The result for the division of the fractions in this problem is given as follows:
[tex]\frac{x^3 + 6x^2 + 7x + 18}{(x - 3)(x + 9)(x^2 - 9)}[/tex]
How to divide two fractions?The division of two fractions is given by the multiplication of the first fraction by the inverse of the second fraction.
The first fraction in this problem is composed by the sum of two fractions, as follows:
[tex]\frac{x + 5}{x + 9} + \frac{x + 7}{x^2 - 9}[/tex]
Applying the subtraction of perfect squares, we have that:
x² - 9 = (x - 3)(x + 3).
The second fraction is given as follows:
(x² - 9)/(x + 3).
Considering the factoring of x² - 9, the second fraction is given as follows:
x - 3.
Hence the inverse is of:
1/(x - 3).
Then the entire quotient is given as follows:
[tex]\left(\frac{x + 5}{x + 9} + \frac{x + 7}{x^2 - 9}\right) \times \frac{1}{x - 3}[/tex]
The addition of the two fractions is given as follows:
[tex]\frac{(x + 5)(x^2 - 9) + (x + 7)(x + 9)}{(x + 9)(x^2 - 9)} = \frac{x^3 + 6x^2 + 7x + 18}{(x + 9)(x^2 - 9)}[/tex]
Applying the multiplication by x - 3 in the denominator, the quotient is given as follows:
[tex]\frac{x^3 + 6x^2 + 7x + 18}{(x - 3)(x + 9)(x^2 - 9)}[/tex]
Missing InformationThe problem asks for the quotient between the two fractions.
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what is the price per pound for chicken and the price per pound of the fish the food stand purchased?
One pound of chicken will cost ${x/y} and one pound of fish will cost ${B/A}.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the price per pound for chicken and the price per pound of the fish.
Assume that the {y} pound of chicken costs ${x}. Now, we can write that -{y} pound of chicken costs ${x}
{1} pound of chicken will cost ${x/y}
Assume that the {A} pound of fish costs ${B}. Now, we can write -{A} pound of fish costs ${B}
{1} pound of fish will cost ${B/A}
Therefore, {1} pound of chicken will cost ${x/y} and {1} pound of fish will cost ${B/A}.
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Write all names that apply to each number
5.45
A pencil case contains 8 blue and 4 green
pens.
A pen is chosen at random and not
returned, and then a second pen is chosen
at random.
Copy and complete the tree diagram.
What is the probability that the first pen is
green and the second pen is blue?
Give your answer as a fraction in its
simplest form.
Help me with this question it’s bugging me
The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.
What is probability and step by step explanation?Probability is a measure of the likelihood of an event occurring, represented as a decimal or fraction between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.(Probability of choosing a green pen on the first draw) x (Probability of choosing a blue pen on the second draw, given that a green pen was chosen on the first draw)= (4/12) * (8/11)= (1/3) * (8/11)= 8/33So the probability is 8/33. This is already in its simplest form as the numerator and denominator share no common factors.To learn more about probability refer:
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The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.
What is probability and step by step explanation?Probability is a measure of the likelihood of an event occurring, represented as a decimal or fraction between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
(Probability of choosing a green pen on the first draw) x (Probability of choosing a blue pen on the second draw, given that a green pen was chosen on the first draw)
= (4/12) * (8/11)
= (1/3) * (8/11)
= 8/33
So the probability is 8/33. This is already in its simplest form as the numerator and denominator share no common factors.
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Car x travel 120 mile on 11 gallon of ga. Car y travel 100 mile on 9 gallon of ga which car get the better ga mileage
Car Y offers you more mileage than Car X per gallon.
The mileage of a vehicle is the number of miles that it can travel using one gallon or litre of fuel or gasoline.
To find the mileage per gallon, we find the distance that each car can travel using 1 gallon of gasoline.
For Car X,
Mileage = No. of miles/No. of gallons
= 120/11 = 10.909
For Car Y,
Mileage = No. of miles/No. of gallons
= 100/9 = 11. 11
Therefore, marginally, Car Y has the better mileage.
Thus, Car Y offers you more mileage than Car X per gallon.
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Given: C is the midpoint of NB; C is the midpoint of MA
Prove: ABC is congruent to NMC
STATEMENTS
tina also worked out the total number of points scored by the 16 students in the game
The mistake in Tina's total of numbers is she written the product of 0 and 1 as 1 instead of 0.
What is total?A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.
Given that, Tina also worked out the total number of points scored by the 16 students in the game.
(0×1)+(1×3)+(2×5)+(3×4)+(4×3)=0+3+10+12+12=37
Tina made a mistake in her working to find the total number of points scored, she written the product of 0 and 1 as 1.
Therefore, the mistake in Tina's total of numbers is she written the product of 0 and 1 as 1 instead of 0.
