The two consecutive odd numbers such that the difference between their reciprocals is of 2/99 are given as follows:
9 and 11.
How to obtain the numbers?The two numbers are odd numbers and consecutive, hence they are symbolized as follows:
n and n + 2. (as n + 1 is even).
Their reciprocals are given as follows:
1/n.1/(n + 2).The difference of their reciprocals is obtained as follows:
1/n - 1/(n + 2) = 2/99.
The least common factor of n and n + 2 is of n x (n + 2), hence:
(n + 2 - n)/[n(n + 2)] = 2/99
2/[n(n + 2)] = 2/99.
As the numerators are equal, we take the denominators to solve for n as follows:
n(n + 2) = 99.
n² + 2n - 99 = 0.
(n - 9)(n + 11) = 0.
Applying the Factor Theorem, the solutions are given as follows:
n - 9 = 0 -> n = 9.n + 11 = 0 -> n = -11.We want the positive numbers, hence the numbers are:
n = 9 and n + 2 = 9 + 2 = 11.
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Determine which two numbers come next in the sequence 5,5,10,15,25, __, __
The two numbers that come next in the sequence 5,5,10,15,25, are 40 and 65.
How can the two numbers that come next in the sequence be calculated?To calculate this , You can figure it out by taking the first number, which is 5. However, since the previous number is 0, the sum is 5, and you proceed in the same manner.
5 + 5 = 10
(5 + 10) = 15
(10 + 15) = 25
(15 + 25) = 40
(25 + 40) = 65
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88 student said they watch TV everyday. This number represents 80% of the students body. What is the total number of students in the student body? And i need you to give me the part,whole,and percent
The total number of students in the student body is 110.
How many students are in the student body?Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.
In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.
In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.
Number of students in the student body = number of students that watch TV everyday / percentage
88 / 80%
= 88 / 0.8 = 110
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a company has issued 8% debentures of rs 10 each at a discount of 10% repayable after 10 years, find out the cost of capital
If a company has issued 8% debentures of INR 10 each at a 10% discount repayable after 10 years. then the cost of capital or pretax cost of debt is 8%.
What is pretax cost of Debt?A bond or other sort of financial instrument that is secured by collateral is referred to as a debenture. Debentures must rely on the issuer's trustworthiness and reputation for support because they lack a collateral backstop. Debentures are commonly issued by both businesses and governments to raise cash or money. The interest paid on these security can be termed as cost of Debt or pretax cost of Debt.
The pretax cost of debt is interest paid on debenture security without giving effect of corporate tax on the rate of interest to be yearly or as per terms and conditions attached to it.
When debt security issued on discount then the loss on issue of these debenture instrument shall also be form part of cost of security or cost of capital.
Thus the year one pretax cost of Debt capital will be Rs. 1 per debenture and 8% cost of debt.
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PLEASE HELP
All numbers less than 17 and greater than or equal to -8
Answer: C
Step-by-step explanation: it says that it's smaller or equal to x and x is smaller than 17
a line has a slope of 5. it passes through the points (-5, -1) and (x, 9). what is the value of x?
A line has a slope of 5. it passes through the points (-5, -1) and (x,9) than the value of x is -3
We are going to use the fact that when a line passes through two points : [tex](x1,y1) and (x2,y2)[/tex]
the slope is given by the following formula:
[tex]slope=y2-y1/x2-x1[/tex]
In the present case, the slope is 5 and the points are (-5, -1) and (x, 9)
Hence,
[tex]5=9-(-1)/x-(-5)[/tex]
[tex]5=10/x+5\\x+5=10/5\\x+5=2\\x=-3[/tex]
Thus, the value of x is -3 when it travels between the coordinates (-5, -1) and (x, 9).
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It cost the shoe factory $26.47 to make a pair of Purple Pedi running shoes. The mall sells them for $128.98. What is the percent mark-up?
If it cost the shoe factory $26.47 to make a pair of Purple Pedi running shoes and the mall sells them for $128.98 then 3.87 is the percent mark-up.
How much of a markup is that?The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.
Some individuals will inform you that a 5% markup equates to a markup of 5% of the price your customer pays. In your illustration, this is stating that you add a specific amount to your cost, $62, to arrive at a price of $P for your customer, and the amount you added is 5% of $P. This means that your cost of $62 is 95% of the price of P.
($128.98 - $26.47)/ $26.47
= 3.87.
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Factorize the expression, 10ab (a − 2b)³ +24ab² (3a − 6b)²
Answer:
226a³b² - 824ab³ + 984b⁴
Step-by-step explanation:
We can factorize the given expression by expanding the two binomials and then combining like terms.
First, expand the two binomials:
10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)
Then, combine like terms:
= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= 226a³b² - 824ab³ + 984b⁴
when a fraction has a small numerator and a bigger denominator what you notice about the percent
when a fraction has a small numerator and a bigger denominator, the percent would be a proper fraction.
What is percent?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.
