The indicated probability of the normal distribution is 0.9332
The natural and social sciences frequently utilize normal distributions to describe real-valued random variables which distributions are unknown, which is why normal distributions are essential in statistics.
The central limit theorem contributes to some of their significance. According to this statement, under some circumstancesThe average of numerous samples (observations) of a random vector with finite mean and variance is itself a random variable, whose distribution conforms to a normal distribution as the number of samples rises. As a result, the distributions of physical quantities, such as error margins, that are predicted to be the sum of numerous distinct processes frequently resemble normal distributions.In the given normal distribution:
mean = 8 and standard deviation = 2
The indicated probability is given by P(7 ≤ x ≤ 11)
The z score of the distribution is given by
Z = ( 11 - 8 ) ÷ 2 = 1.5
From the z-score we can calculate the probability :
P(7 ≤ x ≤ 11) = 0.9332
Therefore the indicated probability is 0.9332
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1. The distance between two cities on the map was 6.5 cm. If the scale of the picture is 1:5000000, find the distance between the two cities.
2. How many centimeters can be used to represent a distance of 650 km on a map with a scale of 1:1500000?
3. If the distance between Ulaanbaatar and Choibalsan is 630 km, and the distance between these cities is shown on the map as 7 cm, find the scale of the map.
Considering the given scale, it is found that:
1. The distance between the two cities is of 325 km.
2. 43.3 cm should be used to represent the distance.
3. The scale of the map is of 1:9000000.
What is a scale?A scale is how much each unit in the drawing represents in actual distance.
For item 1, the scale of 1:5000000 means that each unit on the graph represents 5,000,000 units of actual distance.
The distance on the map is of 6.5 cm, hence the actual distance is of:
6.5 x 5000000 = 32,500,000 cm = 325 km.
For item 2, the scale is of 1:1500000, meaning that each cm of drawing is equivalent to 1,500,000 cm of real distance = 15 km.
Hence, the number of centimeters to represent a distance of 650 km is given by:
650/15 = 43.3 cm.
For item 3, we have that 7 cm represent 630 km = 63,000,000 cm, hence:
63,000,000/7 = 9000000.
Meaning that the scale is given by:
1:9000000.
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At class meeting, Jeff, Chad, and Lane ate a total of 254 marshmallows in the marshmallow-eating contest. Jeff won by eating 7 more marshmallows than Chad, who ate 5 more than Lane. How many marshmallows did Jeff eat?
The equation is formed and solved below.
What is an equation?
A mathematical equation is a calculation that uses the matching sign to represent the similarity of two expressions. A polynomial equation is the most prevalent kind of equation. An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance.
Lane ate = x marshmallows (let)
Chad ate = x + 5 marshmallows
Jeff ate = (x + 5) + 7 = x + 12 marshmallows
Then, the equation formed is
x + x + 5 + x + 12 = 254
The equation is solved as
3x + 17 = 254
or, 3x = 254 - 17
or, x = 237/3 = 79
Jeff ate = 79 + 12 = 91 marshmallows
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in a multiple regression analysis involving two independent variables, if b1 is computed to be 2.0, it means that
In a multiple regression problem involving two independent variables X1 and X2, if b1 is computed to be +2.0, it means that. the relationship between X1 and Y is significant .
What is multiple regression analysis?Multiple regression is a statistical method that may be used to assess a single dependent variable and several independent variables. Multiple regression analysis use known independent variables to anticipate the value of a single dependent variable. Each predictor value is assigned a weight, which indicates how much each predictor contributed to the overall forecast.
CalculationIn a multiple regression problem involving two independent variables X1 and X2, if b1 is computed to be +2.0, it means that. the relationship between X1 and Y is significant .
The estimated value of Y increases by an average 2 units for each increase of 1 unit of X1, holding X2 constant.
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The half-life of a radioactive
substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. Carbon 14 has a half-life
of 5730 years. Suppose given samples of carbon 14 weigh 5/8 of a pound and 7/8 of a pound. What was the total weight of the samples 11,460 years ago?
The total weight of the samples 11,460 years ago is 6 pounds
What is Exponents?
Exponentiation is a mathematical process that involves the base b and the exponent or power n. It is represented as b^n and is pronounced as "b to the n."
The exponential process of radioactive decay is depicted by
[tex]A_{t}[/tex] =[tex]A_{0}[/tex] [tex]e^{-kt}[/tex]
where = Amount of the radioactive element after t years
[tex]A_{0}[/tex] = Initial amount
k = Decay constant
t = time in years
The carbon-14 half life is 5730 years.
