Answer:
The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:
(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i
= 20 - 8i + 15i - 6i^2
= 20 + 7i - 6(-1)
= 26 + 7i
So the answer is (4) 26 + 7i.
I believe the answer is (d) 26 + 7i.
Factorise:
(a - 2b)^3 + (2a - b)^3
Answer:
Step-by-step explanation:
To factorise the expression, we can use the factor theorem which states that if a polynomial p(x) has a factor (x - r), then p(r) = 0.
We can use this theorem to find the factors of the polynomial expression:
(a - 2b)^3 + (2a - b)^3
We can write (a - 2b)^3 as (a - 2b)(a^2 - 4ab + 4b^2). Using the factor theorem, we see that:
(a - 2b)(a^2 - 4ab + 4b^2) = 0 when a = 2b
Similarly, we can write (2a - b)^3 as (2a - b)(4a^2 - 4ab + b^2). Using the factor theorem, we see that:
(2a - b)(4a^2 - 4ab + b^2) = 0 when a = b/2
Now we have two equations: a = 2b and a = b/2, which we can use to solve for a and b in terms of each other. We see that:
a = 2b = b/2
Multiplying both sides by 2, we get:
2a = b
We can substitute this back into the original expression:
(a - 2b)^3 + (2a - b)^3 = (a - 2(2a))^3 + (2a - (2a))^3 = (-3a)^3 + (0)^3 = -27a^3
So the factorised form of the expression is:
(a - 2b)^3 + (2a - b)^3 = -27a^3.
Work Shown:
Use the sum of cubes factoring rule
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
In this case,
x = a-2by = 2a-bSo,
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
(a-2b)^3 + (2a-b)^3 = (a-2b+2a-b)((a-2b)^2 - (a-2b)(2a-b) + (2a-b)^2)
(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-ab-4ab+2b^2) + (4a^2-4ab+b^2))
(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-5ab+2b^2) + (4a^2-4ab+b^2))
(a-2b)^3 + (2a-b)^3 = (3a-3b)(a^2-4ab+4b^2 - 2a^2+5ab-2b^2 + 4a^2-4ab+b^2)
(a-2b)^3 + (2a-b)^3 = (3a-3b)(3a^2-3ab+3b^2)
(a-2b)^3 + (2a-b)^3 = 3*3(a-b)(a^2-ab+b^2)
(a-2b)^3 + (2a-b)^3 = 9(a-b)(a^2-ab+b^2)
The answer has been fully confirmed with WolframAlpha.
You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season
The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.
What is the percentage?The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.
Here,
Total number of students = 93 + 31 + 36 + 54 = 214
The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%
Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%
Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.
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what does x+y=mb mean
Answer: The equation "x + y = mb" represents a linear equation in two variables, x and y. In this equation, m is a constant and b is another constant or a known value. The equation states that the sum of x and y is equal to the product of m and b.
This equation can be used to model a variety of real-world situations where two quantities are related and their sum is equal to a constant value. For example, it could represent the amount of money saved by two people, where x and y are the savings of the two people and mb is the total amount of money saved.
To solve for x and y, we can use either substitution or elimination method, or any other method for solving systems of linear equations. The values of x and y that satisfy the equation "x + y = mb" are called the solutions of the equation.
Step-by-step explanation:
Claudia records the hours is been studying and a test scores for five test
The correlation coefficient when Claudia records the hours she spent studying and her test scores for 5 tests is 0.85. This is a strong positive correlation.
How to explain the correlationAny statistical association between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.
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Claudia records the hours she spent studying and her test scores for 5 tests.
What is the correlation coefficient?
-0.85-0.840.840.85
What is the strength of the model?
A fruit juice recipe calls for 5 parts orange juice and 6 parts pineapple juice. Which proportion can be used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice?
30 over 21 equals j over 100
6 over 5 equals j over 21
6 over j equals 5 over 21
5 over 6 equals j over 21
For given ratio of orange juice and pineapple juice i.e. 5/6, proportion used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
What exactly is a ratio?
Fractions are commonly used to describe ratios and proportions. A ratio is demonstrated when a fraction is expressed as a:b, whereas a percentage indicates that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.
We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.
As a result, when b is larger than zero, the ratio, such as a:b, defines the relationship between two variables. For example, the 2:4 ratio is expressed as 2:4 = 1:2.
Now,
Given that In recipe ratio of orange juice / pineapple juice =5/6
then to make a recipe with 21 L of pineapple juice, the orange juice (j)
needed will be
5/6=j/21
j=17.5 L
hence,
proportion used to find the amount of orange juice, j will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
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Answer: its D
Step-by-step explanation:
pls i belieive most of yall are npcs
Help, please thank you, and have a wonderful day
3ab2 +1
3a²b-1
(a = 2 ; b = -2)
EVALUATE THE EXPRESSION
Answer:
3ab2+1 = -23
3a^2b-1 =-25
Step-by-step explanation:
A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. Find the probability that of the 4 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.
