The required mean of the distribution of x + y for the given data is 2.07.
Explain mean distribution.A statistical distribution, or probability distribution, portrays how values are dispersed for a field. As such, the measurable dissemination shows which values are normal and exceptional. There are numerous sorts of measurable appropriations, including the chime formed typical conveyance.
According to question:We have,
mean = 1 and Standard deviation = 0.94
In distribution of Y
mean = 1.07 and standard deviation = 1.04
mean of distribution X + Y = ?
Then,
the mean of the distribution of X+Y
= mean of x + mean of y
= 1 + 1.07
= 2.07
Thus, the required mean is 2.07.
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Which one of the following compound inequalities has no solution?
O 3x +1 < 5x + 7 and -2x + 5
-5x - 10
O 3x - 7≤ 5x +5 and - 4x + 8 < 5x - 1
-2x + 9 4x + 3 and 8x9 <- 7x - 3
O-2(x-9) < 3(x+4) and - 4(x - 1) > - 5(x - 2)
Inequality -2x + 9 4x + 3 and 8x9 <- 7x - 3 has no solution.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ( ≠ )" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers.
Given,
Compound inequalities has no solution is:
Variables should be moved to the equation's left side:
-8x + 7x > -3 + 9
Combining similar terms
-x < -3 + 9
Determine the total or difference:
-x < -6
Divide the inequality's two sides by the variable's coefficient:
x > -6
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Andrea ordered a computer on the Internet.
The computer cost $1,499 plus 7 12% sales tax.
What was the total amount Andrea paid for her computer? Round to the nearest cent.
Proportions bar also please if possible?
The total amount Andrea paid for her computer is $1611.425.
What was the total amount Andrea paid for her computer?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100
In this situation, Andrea ordered a computer on the Internet and the computer cost $1,499 plus 7 1/2% sales tax.
The amount that will be paid will be:
= Cost of computer + Tax
= $1499 + (7.5% × $1499)
= $1499 + $112.425
= $1611.425
The amount is $1611.425.
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What is the slope of the line that passes through (- 4 5 and 2/3 )?
The slope of the line passing through the two points [tex](-4,5)[/tex] and [tex](2,3)[/tex] is [tex]\frac{-1}{3}[/tex]
The formula for finding the slope when two points are given
[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{3-5}{2-(-4)} \\y=\frac{-2}{6} \\y=\frac{-1}{3}[/tex]
The slope of the line is [tex]\frac{-1}{3}[/tex]
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Question
56 is 80% of what number? Use the percent equation.
56 is 80% of what number?
Formula - [tex]\dfrac{Number\times100}{Percent}[/tex]
______________________
[tex]\dfrac{56\times100}{80} =\dfrac{5600}{80}=\fbox{70}[/tex]
Jacob went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 25 grams of sugar and each bottle of juice has 10 grams of sugar. Jacob purchased a total of 12 bottles of juice and soda which collectively contain 240 grams of sugar. Determine the number of bottles of soda purchased and the number of bottles of juice purchased.
The number of bottles of soda is 4 and the number of bottles of juice purchased is 8.
We know that linear system of equation in two variables is required to solve the problem. Let suppose number of bottles of soda purchased by Jacob is x and number of bottles of juice purchased by Jacob is y
Since, it is given that Jacob bought 25 bottles in total, it means
=>x + y=12-----(eq1)
Also, it is given that total amount of sugar is 240grams.Now,amount of sugar present in soda bottle is 25x and amount of sugar present in juice bottles is 12y
Therefore,25x + 12y=240-----(eq2)
On solving eq1 and eq2,we get
=>x+y=12
and 25x+10y=240
Using elimination technique to solve, make x terms coefficient equal.
Multiplying eq1 by 25,we get
=>25x + 25y=25×12
=>25x +25y=300------(eq3)
Using eq3 and eq4,we get
=>25x+25y=300
and 25x+10y=240
Cancelling x terms, we get
=>15y=60
=>y=(60/15) grams
=>y=4 bottles
Now, putting value of y in eq1 ,we get
=>4+y=12
=>y=12-4
=>y=8bottles.
Hence, required value of number of bottles of soda is 4 and number of bottles of juice is 8.
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3x - 5(x -5) = - 3 + 5x + 7
Answer:
x=3
Step-by-step explanation:
3x-5x+25= 5x+4
-2x+25=5x+4
+2x. +2x
25=7x+4
-4. -4
21=7x
/7. /7
3=x
Hopes this helps please mark brainliest
Answer:
x = 3Step-by-step explanation:
3x - 5(x -5) = - 3 + 5x + 7
3x - 5x + 25 = 4 + 5x
3x - 5x -5x = 4 - 25
-7x = -21
x = -21 : (-7)
x = 3
What is the pair of angle â JKL and â Lkm called?
If the measure of angle JKL is 132° and the measure of angle LKM is 48° . then the pair of angle JKL and angle LKM called a Linear Pair .
In the question ,
it is given that ,
the measure of angle JKL is = 132° and
the measure of angle LKM is = 48° ,
we know that when the sum of two angles is 180° , then the pair is called as Linear Pair .
According to the question ,
angle JKL + angle LKM = 180°
132° + 48° = 180°
180° = 180°
So , the given pair of angles forms a Linear Pair .
Therefore , the angle JKL and angle LKM forms a Linear pair .
The given question is incomplete , the complete question is
If the measure of angle JKL is 132° and the measure of angle LKM is 48° . What is the pair of angle JKL and angle LKM called ?
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Complete the following questions.
Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live.
a. Write two expressions in terms of d to show how much Winona and Takoda would pay in total if they buy their mother the set of power tools.
b. Let the value of d equal $79.00. Calculate the total cost of each of the possible presents for the value you chose. Then write a sentence telling Winona and Takoda which preset to buy for their mother if they want to spend the least amount of money.
a) The expressions are given as follows:
Power tools: 0.85d.Water skis: 0.75(d + 15).Jewelry: 0.9(d - 5).b) The total cost for each present is of:
Power tools: $67.15.Water skis: $69.56.Jewelry: $63.Hence the present that they can buy with the least amount of money is:
Jewelry.
How to obtain the costs?The costs are found applying the proportions in this problem.
As a function of d, the functions are found multiplying the decimal equivalents of each discount by the cost expression.
The decimal equivalents of each discount are given as follows:
Discount of 15% -> 0.85, as 85% of the price is paid.Discount of 25% -> 0.75, as 75% of the price is paid.Discount of 10% -> 0.9, as 90% of the price is paid.Then the actual costs are calculated replacing the instances of d in each item with the numeric value d = 79.
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The diagram shows a regular polygon.
What is the value of x?
Write
your answer as an integer or as a decimal rounded to the nearest tenth.
The value of x in the regular polygon is 120 degrees.
How to find the angle of a polygon?The regular polygon is a triangle. A regular polygon has all it interior angles equal to each other. Therefore, the triangle above is an equilateral triangle.
An equilateral triangle has all its sides equal to each other and the angles are also congruent. Each angle of an equilateral triangle is 60 degrees.
Exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore,
60 + 60 = x
Hence,
x = 120 degrees.
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In which of the options below will the number 10 correctly fill in the blank? Select all that apply. A) 3 : 5 = 6 : ___ B) 2 : ___ = 4 : 16 C) 1 : ___ = 4 : 40 D) 5 : 8 = ___ : 24
a population of cattle is increasing at a rate of 200 10t per year, where t is measured in years. by how much does the population increase between the 2nd and the 7th years?
The population increase between the 2nd and the 7th years as 440.
What is Total Change from a Rate of Change?
We may be able to utilise a function that expresses a rate of change to determine the total change in the quantity being described. This is so that we can take a rate of change and return to a function that defines the initial quantity. An indefinite integral will provide us with a function that depicts the whole quantity, while a definite integral will inform us of the total change between two places.Total increase = ∫ab rate dt
= ∫₁³ 200+10t dt
= 200t +5t² |₁³
= [200(3) + 5(3)²] - [ 200(1) + 5(1)²]
= 600 + 45 - 200 -5
= 440
Hence, the population increase between the 2nd and the 7th years as 440.
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For the player with 450 times at bat, the actual number of hits the player had is approximately how many fewer than the number of hits predicted by the line of best fit?.
the actual number of hits the player had is approximately 10 fewer than the number of hits predicted by the line of best fit
The guy with 450 at bat had about 113 hits, according to the scatterplot (the y-coordinate of the point representing this player is approximately halfway between 100 and 125). The best fit line anticipates around 123 hits. As a result, this player's actual number of hits is around ten lower than the number of hits predicted by the line of best fit.
20,30,40 are inaccurate because they each offer a figure significantly more than 10, which is the best guess of how many fewer hits the player with 450 at-bats made than anticipated by the best-fit line of numbers.