As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol “%” represents it.
Therefore, When a fraction has a small numerator and a large denominator, it is a proper fraction.
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50 POINTSSS!!!!!! PLS HURRRYYYYY!!!!!!! A set of data includes 98 data points ranging from 0 – 160. If the data is split into classes with a range of 10 (1 – 10, 11 – 20, etc), and there are no values that fall in the class 81 – 90, what can you say about the data?
1 The mean of the data will not be between 81 – 90.
2 All the data lies below 80.
3 The relative frequency of the class 81 – 90 is 0.
4 The median could be in the range 81 – 90
Answer:
3
Step-by-step explanation:
Find the value of x .
Answer:
x = 45°
Step-by-step explanation:
x° + 45° + 90° = 180°
x° + 135° = 180°
x° = 180° – 135°
x° = 45°
i hope this helped
Finding area of composite figure
Answer:
73
Step-by-step explanation:
so basically this process is rather easy, okay what u have to do is find the area but since u cant u just have to try your best and go over the answer with a friend, oh you have none? Sorry for assuming, so just ask siri if you have 0 friends, the formula should look a little like this:
A=l*w or A=b*h
which than u would have to add up the circumference (sorry for not mentioning that earlier) so the new formula would be a little like this
A+C=
than thats your answer (it should be 12.)
5+1r-2=9
Please explain step by step
Answer: 6
Step-by-step explanation:
A physically active adult weighing 170 pounds needs to consume about 2815 calories per day in order to maintain his or her weight. A nutritionist recommends that no more than 30% of those calories should come from simple sugars What is the maximum number of calories per day that should come from simple sugars?
Answer:
844.5 calories.
Step-by-step explanation:
If a physically active adult weighing 170 pounds needs to consume about 2815 calories per day in order to maintain his or her weight, and a nutritionist recommends that no more than 30% of those calories should come from simple sugars, the maximum number of calories per day that should come from simple sugars is:
2815 calories * 30% = <<281530.01=844.5>>844.5 calories
So, the maximum number of calories per day that should come from simple sugars is 844.5 calories.
Answer
844.5
Step-by-step explanation:
80+100=180
180÷100=1.80
1.80×2815=844.5
What is the value of m in the figure below? If necessary , round your answer to the nearest tenth of a unit
Using the concept of similar triangles, the value of m to the nearest tenth of a unit in the given figure is 6.71.
What are similar triangles?Triangles with the same geometry but different sizes are said to be similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two triangles that are similar have corresponding sides that are proportionate equal and corresponding angles that are similar.
From the concept of the similar triangle,
3/BD = BD/12
BD² = 12 × 3
BD² = 36
As triangle BDC is a right-angled triangle, use Pythagoras' theorem
m² = BD² + 3²
m² = 36 + 9
m² = 45
m = √45
m = 6.708
m ≈ 6.71
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10,14,18,22,26 find the 12 term of the sequence
Answer:
30,34,38,42,46,50,54,58,62,66,70
8. If you got 27 questions correct on
a test that has 32 questions, what
percent of the questions did you
correct on the test?
SUBJECT: GEOMETRY
Hello!! Could somebody please solve this for me asap, I'm having a bit of trouble? The problem is shown in the picture.
The length of the side CD is 5.195 cm and the Area of ΔABC is 31.17 cm²
How to use trigonometric ratios?
The basic trigonometric functions are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the given triangle ABC, we can see that it is a right angle triangle where ∠ACD = 60°, and as such, ∠CAD = 30°.
Thus;
BC/AC = tan 30°
6/AC = 0.5774
AC = 10.39cm
Thus;
CD/AC = cos 60
CD = 10.39 * 0.5
CD = 5.195 cm
Formula for area of a triangle is;
Area = ¹/₂ * base * height
Area = ¹/₂ * 6 * 10.39
Area = 31.17 cm²
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Drag and drop the numbers into the table to complete the table of values for the equation y=4x+9
These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.
What exactly is circumcenter?the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.
The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.
The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.
The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.
These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.
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An item on sale costs 80% of the original price. The original price was 33%
The sale price of the item is given by the equation A = $ 26.40
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the sale price of the item be represented as A
Now , the equation will be
The original price of the item = $ 33
An item on sale costs 80% of the original price
So , the sale price of the item A = 80 % x original price of the item
Substituting the values in the equation , we get
The sale price of the item A = ( 80 / 100 ) x 33
The sale price of the item A = 0.80 x 33
The sale price of the item A = $ 26.40
Therefore , the value of A is $ 26.40
Hence , the sale price is $ 26.40
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Solve the following quadratic equation for all values of xx in simplest form.
