Answer:
a. Exponential decay
b. f(x) = a (1 - r)^x
c. f(x) = 25(1 - 0.06)^x
d. 16 terms
Explanation:
a. Does this problem represent exponential growth or decay? How do you know?
Each day the number of terms that you know is less than the day before, so there is a decrease in the vocabulary terms memorized. It means that the problem represents exponential decay.
b. Which exponential formula below will you use for this problem? Why?
The formula for the exponential decay is:
[tex]f(x)=a(1-r)^x[/tex]Where a is the initial value and r is the rate of decay.
So, the formula that you will use is f(x) = a (1 - r)^x
c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.
The initial value is 25 terms and the decay rate is 6%, so the specific equation is:
[tex]f(x)=25(1-0.06)^x[/tex]d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.
Now, we need to replace the value of x by 7, so:
[tex]\begin{gathered} f(7)=25(1-0.06)^7 \\ f(7)=25(0.94)^7 \\ f(7)=25(0.6485) \\ f(7)=16.21 \end{gathered}[/tex]Therefore, you will remember 16 terms seven days later.
Unoccupied seats on flights cause airlines to loose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights. The sample mean and standard deviations are
x-bar =11.6 seats s=4.1 seats
Use Central Limit Theorem to help the company estimate its average number of unoccupied seats per flight over the past year.
The mean number of unoccupied seats per flight during the past year will lie between 11.15 and 12.05.
What is mean in mathematics?
There are many mean types in maths, particularly in statistics. Each mean serves to condense a specific set of data, frequently so that the general magnitude and sign of the data set can be better understood.
The arithmetic mean, also referred to as "arithmetic average," is a calculation that divides the total number of values in a data collection by their sum to get the central tendency of that set of numbers.
a) Calculations:
Degrees of freedom = n - 1 = 225 - 1 = 224
For 224 degrees of freedom and 90% confidence interval,
Critical t value = 1.652
Hence,
90% confidence interval will be:
[tex]11.6 \pm 1.652*4.1/\sqrt{225}[/tex]
[tex]11.6 \pm 0.45[/tex]
(11.15, 12.05)
b) Interpretation:
We are 90% confident that the population mean number of unoccupied seats will lie between 11.15 and 12.05
c) Caution with interpretation:
In this scenario, individual confidence interval should be calculated rather than mean number of unoccupied seats since we can't generalize this interpretation for individual flights.
d) To narrow a confidence interval, we can either increase the sample size or can decrease the confidence level.
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Complete question
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights (from text, p. 306, example 6.3; use NOSHOW excel file). Given the mean number of unoccupied seats for the 225 random flights is 11.6 and the standard deviation is 4.1, estimate μ, the mean number of unoccupied seats per flight during the past year, using a 90% confidence interval.
a. Calculations
b.Interpretation
c.Caution with interpretation
d.How to narrow a confidence interval
The net of a right triangular prism is shown below.
What is the surface area of the triangular prism?
The surface area of the triangular prism is 224 square units.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
Surface area = ( S₁ + S₂ + S₃) × Length
S₁ = 6
S₂= 8
S₃ = 2
L = 14
Surface area = ( 6+8+2)14
Surface area = 16(14)
Surface area = 224
The surface area of the triangular prism is 224 square units.
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A university has 10,000 students of which 45% are male and 55% are female. If a class
of 30 students is chosen at random from the university population, find the variance of
the number of male students.
The variance of the number of male students is 7.42 if the university has 10,000 students of which 45% are male and 55% are female.
What are the population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
P(male) = 45% = 0.45
P(female) = 55% = 0.55
Variance = SD²
Variance = nP(male)xP(male)
Variance = 30x0.45x0.55
Variance = 7.42
Thus, the variance of the number of male students is 7.42 if the university has 10,000 students of which 45% are male and 55% are female.