The probability that at least 1 of the 4 cards drawn is a face card is 0.6.
How to find probability of 4 cards drawn?A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.
Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.
A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:
P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).
The likelihood that none of the four draws will produce a face card is:
P(no face cards are present) = (10/13)4 = 0.432
As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:
P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568
The chance, rounded to one decimal place, is roughly 0.6.
Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.
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Consider the line 9x-8y=-9.
Find the equation of the line that is parallel to this line and passes through the point (−3, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 4).
Equation of parallel line:
Equation of perpendicular line:
1
=
X
0=0
5
Question is attached below!
Thanks! :)
The parameters for the home mortgage, and the monthly payment, PMT, for the mortgage are as follows;
Part 1;
P = $175,000, APR = 7%, n = 12, Y = 30
Part 2;
The monthly payment for the mortgage, PMT ≈ $1,164.28
What is a mortgage?A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default
Part 1
The value of the mortgage = $175,000
The fixed Annual Percentage Rate, APR = 7%
The duration of the payment = 30 years
The principal amount of the mortgage, P = $175,000The annual percentage rate, APR = 7% = 0.07The number of payment (periods), per year, n = Monthly = 12The number of years of the loan, Y = 30Part 2; The monthly payment PMT loan formula can be presented in the following format;
[tex]PMT = \frac{P\times \frac{APR}{n} }{1-\left(1+\frac{APR}{n}\right)^{(-n\cdot Y)} }[/tex]Therefore;
[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]
The monthly payment for the mortgage is, PMT ≈ $1,164.28
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Solve: 6(x + 5) = -2(x-3)
Answer:
Step-by-step explanation:
6(x+5) = 6x+30
-2(x-3)=-2x+6
6x+30=-2x+6
8x+30=6
8x=-24
x=-3
Answer: x = -3
Step-by-step explanation:
6(x + 5) = -2(x-3)
1. Distribute: 6x + 30 = -2x + 6
2. Add 2 to both sides: 8x + 30 = 6
3. Subtract 30 on both sides: 8x = -24
4. Divide by 8 on both sides: x = -3
Sarah has 275 red beads and 3 times as many blue beads. She uses a total of 156 beads to make a bracelet. How many beads are left?
Answer: 994 beads
Step-by-step explanation:
Red Beads = 275
Blue Beads = 825 (275 x 3)
825 + 275 = 1100 beads (total)
1100 - 156 = 994 beads
PLEASEE HELPPP!!! 3 QUESTIONS
Consider the function below.
f(x)=8/x−6
What would be the output if the input is 8?
responses:
-1/4
-4
-8/14
-8/6
What is the average rate of change of the function f(x)=3x^2−5 over the interval [2, 6]?
responses:
-3
-48
-12
-24
The average mass of a certain type of microorganism is 2.4×10^−6
grams. What is the approximate total mass of 5,000 of these microorganisms?
responses:
-0.00012 g
-0.0012 g
-0.012 g
-0.12 g
A. The value of the function at x = 8 will be 4. Then the correct option is B.
B. The average rate of change of the function in the interval of [2, 6] will be 24. Then the correct option is D.
C. The total mass of 5,000 of these microorganisms will be 0.012 g. Then the correct option is C.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A. The function is f(x) = 8 / (x - 6), then the value of the function at x = 8 is given as,
f(8) = 8 / (8 - 6)
f(8) = 4
Then the correct option is B.
B. The function is f(x) = 3x² - 5, then the average rate of change of the function in the interval of [2, 6] is given as,
Average rate = [3(6² - 4²)] / (6 - 2)
Average rate = 24
Thus, the correct option is D.
C. The average mass of a certain type of microorganism is 2.4 × 10⁻⁶ grams. Then the total mass of 5,000 of these microorganisms is given as,
⇒ 2.4 × 10⁻⁶ × 5,000
⇒ 0.012 grams
Thus, the correct option is C.
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Question 10 of 20
What is the domain of the exponential function f(x)=3*-5?
O A. (-∞0, +00)
O B. (3,+00)
O C. (-∞0,-5)
O D. (-5,+00)
Answer: The answer is A. (-∞0, +00)
This is a sketch of y = sin x.
The vertex A is at (90°, 1).
Write down the coordinates of the vertex A of the curve with equation
a) y = sin x + 2
b) y=-sin x
Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.
EquationsThe vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:
A = (90°, 1 + 2) = (90°, 3)
Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).
b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:
A = (90°, -1)
Therefore, the coordinates of the vertex A of the curve y = -sin x are
(90°, -1).
