is division. Now, using that, we start with the inverse operations of 1 + 9. That'd be 9 - 1. So, that's 8. Now, according to the order of inverse operations, we divide the 2 by 8. So, 8 divided by 2 is 4. Therefore x = 4.
Now, using the tiles, we need to get 8 tiles, + 1 tile, which should get you your answer. I hope this helped!
. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western)
mean of the sampling distribution of the difference in sample proportions is 0.36.
Which approach is most likely to result in a random sample of your class's members?The best method for the random sampling will be to write the students' names on paper and pick them out of a hat, as each student will have an equal chance of being chosen.
22% of the population of eastern grey squirrels weigh more than 0.5 kg.
36% of the population of western grey squirrels weigh more than 0.5 kg.
Eastern grey squirrel sample size is 60.
There were 120 western grey squirrels in the sample.
Required:
The difference in sample proportions' mean of the sampling distribution (eastern minus western)
The difference of the mean yields the mean of the difference.
Mean = p1 - p2 is the sampling distribution's average for the difference in the sampling proportion from two populations.
Where;
p1 = 22% of the eastern grey squirrel, which equals 0.22.
p2 = 36% of the western grey squirrel, which equals 0.36.
Therefore;
p1 - p2 = 0.22 - 0.36 is the mean.
The right answer is (E) 0.22 - 0.36.
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1. Are the triangles shown below similar? Explain.
Answer:
Step-by-step explanation:
These are the tests for similar triangles:
AA - if 2 pairs of corresponding angles are equal.
SSS - if corresponding sides have the same ratio.
SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.
This diagram does not indicate any of these relationships exist.
Therefore the triangles are not similar.
Jared’s monthly income is 4500 Jared spend 11%of his income on grocies
Answer:
Jared's groceries = 495
Step-by-step explanation:
We calculate 11% from Jared monthly income:
11% x 4500 = 495
Jared's groceries = 495
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The average scores on Mrs. Wilson's test and Mr. Lewandowski's test were normally distributed on the last Algebra 2 test they gave. The average in my class Mrs. Wilson's class, was 86 with a standard deviation of 2. The average in my friend's class, Mr. Lewandowski's class was an 82 with a standard deviation of 2. If I made an 88 on the test and my friend made an 85 on their test, who had the better score relative to the rest of their class?
You had a better score relative to the rest of your class.
To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.
A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.
On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.
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Hi, please help ! (see image)
Answer:
R = 144400000/59 [this is a fraction]
please help me
please help me
What is the solution of 2x^2 3x 5 0?
Answer: The answer is 10x2
Step-by-step explanation:
Thirty eight students are going on a field trip. Parents will drive. Each car can hold 4 students along with the driver. How many cars will be needed?
Answer: you will need 8 cars. 4 can go into 7 evenly so you will have to left over. So 8 cars will be necessary.
Step-by-step explanation: divide 30 by four which equals 7.5 so we can just round up and say we need 8 cars
To determine how many cars are needed to transport 38 students, we need to divide the total number of students by the number of students that can fit in each car.
According to the problem, each car can hold 4 students and a driver. Therefore, the total number of people that can fit in one car is 4+1 = 5.
To transport 38 students, we need to divide 38 by 4 to find the number of cars needed to transport all the students.
38 ÷ 4 = 9 remainder 2
This means that 9 cars can transport 36 students (9 cars x 4 students per car), but we still have 2 students left.
Therefore, we need an additional car to transport the remaining 2 students.
In total, we need 10 cars to transport all 38 students.
Abdul made $162 for 9 hours of work.
At the same rate, how much would he make for 12 hours of work?
Answer:218
explanation: 162 divided by 9 = 18 and 18 multiplied by 12 =218
50 POINTS!!!
I NEED STEPS
Answer:
[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]
Rewrite the third fraction:
[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]
Apply the difference of two squares to the denominator of the third fraction:
[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]
Therefore the expression can be written as:
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).
Adjust the fractions based on the LCM:
[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]
[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]
Factor out 3 from the numerator:
[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]
Cancel the common factor (a + 6):
[tex]\implies \dfrac{3}{a-6}[/tex]
Therefore:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
What quadrant does (-a,b) belong
Coordinate (-a , b ) belongs to second quadrant.
What is a Quadrant?The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle. The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.
"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."
Given, Coordinate ≡ (-a , b)
1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.
2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.
3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.
4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.
Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.
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An office manager is planning to set up three computer workstations
and a file cabinet in a space that is 27 feet wide. The file cabinet takes up
3 feet. What is the width of the space available for each computer work
station?
PLEASE HELP
What does ∧ and ∨ mean in math?
The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .
These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.
We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.
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