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pls be very specific with steps find x and y
Firstly, we want to start by drawing the triangles
We have this as follow;
For triangle HOT, we have;
We want to get the values of x and y firstly
Since both triangles are congruent, the order of the sides match
Hence, we have angle O and H equal
Thus, we have that;
[tex]\begin{gathered} 5x-1\text{ = 3x+ 17} \\ 5x-3x\text{ = 17+1} \\ 2x\text{ = 18} \\ x\text{ = }\frac{18}{2} \\ x\text{ = 9} \end{gathered}[/tex]Now, to find Y, we need the measure of angle N
Angle N is same as W which we already have as 5y+ 26
Substitute N for Y
Since all the angles of a triangle sum up to 180, we have it that;
[tex]\begin{gathered} 5x-1\text{ + 4x + 9 + }(5y\text{ + 26) = 180} \\ 9x+8+5y+26\text{ = 180} \\ 9(9)\text{ + 5y + 34 = 180} \\ 5y\text{ = 180-34-81} \\ 5y\text{ = 65} \\ y\text{ = }\frac{65}{5} \\ y\text{ = 13} \end{gathered}[/tex]Now, we want the measure of each of the angles;
1. W = N = 5y+ 26 = 5(13) + 26 = 91
2. H = O = 5x-1 = 5(9) - 1 = 44
3. Y = T = 4x + 9 = 4(9) + 9 = 45
=
The area of Desert A is five times the area of Desert B. If the sum of their areas is 600,000 square miles, find the area of each desert.
The area of Desert A is 500,000 square miles and the area of Desert B is 100,000 square miles.
What is area?
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Area of a square is side × side.
Let the area of Desert A = x square miles
and the area of Desert B = y square miles
Given that, the area of Desert A is five times the area of Desert B,
i.e. x = 5y ...(1)
and the sum of their areas is 600,000 square miles,
i.e. x + y = 600,000 square miles ...(2)
Putting equation (1) in (2), we get
5y + y = 600,000
or 6y = 600,000 or y = 100,000 square miles
Using equation (1),
x = 5 × 100,000 = 500,000 square miles
Hence, the area of Desert A is 500,000 square miles and the area of Desert B is 100,000 square miles.
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What is the value of p?
when a number is power to a number a, and it is also power to another number b we can apply the property
[tex](x^a)^b=x^{a\cdot b}[/tex]apply this to the expression above
[tex]\begin{gathered} x^{22}\cdot(x^{7\cdot3)} \\ x^{22}\cdot x^{21} \end{gathered}[/tex]continue by applying the property of a product between the same number as a base but with a different exponent
[tex]x^a\cdot x^b=x^{a+b}[/tex]apply this to the expression above
[tex]\begin{gathered} x^{22}\cdot x^{21^{}} \\ x^{43} \end{gathered}[/tex]the value of p is equal to 43.
9) A swimsuit is on sale for $45.50. If the sale price is discounted 5% from the
original price, what was the original price? Round to the nearest cent.
Answer:
47.900
Step-by-step explanation
45.50 plus 2.275 is 47.825 rounded is 47.9
The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angles measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x
REmember that
in a parallelogram, consecutive angles are supplementary
that means
.mmmm
therefore
substitute
120-2x+70+x=180
solve for x
2x-x=190-180
x=10answer is option Cwhat is the equation to 500
The correct equation to be written for 500 will be 5*100 = 500. This same can also be written as 50*10 = 500 in the equational form to represent 500.
What is an Equation?A mathematical equation can be stated as a formula that uses the equals sign in order to represent the equality of two expressions. In other words, it's a statement that shows that the values of two mathematical expressions are equal.
The equality between the equations here is shown by the equals (=) sign
As an example, 3x + 5 = 14 can be stated as an equation, in which 3x + 5 and 14 are two expressions that are connected by an ‘equal’ sign, thus providing an equation form.
Types of EquationsIf you set on typing the actual types of equations, then you will just find many to categorize from.
But mainly the types of equations can be classified as:
1) Algebraic Equations (includes linear, quadratic, cubic, polynomial equations)
2) Radical Equations
3) Exponential Equations
4) Rational Equations
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What is the slope in pages per hour? Number of Hours 2 4 6 8 Pages Completed 3 6 9 12
Hello,
Can someone help me with this paper
Written work please if u dont mind
The value of x is (t - ab)/ad while taking the subject x.