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You deposit $9000 in an account earning 5% interest compounded continuously. The amount of money in the account after t years is given by A(t)=9000e^0.05t
How much will you have in the account in 14 years? $ Round your answer to 2 decimal places.
How long will you have in the account in 14 years? ______years. Round your answer to 2 decimals
How long does it take for the money in the account to double? ____ years. Round your answer to 2 decimal places
The amount of money which would be in the account after 14 years is; $18,123.77.
The number of years it'd take for the money to double is; 13.86 years.
What is the doubling time of the compound interest arrangement?Since the given model of the account is;
A (t) = 9000e^0.05t
After 14 years, it follows that; t = 14.
Therefore;
A (14) = 9000e^0.05(14)
A (14) = 9000 × 2.013752707
A (14) = $18,123.77.
Also, the doubling time implies that; A (t) = 18,000
Therefore, 18000 = 9000e^0.05t
2 = e^0.05t
0.05t = ln (2)
t = ln (2) / 0.05
t = 13.86 years.
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1. ESSENTIAL QUESTION How do you rewrite rational expressions to find sums and differences
The equation is simplified as a rational expression
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 a rational expression
Substituting the values in the equation , we get
And , A ratio of two polynomials is a rational expression. Two rational expressions with the same denominator can be added or subtracted by adding or subtracting the numerators, then writing the result over the shared denominator.
Firstly, we find the LCM of the denominator and then write each expression using the LCD. On simplifying the numerator by either adding or subtracting the values , we simplify the rational expressions
Hence , the rational equations are solved
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Write an equation to describe the sequence below. Use n to represent the position of a term
In the sequence, where n = 1 for the first term.
-25, -50, -100,...
Write your answer using decimals and integers.
a,
Blank 1:
Blank 2:
Submit
C
C
An equation to show the sequence is -25n.
What is a geometric series?When all the terms of the geometric sequence are added, than that expression is known as geometric series.
The sum of terms of a geometric sequence;
Now, lets suppose its initial term is , multiplication factor will be r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
The first term of sequence=-25
D= -50-(-25)
=-25
Now,
an = a + (n-1)d
=-25+(n-1)-25
=-25-25n+25
=-25n
Therefore, the answer of the sequence will be -25n.
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Examine the right triangle below. Let a = 15, b = 20, and c = 25. What is the
sin B=, rounded to the nearest hundredth?
The value of sin B rounded to the nearest hundredth is 0.80.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
The right triangle represented in the question is given below.
We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.
In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.
Sin B = AC / AB
Sin B = b / c
Sin B = 20 / 25
Sin B = 0.8
Hence the value of sine of B is 0.8.
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Find the equation for the line through the points (2,3) and (7,1)
Answer:
Step-by-step explanation:
m=3-1/2-7= -2/5
c⇒ -2
y=mx+c
y=-2/5x-2
please help me with this.
Following are the values of the functions -
1) f(a) = 8a - 4
2) f(a+h) = 8a+ 8h - 4
3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]
Describe function.An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.
To evaluate f(a), we simply substitute the value of "a" into the function:
1) f(a) = 8a - 4
To evaluate f(a+h), we substitute the value of "a+h" into the function:
2) f(a+h) = 8(a+h) - 4
f(a+h) = 8a+ 8h-4
To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then
3) [tex]\frac{f (a+h)-(a) }{h}[/tex]
[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]
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Samir made a scale drawing of a city. He used the scale 5 inches = 1 yard. What scale factor
does the drawing use?
Simplify your answer and write it as a fraction.
Answer:
the scale factor that Samir used in his drawing is 5/1.
Step-by-step explanation:
Here's a step by step explanation of how to find the scale factor of a drawing:
Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.
Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.
Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.
The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.
So, the scale factor that Samir used in his drawing is 5/1.
Determine the more basic function that has been shifted, reflected, stretched, or compressed q(x) = -1/x + 1
The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.
What do you understand by the team function?The transformation applied to f(x) to obtain q(x) is divided into several steps:
Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.
Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.
Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.
The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.
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composite functions homework
The composite function has its value to be g o h(x) = -20x^2 - 30x
How to determine the composite functionfrom the question, we have the following parameters that can be used in our computation:
h(x) = 4x + 6
g(x) = -5x
Using the above as a guide, we have the following:
g o h(x) = g(x) * h(x)
substitute the known values in the above equation, so, we have the following representation
g o h(x) = (4x + 6) * -5x
Evaluate
g o h(x) = -20x^2 - 30x
Hence, the value is g o h(x) = -20x^2 - 30x
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HELPPP PLEASE I NEED HELP
The rule A(x,y) ⇒ (-y,x) describes a transformation. The correct option is D.
