the scores on a test are normally distributed with a mean of 130 and a standard deviation of 26. find the score that is one half a standard deviation below the mean
Answers
The score that is one and a half standard deviation below the mean is 91.
Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.
According to the given problem,
mean (μ) = 130
standard deviation (σ) = 26
Let x be the score that is one and a half standard deviations below the mean.
⇒ x = μ - 1.5σ → 1
Substitute the values μ = 130 and σ = 26 in 1,
x = μ - 1.5σ
= 130 - 1.5(26)
= 130 - 39
x = 91
A score of 91 is one and a half standard deviations below the mean.
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Related Questions
somebody help me I’m struggling
Answers
Answer:
A. $ (5 + 2x), B. = $ 305
Step-by-step explanation:
x miles
A. cost for x miles = 5 + 2x ($)
B. cost for 150 miles = 5 + 2*150 =305 ($)
Answer:
A. let the mile driven = x
5 + 2x
B. × = 150 mile
taxi service = $5 + $2(150)
= $305
*in an equation u dont have to write the symbol . for example, $, ml, km, etc.
5. Suppose X 1and X 2are random variables with mean 10,20 respectively, and SDs 2, 3 respectively.
Let T=11X 1−2X2
Find the mean and SD of T when X 1and X 2are independent.
Find the mean and SD of T when X1and X 2 have correlation of
−0.76
In the case that X1and X 2 are independent, normally distributed
variables, find P(T>30)
Answers
The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.
To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16. We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.
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Which of the following is required to construct the inscribed circle of a triangle?
O A. the perpendicular bisectors of the sides of the triangle
OB. the orthocephyer of the triangle
oc the circumcenter of the triangle
O D. the incenter
Need asapppp
Answers
Inscribed circle of a triangle is the largest circle, contained in the triangle.
To construct the inscribed circle of a triangle the in-center is required. the option 3 is the correct option.
How to construct the inscribed circle of a triangle?
Inscribed circle of a triangle is the largest circle, contained in the triangle.
Steps to construct the inscribed circle of a triangle-
Step 1-Bisect one of the angle of the triangle.Step 2-Now bisect the another angle of the triangle.Step 3-The crossing point of both the angle bisects is the in center of the triangle and center of the required circle.Step 4- Draw a perpendicular from this center to one of the side of the triangle.Step 5-Now draw a circle using the compass with the in center as a center of the and radius equal to the perpendicular from the in center to one of the side.Thus to construct the inscribed circle of a triangle the in-center is required. the option 3 is the correct option.
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If the breadth of a rectangle is reduced by 4cm it's are would be reduced by 240 cm². How long is the rectangle?
Answers
Answer:
Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long
Step-by-step explanation:
hope it will help
How does adding salt to water affect the boiling point?
Answers
When salt is added to water, the boiling point of water is increased. The boiling point elevation depends on the concentration of salt added. The addition of salt increases the boiling point of water.
The extent of the increase in boiling point is directly proportional to the amount of salt added. Boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the pressure exerted on it by the surrounding atmosphere.
In layman's terms, this means that a liquid boils when its vapor pressure equals atmospheric pressure. Boiling point of a liquid can be increased or decreased by the addition of solutes such as salt.When a solute such as salt is added to water, the boiling point of water increases due to the phenomenon of boiling point elevation.
This is because the solute particles in the water interfere with the formation of water vapor molecules at the surface of the liquid. As a result, more energy is required to boil the water, which means that the boiling point is elevated.
The amount of elevation is directly proportional to the concentration of salt added. In short, the addition of salt to water increases the boiling point of water.
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If x=-2 what is the value of 4-5x
Answers
Answer:
14
Step-by-step explanation:
(-5)*(-2)=10 you then add 4 which gives you 14.
Answer:
14
Step-by-step explanation:
4 - 5(-2) = 4 - (-10) = 4 +10 = 14
0.8 overline 3 Your friend's cat weighs times the weight of your cat. Your friend's cat weighs 10 pounds. How much more does your cat weigh than your friend's cat? You cat weighs pounds more than your friend's cat.
Answers
Solving a linaer equation we can see that your cat weighs two more pounds.