What does it mean when some variable is made the subject?Making x the subject of an equation or formula entails rearranging the equation or formula so that the x variable is equal to the other variables. The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own. When changing a formula's subject, we rearrange the formula's components to create a new subject. In other words, alter the operation to do the opposite if you move a term from one side of the equals sign to the other. (An operation's inverse is known as the operation's opposite.)So, t = a(b + dx):
Now, solve taking the subject 'x' as follows:
t = a(b + dx)t = ab + adxt - ab = adx(t - ab)/ad = xx = (t - ab)/adTherefore, the value of x is (t - ab)/ad while taking the subject x.
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Need help with number 1
Okay, here we have this:
Considering the provided information, we are going to analize whether it is better to use a sample or the population in the proposed situation, so we obtain the following:
To know the most popular song in an entire country, it is necessary to use the entire population, since the result of the favorite song if only one sample is used will not give results with certainty, considering that the population that is not covered could generate changes in the result.
Which construction is illustrated above?
O an angle congruent to a given angle
O the angle bisector of a given angle
O a perpendicular to a given line from a point on the line
O a line segment congruent to a given line segment
Answer:
The construction is a parallel line to a given line from a point not on the line.
Step-by-step explanation:
For a given figure,
To construct a parallel line
Step 1 : Draw transversal line through any point not on line which is given.
Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.
Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line
Step-by-step explanation:
-3x + 7y = 24
3x + 2y = 3
Answer: x = -1 y=3
Step-by-step explanation:
yeah just do AP algebra.2 then you'll know the answers
if the sum of the interior Angele measures of a convex ploygon is 2.60 how many sides does the polygon have?
Answer:
The polygon has 14 sides.
Explanation:
Given that the sum of the interior angles of the polygon is 2,160.
[tex]T=2,160[/tex]Recall that the sum of interior angles of a polygon can be calculated using the formula;
[tex]\begin{gathered} T=180(n-2) \\ \text{where;} \\ n=\text{ number of sides} \\ T=\text{ sum of the interior angles of the polygon.} \end{gathered}[/tex]Substituting the value of T, to solve for n;
[tex]\begin{gathered} 2,160=180(n-2) \\ \frac{2160}{180}=n-2 \\ 12=n-2 \\ n=12+2 \\ n=14 \end{gathered}[/tex]Therefore, the polygon has 14 sides.
Find the value of x And y. State the Theron’s you used.
Answer:
x = 5, y = 13
Step-by-step explanation:
Solve for x:
42 = 8x + 2
40 = 8x
x = 5
This is solved using the alternate interior angles theorem, which states that alternate interior angles (in this case, the 42-degrees and 8x + 2 degree angles) are the same.
Solve for y:
180 = 42 + 6(2y - 3)
180 = 42 + 12y - 18
180 = 24 + 12y
156 = 12y
y = 13
This is solved using the same-side interior angles theorem, which states that same-side interior angles (in this case, the 42-degrees and 6(2y-3)-degree angles) add up to 180 degrees.
Simplify the root below and leave your answer in the form \frac{a}{b} \sqrt[]{ \frac{405}{324} } Our value for a is AnswerOur value for a is Answer
We are asked to simplify the following expression
[tex]\sqrt[]{\frac{405}{324}}[/tex]Recall the quotient rule of radicands given by
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]Applying the above rule to the given expression
[tex]\sqrt[]{\frac{405}{324}}=\frac{\sqrt[]{405}}{\sqrt[]{324}}[/tex]Notice that the square root of 324 is equal to 18
[tex]\frac{\sqrt[]{405}}{\sqrt[]{324}}=\frac{\sqrt[]{405}}{18}[/tex]Also, notice that we can break 405 into factors as
[tex]\sqrt[]{405}=\sqrt[]{81\times5}=\sqrt[]{81}\cdot\sqrt[]{5}=9\cdot\sqrt[]{5}[/tex]So, the expression becomes
[tex]\frac{\sqrt[]{405}}{18}=\frac{9\cdot\sqrt[]{5}}{18}=\frac{\sqrt[]{5}}{2}[/tex]Therefore, the simplified expression is
[tex]\frac{\sqrt[]{5}}{2}[/tex]a = √5
b = 2
Give the slope of a line that is parallel to −3x−3y=1.