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How much does 1 kg of butter cost at the rate shown in the picture? Butter: 454 kg & $3.39
Answer:
0.00746696035
Step-by-step explanation:
3.39/454 = 0.00746696035
Rounded that would only be 1 cent per kg. Hummmppp....
Which graph represents y=-2x
Answer:
The graph looks like the image below.
Step-by-step explanation:
-2x means that every time x increases by 1, y increases by -2.
When y increases by -2, y decreases by 2.
Hence, as the x-value increases by 1, the y-value decreases by 2.
Also, the graph goes through the point (0, 0) since when x=0, y=0:
y=-2x ==> 0 = -2(0)
to provide a comparison for evaluating the effects of a specific treatment, experimenters make use of a(n)
The evaluate the value of the expression a(n) is control condition.
Here we have given that to provide a comparison for evaluating the effects of a specific treatment, experimenters make use of a(n).
Here we know that when carrying out an experiment, then the control condition is set up to provide a baseline against which the result of the experiment can be compared.
Here we have to take the example that is when measuring the effects of a new medication, then the control group is usually set up and the members of the group are given a placebo.
Therefore this will not contain any of the active ingredients of the medicine and it acts as a way to evaluate the real effects of the medication.
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a bag contains eight real diamonds and seven fake diamonds. if eight diamonds are picked from the bag at random what is the probability that exactly 4 of them are real
The probability that exactly 4 of the 8 diamonds picked from the bag are real diamonds is 28/256 or 11.1%.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning the event is impossible and 1 meaning the event is certain to occur. Probability theory is used to make predictions and calculate the chances of different outcomes in order to make decisions. Probability theory can also be applied to understand the behavior of complex systems.
This is calculated by first determining the total amount of possible outcomes. Out of the 8 diamonds picked, there are 8C4 = 70 ways in which the 4 real diamonds can be chosen. With 8 real diamonds and 7 fake diamonds, the probability of a real diamond being chosen is 8/15, and the probability of a fake diamond being chosen is 7/15. Therefore, the probability of having exactly 4 real diamonds is 70 x (8/15)^4 x (7/15)^4 = 28/256.
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Determine zα for the following. (Round your answers to two decimal places.)
(a) α = 0.0089
(b) α = 0.09
(c) α = 0.707
Please explain where and how you got the answer.
Thank you.
The value of zα for the following is :
(a) α = 0.0089 is 2.37
(b) α = 0.09 is 1.34
(c) α = 0.707 is -0.545
zα is the inverse function of the standard normal CDF.
(a) Central limit c= 1-α
for α = 0.0089 , c=1-0.0089
∴ c=0.9911
Hence confidence level in percentage= 99.5%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.9911)
zα =2.37
(b) Central limit c= 1-α
for α = 0.09 , c=1-0.09
∴ c=0.91
Hence confidence level in percentage= 91%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.91)
zα=1.34
(c) Central limit c= 1-α
for α = 0.707 , c=1-0.707
∴ c=0.293
Hence confidence level in percentage= 29.3%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.707)
zα= -0.545
Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.
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PLEASE HELP ASAP!!!!!!
Keilantra has $660 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $488.20.
She buys 2 bicycle reflectors for $11.17 each and a pair of bike gloves for $19.05.
She plans to spend some or all of the money she has left to buy new biking outfits for $37.26 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Keilantra can purchase while staying within her budget.
a) An inequality that can determine x the number of outfits Keiland can purchase while staying within her total budget of $660 is 529.59 + 37.26x ≤ 660.
b) The inequality solution shows that x cannot be more than 3.
What is inequality?An inequality is a mathematical statement that two or more mathematical expressions are unequal or not equivalent.
Inequalities are depicted as follows:
Greater than (>)Greater than or equal to (≥)Less than (<)Less than or equal to (≤)Not equal to (≠).These inequality symbols are usually written between two numbers or algebraic expressions.
The total spending budget Keilantra has = $660
The cost of a new bicycle = $488.20
The cost of 2 reflectors = $22.34 ($11.17 x 2)
The cost of a pair of bike gloves = $19.05
The total costs for the above three items = $529.59
The unit cost of new biking outfits = $37.26
The number of outfits Keilantra can purchase = x
Inequality:529.59 + 37.26x ≤ 660
37.26x ≤ 660 - 529.59
37.26x ≤ 130.41
x ≤ 3.5
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Emma has been saving up to go on a big summer trip, visiting the United States and Russia. After working hard throughout the year, she has a total of £2500 in spending money.
The exchange rates are:
£ 1 = $ 1.28, and
$129.35 Rubles
Emma has also discovered that the maximum amount of money she can enter Russia with is 32 285 Rubles.
Assuming Emma wants as much cash as possible in Russia, how much should she spend while in the United States?