[tex]A_{0}[/tex]/2 = [tex]A_{0}[/tex][tex]e^{-5730k}[/tex]
1/2 = [tex]e^{-5730k}[/tex]
At this point, we take ln (Natural log) on both sides.
ln(1/2) = ln [ [tex]e^{-5730k}[/tex]]
-ln(2) = -5730kln(e)
0.69315 = 5730k
k = 0.69315 / 5730
k = 1.21 x [tex]10^{-4}[/tex]
We now need to determine the weight in pounds of the C-14 samples that were taken for the remaining quantities.
5/8 =[tex]A_{0}[/tex] [tex]e(^{-1.21 * 10^{-4} * 11460})[/tex]
5/8 = [tex]A_{0}[/tex] [tex]e(^{-1.3863})[/tex]
[tex]A_{0}[/tex] = (5/8) [tex]e(^{-1.3863})[/tex]
[tex]A_{0}[/tex] = 5/8 x 4
[tex]A_{0}[/tex] = 5/2
[tex]A_{0}[/tex] = 2.5pounds
Similarly for 7/8 pound
7/8 = [tex]A_{0}[/tex] [tex]e(^{-1.21 * 10^{-4} * 11460 })[/tex]
7/8 = [tex]A_{0}[/tex] [tex]e(^{-1.3863 })[/tex]
[tex]A_{0}[/tex] = (7/8) [tex]e(^{-1.21 * 10^{-4} * 11460 })[/tex]
[tex]A_{0}[/tex] = 7/8 x 4
[tex]A_{0}[/tex] = 7/2
[tex]A_{0}[/tex] = 3.5 pounds
Hence, The total weight of the samples 11,460 years ago 2.5 + 3.5 = 6pounds
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if a regression model is constructed from the data given here, what is the residual for the prime interest rate of 8%? bond rate in 5% 12% 9% 14% 7% prime interest rate 14% 6% (x) 8% 5% 7% o a 11.12 o b.-5.16 o cobb od.-0.88
The residual for the prime interest rate is 0.88.
What is a regression equation?
An equation created to explain the relationship between independent and dependent variables is known as an estimated regression equation in statistics.
The relationship between the dependent and study variables is first hypothesized using a simple or multiple regression model. The most popular technique for creating estimates of the model variables is the least squares method.
Predicting the worth of the dependent variable while values for the predictor factors are known is one of the main uses of both the estimated regression equation.
From the given regression model,
n = 5
∑X = 40
∑Y = 47
∑XY = 333
∑X² = 370
n∑X.Y - ∑X.∑Y = -215
n∑X² - (∑X)² = 250
∑Y.∑X² - ∑X∑XY = 4070
FOR REGRESSION EQUATION
a= ( ∑Y.∑X² - ∑X∑XY )/ (n∑X² - (∑X)² ) = 16.28
b = (n∑X.Y - ∑X.∑Y) / (n∑X² - (∑X)² ) = -0.86
ŷ = b x + a = -0.86 x + 16.28
predicted value at x = 6 ;
ŷ = (-0.86 * 6) + 16.28 = 11.12
Residual = y - ŷ = 12 – 11.12 = 0.88
The residual for the prime interest rate is 0.88.
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HELP ASAP GIVE BRAINLY TO RIGHT ANSWER ONLY!!!
Graph D shows the line y - 4 = 2 (x + 1).
slope: 2
How do you represent a equation on a graph?The act of displaying linear equations with one or two variables on a graph is known as "graphing linear equations." A linear equation is a one-degree equation, meaning that the variable's highest power or exponent value may never be more than 1, under any situation. Finding the values of the variables in a linear equation is known as solving it. The graphical approach is one way to solve linear equations, which can have one or two variables.
They are algebraic equations with 2 variables of maximum power 1 and real constants in each term. The linear equation is shown in y=mx+b form, sometimes referred to as the y-intercept form.
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PLS HELP GEOMETRY WILL GIVE BRAINLIEST
Given: line c is parallel to line d, and angle 1 is congruent to angle 7,
Prove: line a is parallel to line b
By corresponding angle we prove a parallel line a ║ b .
What is an example of parallel lines?
Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. They may be vertical or horizontal. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.Lines that are always the same distance apart in a plane are said to be parallel. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Given, c ║d
∠1 ≅ ∠7
∠1 = ∠3 ( corresponding question)
∠5 = ∠7 ( corresponding question)
then a ║ b
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If the quadratic formula is used to find
the roots of the equation 2x² - 5x - 12
= 0, then what are the correct roots?
The two roots obtained for the quadratic equation by quadratic formula are 1.5 and 4.
What is defined as the quadratic formula?A quadratic equation is just a polynomial with a second degree first term. There are several methods for determining the roots, or solutions, of such a quadratic equation. Every quadratic equation has two solutions, that might or might not be real numbers. The quadratic formula is a simple method for resolving a quadratic equation. whether the answer is a whole number, an irrational number, or perhaps an imaginary numberIf the quadratic equation is ax² + bx + c = 0.
Then, the roots are given by x = [-b ± √(b² - 4ac)]/2a.
The quadratic equation is given as; 2x² - 5x - 12 = 0.
On comparing with the standard form;
a = 2b = -5c = -12Put the values in the formula,
x = [-b ± √(b² - 4ac)]/2a.
x = [-(-5) ± √((-5)² - 4×2×(-12))] / 2×2
On simplification,
x = [5 ± 11]/4
There will be two roots of equation,
a; x = [5 + 11]/4
x = 16/4 = 4
b ; x = [5 - 11]/4
x = 6/4 = 1.5
Thus, the two roots obtained for the quadratic equation by quadratic formula are 1.5 and 4.
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Write an equation that expresses the following relationship: x varies directly as a and inversely as the difference between y and z. Then solve the equation for y
Write an equation that expresses the given relationship. Use k as the constant of variation.
Answer:
Where is question
Step-by-step explanation:
Sorty
i really need help!
4) At 5:00am in the morning, the temperature was -14.8 degrees Fahrenheit. By noon, the temperature increased to 6.2 degrees Fahrenheit. How much did the temperature change? Write an equation and then solve. Show all your steps.
Answer:
21 degrees
Step-by-step explanation:
Let the change in temp. be y.
-14.8 + y = 6.2
y = 21
Therefore, the change in temp. is 25 degrees.
could you help answer 1-12
1. The unit cost of red potatoes is $1.45/pound
2. The unit cost of white potatoes is $1.81/pound
3. Red potatoes bag is a better buy as it is cheaper than white potatoes while giving the same values of product.
What is unit cost?A price is referred to as a unit cost when it is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can. Divide the ratio's terms if you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price.
For example,
$5.50 ÷ 5 pounds = $1.10 per pound
4) 4/1.8 5) 5/6
= 2.9 = 0.83
6/2.4 12/14
=2.5 = 0.86
6 envelopes is better buy 5 songs download is a bette buy
6) 3/9 7) 12/6
= 0.3 = 2
5/12 100/28
= 0.42 = 3.57
3 games of laser tag is better buy 12 gifts is a better buy
8) 20/5 9) 16/3.04
= 4 = 5.26
100/20 24/5.04
= 5 = 4.76
20 arcade tokens is better buy 24 bottles of water is a better buy
10) 2/3.50 11) 100/2
= 0.57 = 50
5/6.75 145/4.35
= 0.74 = 33.3
2 pounds box is better buy 145 napkins is a better buy
12) 12/2.88 13) 250/40
= 4.16 = 6.25
15/3.30 600/138
= 4.54 = 4.35
12-ounce box is better buy 600 GB Hard drive is a better buy
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tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. if this continues, what will tacoma's population be in 2010?
4,31,784.999454 will be the population of Tacoma in 2010 .
What is exponents ?The exponent of a number is the number of times it is multiplied by itself.
Positive, negative, zero, and rational/fractional exponents are the four kinds.
The value of the number may be deduced from the exponent, which is the total number of times the base number must be multiplied by the same base.
CalculationIf the population at the beginning of 2000 was 200,000
Then the growth equation is P = Po(1.08)(y) where year year 2000 was year 1 or y = 1
At the end of 2015 or 2010-2000 = 15 years later, or at the end of the 15th year:
Population P(10) = (200,000)(1.08)10 = 4,31,784.999454
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PLSS HELP ASAP!!!!!!!!!!Which of the following is true? (1 point)
a
|–7| < 6
b
|–6| < |–7|
c
|–7| < |6|
d
|–6| < –7
I will give brainiest!!!!!!!!!!!!!!
Find the 60th term of the arithmetic sequence −29, -49, −69,
We see, the second number is 20 less than the first number, the third number is 20 less than the second number, ..