Step-by-step explanation:
y = mX + c
3y = -3x - 1
divide by 3
y = -x -1/3
slope = -1 of this line and parallel lines
Answer:
-1 is the slope beause lines with the same slope are parallel.
The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below:Step 1: 2(y + 6) = 4yStep 2: 2y + 8 = 4yStep 3: 2y = 8Step 4: y = 4Which of the following explains how to correct Step 2 and shows the correct value of y? 2 should be distributed as 2y + 12; y = 62 should be distributed as 2y + 12; y = 3The equation should be y + 6 = 4y after division by 2; y = 2The equation should be y + 6 = 4y after division by 2; y = 1
Solution:
Given the equation;
[tex]2(y+6)=4y[/tex]Now, distribute 2;
[tex]\begin{gathered} 2(y)+2(6)=4y \\ \\ 2y+12=4y \end{gathered}[/tex]Then, step 3;
[tex]\begin{gathered} 12=4y-2y \\ \\ 2y=12 \end{gathered}[/tex]Divide both sides by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{12}{2} \\ \\ y=6 \end{gathered}[/tex]CORRECT OPTION: 2 should be distributed as 2y + 12; y = 6
Name the property which justifies the following conclusion:
Given: m = n
Conclusion: 3m = 3n
A Reflexive Property of Equality
B Multiplication Property of Equality
C Symmetric Property of Equality
D Transitive Property of Equality
Answer:
A) Reflexive Property of Equality
Step-by-step explanation:
If you look at your reflection in a mirror, you see yourself! Likewise, by the Reflexive Property, any number is its own mirror image. Any number (such as a real number) is equal to itself!
What this means is that any number is the answer as no number is given. It could be 3m = 3n, 10m = 10n, or 85m - 85n as long as the number of "m" is the same to the number of "n."
To determine the town pigeon population, researchers tagged and released 27 pigeons. Later,
the researchers counted 380 pigeons. Out of the pigeons they counted, 19 had tags. To the
nearest whole number, what is the best estimate for the pigeon population
The best estimate for the pigeon population is 540.
What is meant by estimation?Finding an estimate or approximation—a value that may be used for a purpose despite the possibility of incomplete, ambiguous, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.
Counting a small sample of something and extrapolating that number to a wider population is how estimation is frequently done. Calculating how many sweets of a certain size are contained in a glass jar is an example of estimation.
380 x 27/19
= 540
So the answer is
540
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find the measure of LH, EL, JG, EK, KG. LG = 34EH = 22LG = 34
Please, give me some minutes to take over your question
I am working on it
______________________________-
LG = 34
EH= 22
JL= 16
_______________________________
Pythagoras theorem
Hypotenuse = H
Side 1 = S1
Side 2 = S2
H^2 = S1^2 + s^2
__________________________
This is a triangle with multiple right triangles inside
JG
34^2 = 16^2 + JG ^2
[tex]JG=\text{ }\sqrt[]{34^2-16^2}=\text{ 30}[/tex]JG = 30
_________________________________
LH
_________________________________
Answer
LH
EL
JG = 30
EK
KG
Solve the equation.
²x+3-2x = 1+²x+5
42
If necessary:
Combine Terms
Apply properties:
Add Subtract
Multiply
Divide
To start over:
The answer to the equation is -3/2.
How to solve equations?
1.Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
2.Identify the variable term on one side of the equation by adding or subtracting.
3.You can find the variable's value by multiplying or dividing.