Emma has been saving up to go on a big summer trip, visiting the United States and Russia. Emma should spend $2951.46 while in the United States.
What is his savings?Generally, To maximize the amount of cash Emma has in Russia, she should spend all of her money in the United States before entering Russia. First, we convert the Ruble limit to USD:
32,285 Rubles / 129.35 =249.594 USD.
Next, we convert Emma's savings from pounds to USD:
£2500 x 1.28 = $3200.
Finally, we subtract the Ruble limit from Emma's total savings in USD: $3200 - $248.54 = $2951.46.
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Use a = 7 and b = 28 to work out the value of these expressions.
The first one is done for you.
a+b
ab
09
(a + b)²
=
||
11
35
The requried value of given expression when a = 7 and b = 28 is 125.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given expression,
(a + b)² = a² + b² + 2ab
We have,
a = 7 and b = 28
(7 + 28)² = 7² + 28² + 2 × 7 × 28
35² = 49 + 786+ 392
125 = 125
Thus, the requried value of given expression when a = 7 and b = 28 is 125.
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A large parallelogram is divided into four small parallelograms as shown. The areas of three of the four small parallelograms are labeled in the diagram. What is the area of the remaining small parallelogram
The width of the last little parallelogram, 10/3, is determined by the provided statement.
Rhombuses are parallelograms, right?Furthermore, despite the fact that this is never the case, every rhombus is considered to be a parallelogram. A quadrilateral is a form that is flat. They arrive in quartets. A parallelogram is formed by two opposing sides that are flat and proportional to one another. Parallelograms come in 4 distinct varieties, including 3 unique varieties. Rhombuses, triangular shapes, cubes, and squares are the four types.
The diagonal area products are equal.
Divide the two sides by 6 20/6 = x = 10/3 since 4*5 Equals 6 * x 20 Equals 6 * x
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The complete question is-
A large parallelogram is divided into four small parallelograms as shown. The areas of three of the four small parallelograms are labeled in the diagram. What is the area of the remaining small parallelogram?
Match the following vector fields with the verbal descriptions of the level curves or level surfaces to which they are perpendicular by putting the letter of the verbal description to the left of the number of the vector field.
Nonvisual language is used to describe the visual world verbally. It can lead people around a museum, help an audience member find their way around an artwork, or provide them access to the visual elements of a performance.
It was in 1981 when Dr. Margaret Pfanstiehl, founder and president of The Metropolitan Washington Ear Inc., and her husband Cody perfected the art and practice of verbal description.
Standard information found on a label, such as an artist's name, nationality, the title of the artwork, date, dimensions or size of the piece, media, and method, can be found in a spoken description as well. In addition, a vocal description can offer a broad overview of the work's subject matter and structural elements.
1. Lines
2. Planes
3. Hyperboloids
4. Lines
5. Spheres
6. Ellipsoids
7. Paraboloids
8. Hyperbolas
9. Ellipses
10. Hyperbolas
11. Circles
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please help me find the answer if u can thanks
Answer:
y = 4/3x - 1
Step-by-step explanation:
(3, 3) and (0, -1)
m = -1-3 / 0-3
m = -4/-3
m = 4/3
y = 4/3x + b
-1 = 4/3(0) + b
-1 = 0 + b
b = -1
y = 4/3x - 1
The equation _____ represents an additive relationship.
as one step in the statistical analysis of the effectiveness of the chw intervention, researchers examined differences in postnatal care use for mothers in 10 different regions. how could the researchers have increased the power of their analysis?
The researchers have increased the power of their analysis by increasing the sample size.
The number of subjects involved in a sample size is referred to as the sample size in market research.
Examine 15 randomly selected groups of subjects.
There are five main ways to increase the power of an experiment or study: increase the alpha level, decrease random error, conduct a one-tailed test, expand the sample size, or increase the effect size. Of these, only the first option, which increases the sample size, will increase power.
Thus, the researchers have increased the power of their analysis by increasing the sample size.
Complete question: As one step in the statistical analysis of the effectiveness of CHW intervention, researchers calculated the average percentage of postnatal care use found in 10 randomly selected groups of 50 mothers. How could the researchers have increased the power of their analysis?
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a toy company packages modeling clay in the shape of a rectangular prism with dimensions 6 inches by 1 inch by 1/2 inch. they want to change the shape to rectangular pyramid that uses the same amount of clay. determine 2 sets of possible dimensions for the pyramid.
Two sets of possible dimensions for the rectangular pyramid that uses the same amount of clay as the rectangular prism are 2 inches base and 1.5 inches height, and 3 inches by a 1-inch base and 1-inch height.
The volume of the rectangular prism is 6 inches * 1 inch * 1/2 inch = 3 cubic inches. To determine the possible dimensions for the pyramid, we need to find the dimensions that will give us the same volume.