So, the pattern is : We minus 20 from a term to get the next term right after.
From the 1st term to the 60th term, there are 59 spaces.
Therefore, the 60th term = -29 - 59 x 20 = -1209
ten is ________ of two and 5
Ten is the product of two and five.
What does product mean?Product is the result of the multiplication process. Multiplication is a mathematical operation that entails adding a number repeatedly over a number of times. The sign that is used to represent multiplication is ×.
In order to determine the product of 2 and 5, add to five times.
2 + 2 + 2 + 2 + 2 = 10
This is usually written as 2 x 5 = 10
Other mathematical operations are addition, subtraction and division. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of finding the difference between two or more numbers. Division is the process of determining the quotient of a number.
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plsss help i just need help on how to do it i’ll give brainliest
The expression that represents the perimeter of the other shape is 9x + 6y.
Option(b) is the correct one.
What is an Expression in Math?Expressions in mathematics are mathematical statements that comprise at least two terms that contain numbers, variables, or both, and are joined by an operator. Addition, subtraction, multiplication, and division are all examples of mathematical operators.
Given:
Expression for the sum of the perimeter of two shapes = 13x + 4y
Expression for the perimeter of one shape = 4x - 2y
Expression for the perimeter of the other shape is,
(13x + 4y) - (4x - 2y)
= 13x - 4x + 4y + 2y (combine the like terms and solve)
= 9x + 6y
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You are completing a math assessment. The number of questions you complete and the time it takes you to complete them have a proportional relationship, as shown in the table. Number of Questions 4 7 Time (in minutes) 6 ? How much time does it take to complete 7 questions? 3 minutes 5 minutes, 30 seconds 9 minutes 10 minutes, 30 seconds
Through direct proportionality, we calculated that Seven questions will be answered in 10 minutes and 30 seconds.
Seven questions will need to be answered in 10 minutes and 30 seconds.
Direct proportionality: What is it?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. In mathematics, a straight line is used to express direct proportionality, and its equation is of the form y = kx , k = y/x, where [k] is the constant.
The assumption is that the time it takes to finish each question and the number of completed questions [y] are inversely proportional to one another.
The time [x] it takes to complete them is directly proportional to the number of questions [y] that are answered. As a result, y = kx, k = y/x, and y is directly proportional to x.
Thus, we can write:
y₁/x₁ = y₂/x₂
Substituting the values,
4/6 = 7/x₂
x₂ = (7 x 6)/4
x₂ = 21/2
x₂ = 10.5
x₂ = 10 minutes 30 seconds
Therefore, Seven questions will be answered in 10 minutes and 30 seconds.
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Multiply.
3c^6(9c+4c^3)
Simplify your answer as much as possible
Answer:
[tex]12c⁹+27c⁷[/tex]
Step-by-step explanation:
3c⁶(9c+4c³)
=(3c⁶)(9c+4c³)
=(3c⁶)(9c)+(3c⁶)(4c³)
=27c⁷+12c⁹
=12c⁹+27c⁷
Use properties of rational numbers to multiply the following.
-10.8 × (-54.3)
A.
586.44
B.
-586.44
C.
58.644
D.
-58.644
Jack is baking a cake. the recipe says that it must bake for 2 1/2 hours it has been baking for 3/4 hours how much longer must to bake? PLEASE HELP AND EXPLAIN TYSM
Answer:
Step-by-step explanation:
60 divided by 4 is 15 so 1/4 of an hour is 15 minutes. so three fourths is 45 minutes and one hour and a half is the extra hour that has not been touched so add the last 15 min from the 3/4 onto that so it still has 1 hour and 45 minutes to bake
Answer:
It still has to bake for 1 3/4 hours
Step-by-step explanation:
So, the way I do it, you start by making 2 1/2 an improper fraction, which would be 5/2. Then, you have to get it so 5/2 and 3/4 have common denominators. The fastest way to do this is to multiply the denominator 2 by 2, which means you have to do the same to the numerator. So, you have 10/4-3/4, which equals 7/4. Now, you can simplify. 7/4 = 1 3/4
machine A creates 6 products in 20 minutes .machine B can create the same products at a rate of 1 product per 4 minutes which machine works faster
Answer: Machine A is faster
Step-by-step explanation:
1) Make them into fractions.