4(x^2-5)-1=
4(x
2
−5)−1=
\,\,3
3
The quadratic equation 4(x² − 5) − 1 = 3 has its solutions to be are √6 and -√6
How to determine the solutions to the equation?From the question, we have the following parameters that can be used in our computation:
4(x 2−5)−1=3
Express properly
This gives
4(x² − 5) − 1 = 3
Subtract -1 from both sides of the equation
So, we have the following representation
4(x² − 5) = 4
Divide both sides by 4
This gives
x² − 5 = 1
Subtract -5 from both sides of the equation
So, we have the following representation
x² = 6
Take the square root of both sides
x = ±√6
Hence, the solution is ±√6
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A parent function is a linear function of the form y=b true of false
False
Step-by-step explanation:The parent function is the simplest function within a family of functions that defines the general form of that family.
Parent Functions
Parent functions are given in terms of y and x, where y is the output and x is the input. In linear functions, b represents a constant, specifically the y-intercept. Since the form y=b does not have an input it cannot be the parent function of linear lines. The graph of y=b would be a horizontal line with no slope. This does not define the general form of most linear functions. Additionally, since the slope has been changed to zero, it is not considered the simplest form of linear functions.
Linear Parent Function
The true parent function of linear functions is y=x. This function is the simplest linear function and has no transformations. Additionally, when graphed it is a diagonal line that defines the general shape of lines.
To create new linear functions the parent function, y=x, can be transformed by changing the coefficient of x to change the slope or by adding a constant to shift the graph vertically.
Which radicals are already in the simplest form?
3 2/3 Divided by 1 2/7
Answer:
[tex]2 \frac{23}{27} [/tex]
I wish you luck in your assignments.
help me pls
Angle Relationships
As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.
Define angle.When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles. 360 degrees make up a circle. A 720° angle indicates that the object has completed two full rotations.
Here,
You can compare angles and take into account their relationships to other angles in addition to calculating degrees or radians.
Since we are comparing the position, measurement, and congruence of two or more angles, we refer to them as having "angle relationships."
For instance, two lines or line segments that cross each other create two pairs of vertical angles.
When a transversal intersects two parallel lines, complex angle relationships, such as alternating interior angles, matching angles, and so forth, result.
As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.
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Suppose $28,000 is deposited into an account paying 5.25% interest, which is compounded continuously. How much money will be in the account after 4 years if no withdrawals or additional deposits are made?
The formula for continuously compounded interest is:
A = P * e^(rt)
where:
A is the final amount
P is the initial amount (the principal)
r is the annual interest rate (in decimal form)
t is the number of years the interest is compounded
Substituting in the given values, we get:
A = $28,000 * e^(0.0525 * 4) = $28,000 * e^0.21 = $28,000 * 1.23 = $28000*1.23 = 34,540
Therefore, there will be $34,540 in the account after 4 years.
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Mario had 8 1/5
yards of ribbon for a project. Sue gave him 2 3/4 more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?
The closest to the number of yards of ribbon Mario had altogether will be ;
⇒ 11 yards
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Now,
Since, Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards
= 41/5 + 11/4
= (164 + 55) / 20
= 219 / 20 yards
= 10.95 yards
≈ 11 yards
Thus, Total ribbon for the project Mario have = 11 yards
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A mechanic charges $45 per hour for labor plus $55 for a computer diagnostic test. The mechanic charges a customer $595 to repair a vehicle. How many hours did the mechanic spend on the repair?
Answer:
The mechanic spent 12 hours on the repair.
Step-by-step explanation:
$595-$55=£540. £540 is the total of the amount the mechanic charges for an hour, MINUS the computer diagnostic testTo find out how many hours the mechanic spent on the repair, we have to do $540 divided by $45, which is 12.The mechanic spent 12 hours on the repair.
-50 POINTS- Already asked 3 times someone help pls. Don’t guess either.
Answer:
To find the coordinates of the point on the x-axis that is reflected over the x-axis from the point P, you can use the formula (x, -y). In this case, the x-coordinate of point P is 4, so the x-coordinate of the reflected point will also be 4. The y-coordinate of point P is 7, so the y-coordinate of the reflected point will be -7. Therefore, the coordinates of the reflected point are (4, -7).
Use the decimals 2.49, 9.19, and 6.7 to write two different addition facts and two different subtraction facts.
The solution to the equations is
Addition : 2.49 + 6.7 = 9.19 ; 6.7 + 2.49 = 9.19
Subtraction : 9.19 - 6.7 = 2.49 ; 9.19 - 2.49 = 6.7
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the three decimals be represented as set x = { 2.49 , 6.7 , 9.19 }
Now , the addition facts are given by equations ,
2.49 + 6.7 = 9.19 be equation (1)
6.7 + 2.49 = 9.19 be equation (2)
And , the subtraction facts are given by the equations ,
9.19 - 6.7 = 2.49 be equation (3)
9.19 - 2.49 = 6.7 be equation (4)
Hence , the equations are solved
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Which symbol makes the number sentence true?
-2.5O 10/4
A. <
B. >
C. =
Answer: I'm sorry if it's wrong I'm pretty sure it's ≥ if not I'm sorry
Step-by-step explanation: