Answer:
4y = (1/2)^x -5
Step-by-step explanation:
The first three equations are lines. All the variables have a power of just one (power of one is a math number that is not written) They are actually all written in slope-intercept form even. Line equations are linear function. Yay the words match!
You get a curve (not linear) when you have exponents, square roots or variables in the denominator of a fraction. Or as here, a variable for an exponent!
40 POINTS
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
Horizontal translation
Vertical translation
Reflection across the y-axis
270° counterclockwise rotation
Reflection across the y-axis is the transformation used to the polygon ABCD.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
ABCD is the original image and prime B prime C prime D prime is the transformed image.
ABCD rectangle is transformed to A'B'C'D'.
As we observe the diagram, the two rectangles look the same which means the shape remains constant.
The translation is applied to the original image which move to the right side.
A translation is a movement of the graph either horizontally parallel to the x axis or vertically parallel to the y axis.
We can reflect the graph of any function f about the x-axis by graphing y=-f(x) and we can reflect it about the y-axis by graphing y=f(-x).
Hence, Reflection across the y-axis is the transformation used to the polygon ABCD.
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Answer: reflection across the y axis
Step-by-step explanation: I hope that helps :)
How much would you need to deposit in an account now in order to have $4,000.00 in the account in 1541 days?
Assume the account earns 7% simple interest.
in your account now.
You would need to deposit _____ in your account.
Assume the account earns 7% simple interest. in your account now. You would need to deposit $3,007.52 in your account.
How to find the deposited amount?1541 days = 4.2219 years
Hence,
Time = 4.2219 years
Interest rate = 7%
Principal = $4,000
Hence,
4000=Po(1+.07)^4.2219 years
4000=1.33×Po
Po = 4,000 /1.33
Po = $3,007.52
Therefore the amount you need to deposit is $3,007.52.
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in a -page manuscript, there are randomly distributed misprints. find the mean number of misprints per page. round the answer to one decimal place as needed.
The mean number of misprints per page on manuscript is 0.5 and If a page is selected then the probability that it has 3 misprints is 0.0126..
What is Poisson probability distribution ?The Poisson distribution is a theoretical discrete probability, also known as the Poisson distribution probability mass function. It is used to find the probability that independent events occur at regular time intervals and have a constant average rate. λ is the Poisson rate parameter, the expected average number of events over a given time interval.
Using the Poisson distribution formula:
P(X = x) = (e-λ (λˣ) )/x!
where λ is mean number or poisson rate parameter ; x = 0, 1, 2, 3...
e is the Euler's number(e = 2.718)
We have given that,
Total number of Manuscript Pages = 400
total misprinted pages = 200
let X be random variable that the page is misprinted .
Mean number, λ = 200/400 = 0.5
the probability that it has 3 misprints, P(X= 3) = (e⁻⁰·⁵ (0.5)³ )/3!
= e⁻⁰·⁵ ( 0.125 )/6 =0.075816/6 = 0.0126
Hence, the required probability is 0.0126..
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Complete question:
Misprints on Manuscript Pages In a 400-page manuscript, there are 200 randomly distributed misprints Part 1 of 2 Find the mean number of misprints per page. Round the answer to one decimal place as needed. If a page is selected, find the probability that it has 3 misprints.
A-Level Cambridge
PURE MATHEMATICS - PI
CH1 COORDINATES GEOMETRY
1-(9709-S 2012-Paper 1/2-Q4) COORDINATES GEOMETRY
[6]
The point A has coordinates (-1, -5) and the point B has coordinates (7, 1). The perpendicular
bisector of AB meets the x-axis at C and the y-axis at D. Calculate the length of CD.
ШОә
Answer:
either 8.6 or 9. check if it's correct?
7² + 5² = 74
square root 74 = 8.6
An experiment consists of drawing one card from a bridge deck. The sample space contains 52 outcomes, one for each of the 52 cards. Suppose we assign a probability of 1/52 to each of the cards. Find the probability that the following happens.
(a) A king is drawn
(b) The card drawn is a king or a queen.
(c) The card drawn is a diamond.
(d) The card drawn is a black card.
The probability of drawing a king, a king or queen, a diamond, or a black card from a deck of 52 cards is 1/52, 4/52, 13/52, and 26/52, respectively.
(a) The probability that a king is drawn is 1/52, since there is only one king in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king is 1/52.
(b) The probability that a king or a queen is drawn is 4/52, since there are four kings and queens in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king or queen is 4/52.
(c) The probability that a diamond is drawn is 13/52, since there are 13 diamonds in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a diamond is 13/52.
(d) The probability that a black card is drawn is 26/52, since there are 26 black cards in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a black card is 26/52.
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Which graph shows an image and preimage after reflecting across y = -x ? *
Option 1
Option 2
Option 3
Option 4
The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.
Which answer choice represents an image and pre-image after a reflection across y = -x?It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.
First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.
On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.
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If a_1=1a
1
=1 and a_n=2a_{n-1}+1a
n
=2a
n−1
+1 then find the value of a_4a
4
The fourth term of the recursive sequence in this problem is given as follows:
[tex]a_4 = 15[/tex]
How to solve the recursive sequence?The nth term of a recursive sequence is obtained applying the recursive rule n times, considering that the first term of the sequence is given.
The recursive rule for this problem is given as follows:
[tex]a_n = 2a_{n - 1} + 1[/tex]
The first term of the sequence is given as follows:
[tex]a_1 = 1[/tex]
Then the second term of the sequence is given as follows:
[tex]a_2 = 2(1) + 1 = 2 + 1 = 3[/tex]
The third term of the sequence is given as follows:
[tex]a_3 = 2(3) + 1 = 6 + 1 = 7[/tex]
The fourth term of the sequence is given as follows:
[tex]a_4 = 2(7) + 1 = 14 + 1 = 15[/tex]
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At a local print shop, 18 copies can be made for $6. At this rate, how how many copies could be made for $28? Fill out the table of equivalent ratios until you have found the value of x. Copies Dollars 18 18 6 6 x x 28 28 It would cost $28 to make copies.
Answer:
84 copies
Step-by-step explanation:
18 copies: $6 ==> 18:6
18:6 ==> 18/6 = 3
18 copies: $6 = 3 copies: $1 ==> common ratio of copies to cost
3 copies: $1 =
(3 copies: $1)*28 = ==> multiply by 28 to get the number of copies for $28
3*28 copies: $28 = 84 copies: $28
Answer: 84 copies
Answer:
(18 copies for $6 = x copies for $28)
18:6 = x:28
6x = 18(28)
6x = 504
x = 84 copies
Copies | Dollars
18 | $6
84 | $28
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Find X,Y,Z Please Help!!!
The values of the angles x, y, z are x=56°, y=124°, z=56°
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
From the given figure,
∠y=124°
∠x+124°=180°
∠x=180°-124°
∠x=56°
∠x=∠z=56°
Therefore, The values of the angles x, y, z are x=56°, y=124°, z=56°
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can some one please help me with this question
The measure of the largest exterior angle of the triangle will be 162°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The exterior angles of the triangle are 3x°, 8x°, and 9x°. Then the measure of the interior angle of the triangle will be 180° - 3x°, 180° - 8x°, and 180° - 9x°.
The sum of the interior angle of the triangle is 180°. Then the equation is given as,
180° - 3x° + 180° - 8x° + 180° - 9x° = 180°
360° - 20x° = 0
x = 18°
Then the measure of the exterior angles of the triangle will be given as,
3x° = 3 × 18° = 54°
8x° = 8 × 18° = 144°
9x° = 9 × 18° = 162°
The measure of the largest exterior angle of the triangle will be 162°.
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The scatter plot below shows the average rent (in dollars per month) for a 1 bedroom apartment in new york city each year between 2000 and 2013. A line was fit to the data model the relationship.
which of these liner equations best describes the given model?
a.y=2/5x+800
b.y=40x+800
c.y=800x+2/5
d.y=800x+40
based on this equation,use this equation to estimate the average rent in 2020.round your answer to the nearest dollar.
Therefore , the solution to the given problem of equation that the estimated rent comes out o be $1600.
Investigate the equation.The equivalent sign connects two expressions to form a mathematical statement known as an equation. An equation is, for instance, 2x - 5 = 15. By solving this equation, we can determine that the value of the variable x is 5.
Here,
In 2020, a one-bedroom apartment in New York City will cost $1600.
The formula for a straight line graph is often y = mx + c, where;
m = gradient
c is the vertical intercept.
With this knowledge, the graph clearly shows that the ideal line of fit for the data plot is y = 40x + 800.
This means that a one bedroom flat in New York City will cost; in the year 2020, which is 20 years after the year 2000;
y = 40(20) + 800 = $1600
Therefore , the solution to the given problem that the estimated rent comes out o be $1600.
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What is the measure of AK
Measure of angle AKQ is 90°.
Define angle.There are several different kinds of angles in geometry. Angle is one of the most significant and fundamental units. When two rays or lines are connected at their common terminus, an angle is created. Angles are used in many facets of daily life, including the construction of buildings, dams, and statues, starting with a pizza slice. Angle has a crucial role in civil engineering. A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
Given
Measure of angle AKQ is 90°.
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Leslie wants to invest $3,800.00 in a savings account that pays 4.8% simple interest.
How many years will it take for this investment to triple in value? Round your answer to the nearest tenth of a year.
It will take _______ years for this investment to triple in value.
Answer:
It will take 41.7 years for this investment to triple in value.
Step-by-step explanation:
Here is the formula for simple interest
[tex]A=P(1+rt)[/tex]
Lets solve for [tex]t[/tex].
Divide both sides by [tex]P[/tex].
[tex]\frac{A}{P}=rt+1[/tex]
Subtract 1 from both sides.
[tex]\frac{A}{P}-1=rt[/tex]
Divide both sides by [tex]r[/tex].
[tex]\frac{\frac{A}{P}-1}{r} =t[/tex]
To write [tex]-1[/tex] as a fraction with a common denominator, multiply by [tex]\frac{P}{P}[/tex] .
[tex]\frac{\frac{A}{P}-1*\frac{P}{P}}{r} =t[/tex]
[tex]\frac{\frac{A}{P}*\frac{-P}{P}}{r} =t[/tex]
Combine the numerators over the common denominator.
[tex]\frac{\frac{A-P}{P} }{r} =t[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]t=\frac{A-P}{Pr}[/tex]
We are given
[tex]P=3800\\r=0.048[/tex]
We need to find what amount is triple his money.
[tex]3800*3=11400[/tex]
[tex]A=11400[/tex]
Substitute our numbers into the equation for [tex]t[/tex].
[tex]t=\frac{11400-3800}{3800*0.048}[/tex]
Factor 3800 out of 11400.
[tex]t=\frac{3800*3-3800}{3800*0.048}[/tex]
Factor 3800 out of −3800.
[tex]t=\frac{3800*3-3800*-1}{3800*0.048}[/tex]
Factor 3800 out of [tex]3800*3-3800*-1[/tex].
[tex]t=\frac{3800*(3-1)}{3800*0.048}[/tex]
Cancel the common factor of 3800.
[tex]t=\frac{3-1}{0.048}[/tex]
Simplify.
[tex]t=\frac{2}{0.048}[/tex]
[tex]t=41.666[/tex]
Merry Christmas!
The sum of heart rate readings taken five times for of Kundaval and Kulazhi are 400 and 360 respectively. And their projected deviations are 3,16 and 2.0 respectively. If you were. a doctor, who would you treat immediately?
Answer:
Overall, as a doctor, I would prioritize treating Kundaval immediately due to their higher heart rate and larger projected deviation.
Step-by-step explanation:
As a doctor, I would prioritize treating the patient with the higher heart rate and larger projected deviation. In this case, that would be Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16.
Heart rate is an important vital sign that reflects the health and function of the cardiovascular system. It is measured in beats per minute (bpm) and can vary based on factors such as age, activity level, and overall health. A high heart rate, especially in combination with a large projected deviation, can be a sign of a potential health problem or underlying condition that requires immediate medical attention.
In contrast, Kulazhi has a lower heart rate and smaller projected deviation, which may indicate that their cardiovascular system is functioning normally. However, it is still important to monitor and track their heart rate over time to ensure that it remains within a healthy range.
If I were a doctor, the immediate patient I would treat is; Kundaval because he has a higher projected deviation and a faster heart rate.
What is the standard deviation?Instead of computation or experimentation, the standard deviation is an abstract concept based on observation.
A metric that is used to express the amount of variation or dispersion in a group of data is the standard deviation, which is also represented by the Greek letter sigma(σ).
To put it another way, it specifies the degree to which the members of a data group differ from the group's average value.
Given
The sum of heart rate readings taken five times for Kundaval is 400
The sum of heart rate readings taken five times for Kulazhi is 360
and their projected deviation are 3.16 and 2.0,
Now, the standard deviation is a measure of how dispersed the data are in relation to the mean, whereas the mean simply refers to the average of a set of given data.
As a result, as a doctor, I would prioritize treating the patient whose heart rate and projected deviation are higher. As a result, we would conclude that Kundaval, with a projected deviation of 3.16 and a sum of 400 heart rate readings, should be treated first.
Therefore, The immediate patient I would treat if I were a doctor is; Kundaval because he has a faster heart rate and a higher projected deviation.
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Select <, >, or = to make the expression true.
Answer:
the answer is < explanation at the step by step
Step-by-step explanation:
Do the Basic equation
2.18 x 10 - 6= 15.8
4.36 x 10 - 7= 36.6
determine the 97.5th percentile of the standard normal distribution as a decimal rounded to the nearest hundredth.
given the function of f(x) = 1234999x as the values of x increase towards infinity, what happens to the values of f(x)
(no clue why this says college this is 11th grade finacial algebra)
Using the Leading Coefficient Test the end behavior of the function f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity
as x tends to ∞, f(x) tends to ∞ What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThe given function is:
f(x) = 1234999x
The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient
x ⇒ ∞ f(x) ⇒ ∞
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X) 4.6.PS-15
The width of a rectangle is 4x-7.5 feet and the length is 7.5x+8 feet. Find the perimeter of the rectangle.
GT
The perimeter of the rectangle is feet.
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Question Help
The perimeter of the rectangle 24x + 1 feet. The perimeter of a geometric figure is the total length of its sides.
What is perimeter ?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
To find the perimeter of a rectangle, you need to add the lengths of all four sides of the rectangle.
The width of the rectangle is 4x-7.5 feet and the length is 7.5x+8 feet.
The perimeter is therefore equal to 2 times the sum of the width and the length,
= 2 * (4x-7.5 + 7.5x + 8) feet.
This simplifies to 2 * (12x + 0.5) feet,
which is equal to 24x + 1 feet.
The perimeter of the rectangle 24x + 1 feet
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To which of the following expressions could you apply the associative property?
A.9-5-2
B.5+3-2
C.8÷4÷1
D.7+3+1
The associative property states that the order in which three or more numbers are added or multiplied does not affect the result of the operation. You can apply the associative property to the expressions A. 9-5-2, B. 5+3-2, and D. 7+3+1.
In expression A, 9-5-2, you can rearrange the numbers as follows: 9-5-2 = (9-5)-2 = 4-2 = 2.
In expression B, 5+3-2, you can rearrange the numbers as follows: 5+3-2 = (5+3)-2 = 8-2 = 6.
In expression D, 7+3+1, you can rearrange the numbers as follows: 7+3+1 = (7+3)+1 = 10+1 = 11.
You cannot apply the associative property to expression C, 8÷4÷1, as this is a division expression, and the associative property does not apply to division.
Overall, the associative property allows you to rearrange the order of addition or multiplication of three or more numbers without affecting the result of the operation.
The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A mathematical principle that states the product of a multiplication issue is unaffected by the way the elements are organized.
The associative property for addition and multiplication is valid but not for division.
The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.
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Joyce wants to survey a simple random sample of 10 people from members of a gym.
Which of the following sampling methods are not examples of simple random sampling?
Select all that apply.
Select the first 10 people from alist of members
Ask 10 members in the gym on a Monday morning
Use a random number generator to select 10 members from a list
Select 10 members' names from a box without looking.
Select every 20th person from a list of members until she has 10 .
Ask all members of the gym
The sampling methods here that are not examples of simple random sampling are;
A) Select the first 10 people from a list of members.
B) Ask 10 members in the gym on a Monday morning
E) Select every 20th person from a list of members until she has 10 .
F) Ask all members of the gym
What is the importance of simple random sampling?A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.
The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.
A) Select the first 10 people from a list of members; This is not simple random sampling because it is not random but specific.
B) This is not random because it is specific which is just a monday morning and we don't have an idea of the type of people that come on the other days.
C) Use a random number generator to select 10 members from a list; This is simple random sampling because a random number generator is used.
D) Select 10 members' names from a box without looking; This is random because all members have an equal chance of being selected.
E) Select every 20th person from a list of members until she has 10; This is not random as all members don't have an equal chance of being selected.
F) Ask all members of the gym; This is not random selection.
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lf mike is 13 and leslie is 7 how old will leslie be when mike is 24?
Spotless and As Good as New, offer house cleaning services. Spotless charges a flat fee of $30 and an additional $6 per hour while As Good as New charges $11 per hour with no flat fee. How long would cleaning a house have to take in order for the two companies to charge the same amount?
Answer:
x = 6
Explanation:
If x is reserved for the number of hours it'll take, then the first equation is saying that $6 is being multiplied by an x amount of hours, which is then added by $30. The second equation states that $11 is being multiplied by an x amount of hours, but there is no flat fee. This makes the equation:
6x + 30 = 11x
The steps to solving this are:
1) Make the variables on one side. In this case, it is easier to put them on the right.
11x - 6x = 5x
5x = 30
2) Divide both sides by 5.
5x / 5 = 30 / 5
x = 6
This means it will take 6 hours for them to charge the same amount of money.
The chart shows the ratio of water to pancake mix used in a pancake recipe.
Water Pancake Mix
29
4
7
13
?
O
21
2
How many cups of pancake mix are used with 1 cup of water?
(Write the answer as a fraction.)
Answer:
Doing the math, it should be 7.25/1
A coin is thrown until a head occurs and the number X of tosses recorded. After repeating the experiment 256 times, we obtained the following results:x 1 2 3 4 5 6 7 8f 136 60 34 12 9 1 3 1Test the hypothesis, at the 0.05 level of significance, that the observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3
The hypothesis, at the 0.05 significance level,
H₀ : the observed distribution of X may be fitted by the geometric distribution
Hₐ : the observed distribution of X may not be fitted by the geometric distribution
we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3
A coin is thrown until a head occurs and the number X of tosses recorded.
The probability that head occur on toss ,p = 0.5
Consider the null and alternative hypothesis,
H₀ : the observed distribution of X may be fitted by the geometric distribution
Hₐ : the observed distribution of X may not be fitted by the geometric distribution
The chi square test statistic here as:
χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ
where Oᵢ--> observed value
Eᵢ --> expected value
and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)
The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾
where x = 0, 1,2 ,3,......
Observed values are f :136 60 34 12 9 1 3 1
Using the data,we calculate the expected values
E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰
= 128
E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹
= 64
E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32
E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³
= 16
E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴
= 8
E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵
= 4
E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶
= 2
E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷
= 1
Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ
= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1
= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75
Significance level is α =0.05
Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.
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Help me solve I will give you 15 points the answer is 720m3
Answer:
Step-by-step explanation:
You split it up into two 3-D triangles.