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please help me with this, u dont even have to explain ur answer
Answer:
perpendicular bisector __D ,angle bisector__C
Step-by-step explanation:
1.becausein choise c the angle A is been bisected 2.am sorry but i can only answer the two questions as for the perpendicular bisector i guess it is self explanatory am sorry if i have not assisted
3. The length of each side of an equilateral triangle is (4x 2 7) cm.
Write an equation to determine the value of x that will produce a
triangle with a perimeter of 27 cm.
Answer:
Step-by-step explanation:
uhmm 4x +27 ? 4 times 27? what number is that supposed to be
let me try
4x + 27 + 4x + 27 + 4x + 27 (equilateral means all sides r the same length so 3 times cuz 3 angles in triangle)
12x + 81 = 27 (ok its prob not 4x +27 since x would be a negative number but just change 27 to the number it actually is)
12x = -54
x = -4.5
there enjoy it should be right if the numbers u gave me r correct
The choice of the probability distribution for a random variable can be guided by: ________
The choice of the probability distribution for a random variable can be guided by Historical Data
What is Probability ?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
What is Random Variable Distribution ?In probability theory and statistics, a probability distribution is a mathematical function that calculates the likelihood of a range of potential experiment results. It is a mathematical explanation of a random phenomenon in terms of its sample space and event probability.
The choice of the probability distribution for a random variable can be guided by Historical Data
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what is 4 Divided 1/3
Answer: 12
You're Welcome :D
Answer:
4 / 1 /3 = 4/3
Step-by-step explanation:
according to the information that comes with a certain prescription drug, when taking this drug, there is a 24% chance of experiencing nausea (n) and a 46% chance of experiencing decreased sexual drive (d). the information also states that there is a 16% chance of experiencing both side effects.what is the probability of experiencing neither of the side effects? your answer should be to two decimal places.
There is 46% probability of experiencing neither of the side effects.
What is probability ?Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.
Given that,
While taking drug, chances of experiencing nausea (n)= 24 %,
Chances of experiencing decreased sexual drive (d) = 46 %.
Also, there are 60% chances of experiencing both side effects.
Use vain diagram to solve this type of questions,
Total chances of experiencing side effects = 8 + 30 + 16 = 54
The chances of experiencing neither of the side effects = 100 - 54 = 46
So there is 46% probability of experiencing neither of the side effects.
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What is 1/3 of a figure?
One third of a figure would be 1/3 of its total size or area.
The area of a form or planar lamina is referred to as the plane region or plane area, as opposed to surface area, which denotes the area of an open surface or the boundary of a three-dimensional object.Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).
1. A figure is a shape or an image that can be drawn or represented on a flat surface.
2. 1/3 of a figure would mean dividing the figure into three equal parts.
3. The resulting parts would be 1/3 of the size or area of the original figure.
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Solve the inequality and write the solution in set-builder notation.
3h+5<4h
The inequality 3h + 5 < 4h in set builder form is {h : h ∈ R, and h > 5}.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality 3h + 5 < 4h.
3h - 4h < - 5.
-h < - 5.
h > 5 (Make the variable positive by moving it to the other side)
So, The inequality in the set builder form is {h : h ∈ R, and h > 5}
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Gavin deposited $12,000 at 2% interest mounted quarterly what is the value after 16 years round to the nearest cent
Answer:
final amount = $16512.36
Step-by-step explanation:
The question asks us to find the value of Gavin's deposit of $12,000 after 16 years, given that the interest rate of 2% is compounded quarterly.
To do this, we have to use the following formula for compound interest:
[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],
where:
A → amount at the end
P → principal (original) amount
r → interest rate (in decimal)
n → number of times per year that the interest is compounded
t → time (in years).
From the question, we know that the initial amount deposited is $12,000. Therefore, P = 12000. We also know that the interest rate is 2%, but the formula requires the rate to be in decimal, so r = 0.02. The time for which the money is deposited is 16 years, and therefore, t = 16. We are told that the interest is compounded quarterly, that is, every 3 months. This means that the interest is compounded 4 times yearly, so n = 4.
From the above information and formula, we can calculate the final amount:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
⇒ [tex]A = 12000(1 + \frac{0.02}{4})^{4 \times 16}[/tex]
⇒ A = $16512.36
Therefore, the final amount after 16 years is $16512.36.
College administrators noticed that students who had higher high school gpas tend to have higher college gpas. The data in the table show various high school gpas and college gpas for a sample of students. A 2-column table with 16 rows. Column 1 is labeled high school g p a with entries 3. 25, 3. 5, 3. 5, 3. 25, 2. 5, 4, 4, 3. 5, 3. 25, 3. 5, 3. 5, 4, 3, 3. 5, 2. 25, 2. 5 column 2 is labeled college g p a with entries 3. 2, 3. 0, 2. 9, 3. 0, 3. 0, 3. 0, 3. 1, 3. 1, 3. 1, 3. 0, 3. 0, 3. 1, 3. 0, 3. 1, 2. 9, 2. 8. Which scatterplot represents the student data?.
Values are paired in the form:
(X1, Y1),.. (Xn, Yn)
(3.25, 3.2)
"Information available from the question"
In the question:
College administrators noticed that students who had higher high school GPAs tend to have higher college GPAs.
The data in the table show various high school GPAs and college GPAs for a sample of students. A 2-column table with 16 rows.
Column 1 is labeled high school g p a with entries.
3. 25, 3. 5, 3. 5, 3. 25, 2. 5, 4, 4, 3. 5, 3. 25, 3. 5, 3. 5, 4, 3, 3. 5, 2. 25, 2. 5
Column 2 is labeled college g p a with entries 3. 2, 3. 0, 2. 9, 3. 0, 3. 0, 3. 0, 3. 1, 3. 1, 3. 1, 3. 0, 3. 0, 3. 1, 3. 0, 3. 1, 2. 9, 2. 8
Now, According to the question:
Column 1 High School G P A:
3.25, 3.5, 3.5, 3.25, 2.5, 4, 4, 3.5, 3.25, 3.5, 3.5, 4, 3, 3.5, 2.25, 2.5
Column 2 College G P A :
3.2, 3.0, 2.9, 3.0, 3.0, 3.0, 3.1, 3.1, 3.1, 3.0, 3.0, 3.1, 3.0, 3.1, 2.9, 2.8.
To prepare a scatter plot ; with x - axis plotted against y - axis ;
Each point on the x - axis is paired with a corresponding point on the y - axis ;
With high school GPA on the x axis and College GPA on y :
Values are paired in the form:
(X1, Y1),.. (Xn, Yn)
(3.25, 3.2)
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The distribution of heights in a population of women is approximately normal. sixteen percent of the women have heights less than 62 inches. about 97.5% of the women have heights less than 71 inches.Use the empirical rule to estimate the mean and standard deviation of the heights in this population.
The mean is 65 inches and the standard
standarddeviation is three (3) inches for the women have heights less than 62 inches. about 97.5% of the women have heights less than 71 inches.
In a set of girls, the distribution of heights is more or less normal. Women who're shorter than sixty two inches in top make up 16% of the population.
The empirical rule, much less than µ - o of 16% of the records is accurate.
P(x < mu sigma) =16%>mu - sigma = sixty two -> (l)Approximately 97.5% of the girls are beneathneath seventy one inches in top,P(x < mu sigma) =97.5%>mu + 2sigma = seventy one (||)By solving (l)& (ll) ;mu - sigma = 62u + 2sigma = 713sigma = 9sigma = 3From (1);mu - sigma = 62mu - 3 = 62mu = 65Hence, Mean = 65 inchesStandard deviation = 3 inchesTo read more about Mean here:
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there are 123 students in a drama club. 65 of them are girls. what is the ratio of the numbers of boys to the number girls?
Answer:
Step-by-step explanation:
123(students in general) - 65 (girls) = 58
Cheatem loans will lend you $400 with the understanding that you will repay them $500 in one month. What is the APR for this loan?
The APR for the loan is 300%
How to determine the APR for the loan?APR stands for annual percentage rate. It is a standardized way of measuring the cost of borrowing money. It takes into account not only the interest rate on a loan but also any fees that are charged as part of the loan.
Given: Cheatem loans will lend you $400 and you will repay them $500 in one month
interest = 500-400 = $100
duration = 1 month
1 year = 12 months
APR = (interest/amount borrowed) / (duration/duration in a year)
APR = (100/400) / (1/12)
APR = 300%
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I need help pleaseeee
The words that fills the blank space on the method used to find the length of the diagonal AG, using Pythagorean Theorem are as follows;
Blank 1; The Pythagorean Theorem
Blank 2; Square root of 73
Blank 3; A leg
Blank 4; The hypotenuse
Blank 5; 9.4 cm
What is the Pythagorean Theorem?Pythagoras Theorem indicates that the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.