Given equation is x²+ 3-2x= 1+ x² +5
Thus x² from both sides gets cancelled because x²-x²= 0
Now we get 3-2x = 6
-3 = 2x
On dividing by 2 we get,
-3/2 = x
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7/5 15/4 3/2 11/4 13/3 what is the least to greatest
We can conclude that the ascending to descending order of the given fractions are, 7/5, 3/2, 11/4, 15/4, and 13/3.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The terms with a numerator and a denominator are called fractions.So, first, we need to find the LCM of all the denominators:
LCM of 5, 4, 2, 4, 3: 60(Refer to the attached image for calculation)Now, the fractions will be:
12(7)/60, 15(15)/60, 30(3)/60, 15(11)/60, 20(13)/6084/60, 225/60, 90/60, 165/60, 260/60So, ascending to descending order will be:
84/60, 90/60,165/60, 225/60, 260/60That is 7/5, 3/2, 11/4, 15/4, 13/3
Therefore, we can conclude that the ascending to descending order of the given fractions are, 7/5, 3/2, 11/4, 15/4, and 13/3.
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Approximate -16 + square root of 40
The result of the approximation of -16 + square root of 40 is -3.35.
What is defined as the approximation?An approximation refers to anything which is similar to but not identical to something else.
Rounding can be used to approximate a number. Before performing the operations, an estimate can be approximated by rounding this same values within it.
Look just at digit with in tens column to get an approximation to the nearest ten.Look at the digit with in hundreds column to get an estimate to the nearest hundred.Look at the digit with in thousands column for the nearest thousand.For the given number;
-16 + square root of 40 can be written as.
= -16 + √40
Find the factors of 40 by prime factorization;
40 = 2×2×2×5
Put the value in expression.
= -16 + √2×2×2×5
Take out square root of 2.
= -16 + 2√2×5
= -16 + 2√10
Fine the approximate value of √10 as this is near to √9.
Thus, √10 = 3.12
Put the value in expression.
= -16 + 2×3.12
= -16 + 12.649
= -3.35
Thus, the approximation of -16 + square root of 40 is -3.35.
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Can you guys help me solve this
q + r = p is the equation formed by using the details in the question
What is a linear equation ?In an algebraic equation of the form y=mx+b, where m denotes the slope and b the y-intercept, a linear equation is a first-order (linear) term and a constant. Sometimes the phrase "linear equation with two variables" is used to describe the previous equation, which contains the variables y and x.
Ax+By=C is the standard form for two-variable linear equations. Standard form is used, for instance, in the linear equation 2x+3y=5. This method makes it simple to find an equation's two intercepts (x and y).
Calculationp the stove is hot
q the soup is cold
r the food is done
equation to be created was
the food is done and the soup is cold , then the stove is hot.
and means +
therefore equation formed by plugging in the values will be ,
q + r = p
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1) Analia thought of two different ways to define this quantity. Identify these two definitions among the
following options.
Choose 2 answers:
Graduation rate divided by number of teachers
Graduation rate divided by teachers per student
SAT average divided by number of teachers
SAT average divided by teachers per student
Analia proposed the following two measures to determine which school had a better academic record:
B. Graduation rate and student budget
D. Average SAT score / Per-student budget
How to determine the various amounts Which school has the best academic performance, according to Analia?To specify a number that represents academic accomplishment;
We compare the budget per pupil for each school to a corresponding metric or parameter that measures the academic performance of the students in each school.
The following variables could be used to gauge academic achievement:
the success rate of every school.
The SAT score of each institution.
Consequently, the amount to assess academic success in relation to each student's budget may be represented as;
Graduation rate and student budget
Average SAT score / Per-student budget
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|x-4|=7x+12 solve for x
Step-by-step explanation:
................ N.....
A bookshelf has 7 shelves, each measuring 4 feet 3 inches in length.
The average width of a book is ; inch. How many books will the
shelves hold?
Answer:
I think its 64 please let me know if its wrong
The point E is plotted on the coordinate grid below. Plot the point E’, the reflection of E over the x-axis.
Answer:
E' will be at (2, -6)
Step-by-step explanation:
Here we are given point E at (2, 6).
A reflection over the x-axis will keep the x coordinate the same while changing the y value to become the additive inverse (the number in which adding to the current value will get you zero). In this case, it is -6.
E (2,6) --> E' (2, -6)
Another way of thinking of it is reflecting on the x-axis while change the value from (x, y) to (x, -y).