What is a transformation of rotation?The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.
The transformation is described by the rule A(x,y) (-y,x). The right answer is D.
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The function f(x) = x³ +9 is one-to-one.
a. Find an equation for f1, the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¹(f(x)) = x.
a. Select the correct choice below and fill in the answer box(es) to complete your choice.
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
OA. f¹(x)=, for all x
O B. f¹(x)=, for x ≥
O c. f¹(x)=, for x‡|
x#
OD. f¹(x)=, for xs
Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.
What is functio ?
Function can be defined in which it relates an input to output.
Given function ,
The function f(x) = x³ +9 is one-to-one.
To find the inverse function f1, we need to switch the roles of x and y in the equation for f(x). So, we have:
y = x³ + 9
Next, we need to solve for x in terms of y:
x³ + 9 = y
x³ = y - 9
x = (y - 9[tex])^{(1/3)}[/tex]
So, the inverse function is:
f1(y) = (y - 9[tex])^{(1/3)}[/tex]
To verify that f1 is the correct inverse function, we need to show that f(f1(y)) = y and f1(f(x)) = x:
f(f1(y)) = f((y - 9[tex])^{(1/3)}[/tex] = (y - 9[tex])^{(1/3)}^3[/tex] + 9 = y - 9 + 9 = y
And:
f1(f(x)) = f1(x³ + 9) = (x³ + 9 - 9[tex])^{(1/3)}[/tex] = [tex]\mathrm{ x^3^{(1/3)}}[/tex] = x
Therefore, Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.
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In a new study, Dr Matti Uhari and colleagues at the University of Oulu in Finland, randomly gave 857 healthy children in daycare centers xylitol in syrup, gum or lozenge form, or a placebo gum, syrup or lozenge in five doses per day for 3 months. According to a report in the October issue of the Journal of Pediatrics, the incidence of ear infections were reduced by 40% in children given xylitol chewing gum, 30% in those given syrup and 20% in those given lozenges when compared to children give a placebo. a) is this an observational study or a randomized experiment? b)If this is an experiment, what are the 3 criteria in this case? c) What are the explanatory and response variables? d)If it is an experiment, diagram the randomized comparative experiment.
(a) Randomized experiment, (b) There are three criteria for a randomized experiment
a) This is a randomized experiment.
b) The three criteria for a randomized experiment are:
Random assignment, the children were randomly assigned to the xylitol or placebo group.
Control group, a placebo group was used as a control.
Manipulation, the children were given different forms and doses of xylitol or placebo.
c) The explanatory variable is the form and dose of xylitol or placebo given to the children. The response variable is the incidence of ear infections.
d) Diagram of the randomized comparative experiment:
Population of healthy children in daycare centers
↓
Random assignment to xylitol or placebo group
↓
Intervention group: given xylitol in syrup, gum or lozenge form
Control group: given a placebo in gum, syrup or lozenge form
↓
Comparison of incidence of ear infections in intervention and control groups
↓
Analysis of results to determine the effectiveness of xylitol in reducing ear infections.
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3. If an angle measures 2π radians, what is the measure of the angle in degrees?
Answer:
360 degrees
2 pi radians, means you have 2 pi of something and they are radians. It is the same 360 degrees. A radius is the line from the side of the circle to the center.
Reason: pi radians is 180 degrees. Double each value to find that 2pi radians is 360 degrees. It's a full revolution of a circle. Use a unit circle if necessary.
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 4x+10 and MP = 9x-5
X =
Answer:
x=5 and LN= 30, MP= 40
Step-by-step explanation:
Add like terms to both sides of the equation and you will get your answer
Students are reading a book that has 280 pages. Nora already read 30% of the book. She is choosing between two options to finish reading the book.
Option 1: read 25% of the remaining pages each night
Option 2: read 28 pages each night
Which option should Nora use to finish the book in the least amount of time?
Explain your reasoning.
Answer:
Step-by-step explanation:
To determine which option is faster, we need to determine the total number of nights required for each option.
First, let's find the number of pages Nora still needs to read by subtracting the number of pages she's already read from the total number of pages: 280 pages * 30% = 84 pages
So, Nora still needs to read 280 pages - 84 pages = 196 pages.
For Option 1, Nora would read 25% of the remaining pages each night, so the number of pages she reads each night would be: 196 pages * 25% = 49 pages
The total number of nights required would be 196 pages / 49 pages/night = 4 nights.
For Option 2, Nora would read 28 pages each night, so the total number of nights required would be 196 pages / 28 pages/night = 7 nights.
Since 4 nights is less than 7 nights, Nora should choose Option 1 to finish reading the book in the least amount of time.