Machine A: 6/20
Machine B: 1/4
2) Make the denominator the same
Machine A: 6/20
Machine B: 1/4 * 5/5
Machine A: 6/20
Machine B: 5/20
6/20 > 5/20
Machine A > Machine B
Question
What is the slope of this graph?
Responses
1 fourth
negative 4
negative 1 fourth
4
Answer: The slope of the graph is negative 4.
factor out the GCF -2x^2 - 4x - 6
The Greatest Common factor(GCF) of -2x^2-4x-6 is -2(x+1)(x-3)
What is Greatest Common Factor?The greatest common factor (GCF) is the largest factor two or more numbers have in common
From the question,
-2x^2-4x-6
By collecting like terms
-2(x^2-2x-3)
By factoring x^2-2x-3
-2(x^2-3x+1x-3)
Collecting like terms
-2(x^2-3x)+(x-3)
-2(x(x-3)+1(x-3))
-2(x+1)(x-3)
hence -2(x+1)(x-3) is the Greatest Common factor of -2x^2-4x-6 is
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How do you solve (x+3)^2=121? Sorry it's been a while...
Answer: x = 8
Step-by-step explanation:
(x + 3)^2 = 121
Take the square root of both sides
x + 3 = 11
x = 8
Plug it back in to double check
(8 + 3)^2 = 121
(11)^2 = 121
121 = 121
22 Here is a right-angled triangle.
Work out the value of x.
4 cm
8.5 cm
xcm
x = 7.5 cm is value of v by Pythagorean theorem.
What is the Pythagorean theorem ?
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the total of the squares on the legs.For an acute triangle, c2 a2 + b2, where c is the side across from the acute angle, given the Pythagorean Theorem that states a2 + b2 = c2. For a right triangle, c is the side of the 90-degree angle and c2 = a2 + b2.use Pythagorean theorem in triangle,
8.5² = 4² + x²
72.25 = 16 + x²
72.25 - 16 = x²
56.25 = x²
x = √56.25
x = 7.5 cm
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A football team scored 3 touchdowns 3 extra points and 4 field goals write an expression to represent the total points the football team scored
Expression to represent the total points 3t + 3e + 4f
What is Algebra?
Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.
Let t represent the number of points for a touchdown, e represent the number of points for the extra point and f represent the number of points for a field goal.
Total points = 3(t) + 3(e) + 4(f)
= 3t + 3e + 4f
Hence, Expression to represent the total points the football team scored
3t + 3e + 4f
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Of the following situations, which is best represented by the product
5x-3
A
The amount of money a snack bar earns for selling 333 sandwiches for $555 per sandwich
B
The change in elevation of a submarine as it sinks 333 meters every second for 555 seconds
C
The change in temperature as it decreases 555 degrees every hour for 333 hours
D
The height of a child who grew 333 inches each year for 555 years
i need the answer fast pls
Answer: b
Step-by-step explanation:
if during a typical week susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?
The probability that the average score for the week is between 220 and 228 = 0.7641
Susan's score on bowling follows Normal Distribution.
Average score or mean, μ = 225
Standard Deviation, σ = 13
Number of times Susan bowled, n = 16
Since the scores follows Normal Distribution, the z-score = (x-μ)√n/σ
When the score, x = 220,
z = (220-225)√16/13
= -20/13
= -1.538
When the score, x = 228,
z = (228-225)√16/13
= 12/13
=0.923
Hence The probability that the average score for the week is between 220 and 228 = P(220 < x < 228)
= P(-1.538 < z < 0.923)
= P(z < 0.923) - P(z < -1.538)
= (0.5 + 0.3212) -( 0.5 - 0.4429) [From the z-tables]
= 0.7641
The question is incomplete. Find the complete question below:
Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?
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Answer the following
Answer:
Don't know
Step-by-step explanation:
in the diagram below, all the measurements are given correct to the nearest cm. Not drawn o scale 15 cm 21 cm 28 cm 42 cm Calculate the greatest possible area of the shaded region.
Using the diagram and given measurements the area of the shaded potion is solved to be 46 cm^2
How to find the area of the shaded portionArea of the shaded portion is solved using the following factors
Entire area of the rectangleArea of the smaller rectangleEntire area of the rectangle
= length * width
= 42 * 21
= 882 cm^2
Area of the smaller rectangle
= length * width
= 28 * 15
= 420 cm^2
Area of the shaded portion
= Entire area of the rectangle - Area of the smaller rectangle
= 882 cm^2 - 420 cm^2
= 462 cm^2
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