The diagonals from point A to point G in the cuboid can be found using Pythagoras Theorem as follows;
The diagonal of the base rectangle, ABCD, is found as follows;
AC = √(8² + 3²) = √(73)
Using the side CG as the leg of the right triangle ΔACG, with AG being the hypotenuse, we get;
CG = 4 indicated in the diagram in the question
(AG)² = (AC)² + (CG)²
(AG)² = 73 + 4² = 89
AG = √(89) ≈ 9.4
The completed statement is therefore;
To find the length of the diagonal from point A (front/bottom /left) to point G (back/top/right); You would first use the Pythagorean Theorem on the bottom of the box rectangle to find the diagonal AC = square root 73 cm. Then use CG as a leg of the triangle ACG, with AG being the hypotenuse. AG is approximately 9.4 cm.Learn more about Pythagorean Theorem here:
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What is the total number of degrees in a triangle?
60
90°
30°
Answer:
180 degrees in a triangle
the scores in an exam were normally distributed with unknown mean and a standard deviation of 5 . if 30.85 % of students scored more than 72.5 . what is the value of the mean? ( round to a whole number
The value of the mean for the scores in an exam which are normally distributed is 70.
Given:
the scores in an exam were normally distributed with unknown mean and a standard deviation of 5 .
if 30.85 % of students scored more than 72.5 . what is the value of the mean = ?
Mean = µ
σ = 5
x = 72.5
The z score corresponding to the area 30.85% in the right tail is :
Zi score = Z 0.3085
= 0.500
Again : Z₀ = x- µ/σ
⇒ x- µ = Z₀σ
⇒ µ = x - Z₀σ
= 72.5 - 0.500 × 5 (using z table)
= 72.5 - 2.5
= 70
Hence we get the unknown mean as 70.
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Please help me find the answer!
f and g are inverses of each other and g is a reflection of y = x thus options (B) and (C) are correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given functions,
f(x) = [tex]2^{x}[/tex] and g(x) = [tex]log_{2} x[/tex]
It is known that the exponential function and logarithm function are inverse of each other for the same base as shown below.
It is also clear that g(x) is the reflection of x = y.
Hence "g is a reflection of y = x and f and g are inverses of one another.".
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A group of friends went to buffalo wild wings for dinner. There were nine people in your group. some of the group ordered chicken wings for $14.99 and the rest of the group ordered the chicken wrap for $8.49. If the total bill was $115.41, how many people ordered each dinner?
6 people ordered chicken wings and 3 people ordered chicken wrap.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given that there were 9 people in a group. Some of them ordered chicken wings and rest people ordered the chicken wrap.
The cost of chicken wings is $14.99.
The cost of chicken wrap is $8.49.
The total bill was $115.41.
Assume that, x number of people ordered chicken wings.
Then (9 - x) number of people ordered chicken wrap.
The cost of 1 chicken wings is $14.99
The cost of x chicken wings is $14.99x.
The cost of 1 chicken wrap is $8.49.
The cost of (9 - x) chicken wrap is $8.49(9 - x).
The total cost of x chicken wings and (9 - x) chicken wrap is $[14.99x + 8.49(9 - x)]
= $[14.99x + 76.41 - 8.49x]
= $[6.50x + 76.41] [ Subtract like terms]
According to the question,
6.50x + 76.41 = 115.41
Subtract 76.41 from both sides:
6.50x = 39
x = 6
Putting x = 6 in the expression (9 - x)
9 - x = 9 - 6 = 3
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1. The cost y of movie tickets varies directly
with the number of tickets x as shown in the
graph. Write a direct variation equation to
represent this relationship. Then identify the
constant of variation and interpret its
meaning. (Example 1)
Movie Tickets
Cost ($)
56
48
40
32
24
16
8
y
X
0 1 2 3 4 5 6 7 8 9
Number of Movie Tickets
The direct variation equation to represent the relationship between the number of tickets and the cost of the ticket is y = 8x.
What is graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given:
56, 48, 40, 32, 24, 16, 8, 0, y
7, 6, 5, 4, 3, 2, 1, 0, x
Here, x is the number of tickets and y is the cost of the ticket
As you can see that the cost of each ticket is $8,
Then the equation will be,
y = 8x
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