One of them has a volume of ((6*(5+5))/2)*8 = (60/2)*8=240
For the other one, you are missing a side on the 2-D face, so in order to apply pythagorean's theorem you need to split it into two more triangles. You know that 13^2=5^2+x^2 169-25=x^2 144=x^2 x=12
now that you know the missing side of the triangle you can recombine them. The volume of the remaining 3-D triangle is (((5+5)*12)/2)*8 = 60*8=480
480+240=720 meters cubed
I need help
[tex]log_2(3x+2) - log_4(x)=3[/tex]
Answer:
[tex]x = \frac{26 + 8 \sqrt{10} }{9} [/tex]
or
[tex]x = \frac{26 - 8 \sqrt{10} }{9} [/tex]
Step-by-step explanation:
I apologise for my messy explanation.
The solution of the expression will be;
⇒ x = 5.7
or ⇒ x = 0.07
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ log ₂ (3x + 2) - log ₄ (x) = 3
Now,
Since, The expression is,
⇒ log ₂ (3x + 2) - log ₄ (x) = 3
Solve as;
⇒ log ₂ (3x + 2) - 1/2 log ₂ (x) = 3
⇒ log ₂ (3x + 2) - log ₂ √(x) = 3
⇒ log ₂ (3x + 2) / (√x) = 3
⇒ (3x + 2) / √x = 2³
⇒ (3x + 2) / √x = 8
⇒ (3x + 2) = 8√x
Taking square both side, we get;
⇒ (3x + 2)² = (8√x)²
⇒ 9x² + 12x + 4 = 64x
⇒ 9x² + 12x - 64x + 4 = 0
⇒ 9x² - 52x + 4 = 0
By applying quadratic formula, we get;
⇒ x = - (- 52) ± √ (-52)² - 4×9×4 / 2×9
⇒ x = 52 ± √ 2704 - 144 / 18
⇒ x = 52 ± √2560 / 18
⇒ x = 52 ± 50.6 / 18
This gives two solution as;
⇒ x = (52 + 50.6) / 18
⇒ x = 102.6/18
⇒ x = 5.7
And, We get;
⇒ x = 52 - 50.6 / 18
⇒ x = 1.4 / 18
⇒ x = 0.07
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Find the inverse of f restricted to this domain f ( x ) = ( x − 6 ) 2 f ( x ) = ( x - 6 ) 2
Answer:
The inverse of f is x=8
Step-by-step explanation:
I did it
Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. In the GSS 2014, respondents were asked to indicate their level of agreement to the statement: "A working mother hurts children". Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children. a, What is the 90% confidence interval for this statistic for males? b. Of the 566 respondents who answered the question, 40% strongly agree that a working mother does not hurt children. What is the 90% confidence level for this statistic?
a) The 90% confidence interval for this statistic for males is of: (0.1497, 0.2103).
b) The 90% confidence level for this statistic is of: (0.3661, 0.4339).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
For males, the parameters are given as follows:
[tex]\pi = 0.18, n = 435[/tex]
Hence the lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.645\sqrt{\frac{0.18(0.82)}{435}} = 0.1497[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.645\sqrt{\frac{0.18(0.82)}{435}} = 0.2103[/tex]
For the statistic, the parameters are given as follows:
[tex]\pi = 0.4, n = 566[/tex]
Hence the lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.645\sqrt{\frac{0.4(0.6)}{566}} = 0.3661[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.645\sqrt{\frac{0.4(0.6)}{566}} = 0.4339[/tex]
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David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14. What were David's three exam scores?
Group of answer choices
88, 88, 90
84, 88, 98
81, 88, 95
84, 88, 90
86, 88, 90
David's three exam scores are B. 84, 88, 98
What were David's three exam scores?From the information, David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14.
The scores are 84, 88, and 98. The middle number is 88. It's the median.
The mean is:
= (84 + 88 + 98) / 3
= 270 / 3.
= 90
Range will be:
= Highest number - Lowest number
= 98 - 84
= 14
In conclusion, the correct option is B.
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What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12