One set of possible dimensions for the pyramid would be a base that is 2 inches by 2 inches, and a height of 1.5 inches. This would give a volume of 2 inches * 2 inches * 1.5 inches / 3 = 2 cubic inches, which is the same as the original rectangular prism.
Another set of possible dimensions would be a base that is 3 inches by 1 inch and a height of 1 inch. This would give a volume of 3 inches * 1 inch * 1 inch / 3 = 1 cubic inch, which is the same as the original rectangular prism.
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Find the perimeter of the shape, round to the nearest tenth.
(Will give brainliest for the quickest answer :))
Answer: The perimeter of the shape is approximately 18.0 feet.
Step-by-step explanation:
The shape you described is a triangle, with one side of 8 feet and two sides of 5 feet. To find the perimeter of a triangle, we add up all the side lengths:
Perimeter = 8' + 5' + 5'
Perimeter = 8' + 10'
Perimeter = 18'
Rounding to the nearest tenth:
18 feet is the same as 18.0 feet rounded to the nearest tenth.
So, the perimeter of the shape is approximately 18.0 feet.
Answer This Question Please!!!!!
Answer:
Step-by-step explanation:
none of these the corrct answer is 5
Consider the two equations below. Explain completely the similarities and differences in how you would solve each equation. Be clear and complete.
3^x=12 and x^3=12
The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:
x = log3(12)
The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:
x = ∛12
How does the equation compare?The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.
The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.
As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.
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Whether the function is even or odd
The given graph is not symmetric with respect to the y-axis. Hence, this is not even function.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
An example of a rule is a function, which produces one output for a single input.
If the graph of a function is symmetric with respect to the y-axis, then it is said to be an even function. Otherwise, it is odd function.
The given graph is not symmetric with respect to the y-axis. Hence, this is not even function.
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If 10% of 170 is 17, then 90% of 170 is 153.
By calculating, If 10% of 170 is 17, then 90% of 170 is 153 is true.
What is Algebraic expression ?
Algebraic expressions are mathematical phrases that combine numbers, variables, and operations (like addition, subtraction, multiplication and division). They provide a way to represent and analyze mathematical relationships. Examples of algebraic expressions include "3x + 5" and "6y - 3x".
Given expression,
10% of 170
10/100 * 170
= 17
which is equals to RHS
Then,
90% of 170
= 90/ 100 * 170
= 9*17
= 153
which is also equals to RHS .
And the yes the given expressions are true.
Hence, If 10% of 170 is 17, then 90% of 170 is 153 is true.
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HELPPP
What number would make (24, 45, c ) a Pythagorean triple, where c represents the hypotenuse? Be sure to show your work.
Answer: 51
Step-by-step explanation: 24^2+45^2=C
24*24=576
45*45=2025
576+2025=2601
Square root of 2601 is 51
Review the table of values.
Which description best fits the regression model for the data?
power model; y = 10.15x–0.68
exponential model; y = 12.80(0.78)x
logarithmic model; y = 9.98 – 3.85 ln x
quadratic model; y = 0.13x2 – 2.38x + 12.27
quadratic model; y = 0.13x2 – 2.38x + 12.27 is the best to fit the regression model for the data.
What is a Quadratic equation?ax2+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
For the given Dataset
Sum of X = 27
Sum of Y = 22
Mean X = 5.4
Mean Y = 4.4
Sum of squares (SSX) = 45.2
Sum of products (SP) = -42.3
Regression Equation = ŷ = bX + a
b = SP/SSX = -42.3/45.2 = -0.93584
a = MY - bMX = 4.4 - (-0.94*5.4) = 9.45354
ŷ = -0.93584X + 9.45354
Thus Given linear Equation is not the best fit
Since the graph is decreasing Option b and c are also not possible
Therefore, the best to fit the regression model for the data is the quadratic model; y = 0.13x2 – 2.38x + 12.27.
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7 less than the product of k and 43 is k
Step-by-step explanation:
so, write that down mathematically :
7 - k×43 = k
to bring k to only one side of the equation we add e.g. 43k to both sides (it is important to perform any operation on an equation always on both sides, otherwise the equality relation is destroyed)
7 - 43k + 43k = k + 43k
7 = 44k
k = 7/44
Complete the following statement. Use the integers that are closest to the number in the
middle.
<-√14<
The completed statement using the integers that are closest to the number in the middle is 3<-√14<4
The statement: <-√14< can be interpreted as the set of all real numbers that are less than the square root of 14, which is approximately 3.74166.
The integers closest to this number are 3 and 4, so the set of integers that are closest to the number in the middle can be represented as:
(-∞, 3) U (4, ∞)
The statement says that the value of the square root of 14, when multiplied by -1 (the square root of a negative number), is between 3 and 4. The closest integers to the value of the square root of 14 are -3 and -4.
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