How much more does your cat weigh than your friend's cat?Let's define the variables:
x = your cat's weight.
y = your friend cat's weight.
We can write the linear equation:
y = 0.833...*x
And we also know that.
y = 10 lb, replacing that we will get:
10lb = 0.833...*x
Solving that for x:
x = 10lb/ 0.833...
x = 12 lb
Then you can see that your cat weighs 2 pounds more.
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A line's y-intercept is 0, and its slope is 5. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y = 5x
Step-by-step explanation:
slope intercept form is y=mx+b
m = slope
b = the y-intercept
so you just have to plug in those values
Answer detailed please
Answers
Answer:
container A
Step-by-step explanation:
In Container A, we can plot the points (0,60) adn (2, 35)
The slope is :
\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)
For container B, the slope is:
\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)
The negative sign of the slope indicates the direction of the slope
\(|m_A| = 12.5\\\\|m_B| = 11\)
12.5 > 11
The slope of container A is steeper than container B
Therefore, the water is draining out of container A at a faster rate than container B
A certain basketball player practices shooting free throws over and over again. The shots are independent, with probability p of success.
a) In n shots, what is the expected number of streaks of 7 consecutive successful shots? (Note that, for example, 9 in a row counts as 3 streaks.)
b) Now suppose that the player keeps shooting until making 7 shots in a row for the first time. Let X be the number of shots taken. Sow the E(X) <= 7/p^7.
Answers
The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p7, where n is the number of shots and p is the probability of success.The probability of making 7 consecutive successful shots in exactly k shots is given by Pk = (1-p)k-7 * p7. The expected value of X is given by E(X) = [k=7,] k. We can use the formula for the sum of an infinite geometric series to simplify the expression and evaluate the numerator of the expression. Thus, E(X) 7 / p7.
a) In n shots, the expected number of streaks of 7 consecutive successful shots is given by the formula below:The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p^7, where n is the number of shots and p is the probability of success. In other words, for each block of 7 shots, we have a probability of p^7 of making 7 consecutive successful shots, and there are (n-6) blocks of 7 shots in n shots. Therefore, the expected number of streaks of 7 consecutive successful shots is the product of these two values.
b) We know that X is the number of shots taken until the player makes 7 consecutive successful shots for the first time. Therefore, X is a random variable that follows the geometric distribution with parameter p. The probability of making 7 consecutive successful shots in exactly k shots is given by:Pk = (1-p)^{k-7} * p^7Therefore, the expected value of X is given by:E(X) = Σ[k=7,∞] k * PkWe can use the formula for the sum of an infinite geometric series to simplify this expression:
\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (1 - (1-p)^7)\) We can also use the formula for the sum of a geometric series to simplify the denominator:
\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (p^7 + Σ[j=1,6] (1-p)^j * p^7)\)
\(E(X) = (p^7 * Σ[k=1,∞] k * (1-p)^{k-1}) / (p^7 * (1 + Σ[j=1,6] (1-p)^j))\)
\(E(X) = (1 / p^7) * (Σ[k=1,∞] k * (1-p)^{k-1}) / (1 + Σ[j=1,6] (1-p)^j)\)
We can use the formula for the derivative of a geometric series to evaluate the numerator of this expression:
\(Σ[k=1,∞] k * (1-p)^{k-1} = d/dp\)
Σ[k=1,∞] (1-p)^k
= d/dp (1-p) / (1 - (1-p))²
= 1 / p^2
Therefore, \(E(X) = (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^2) ≤ (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^7) = 1 / p^{14} ≤ 7 / p^7\)
Thus, \(E(X) ≤ 7 / p^7.\)
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Mark ran 12 miles in 132 minutes. Assume Mark maintains a constant speed. How many minutes does it takes Mark to run 1 mile.
Answers
Answer:
11
Step-by-step explanation:
132 divided by 12=11
12x12=144, subtract 12 and you get 12x11=132
BRAINLIEST PLZ???
A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller number. If y represents the larger number and x represents the smaller number, which equations model the situation? Check all that apply.
y=3x-2
3x-y=2
3x-y=-2
y=2-3x
y=2(x+3)
Answers
Answer:
1,2, and 5
Step-by-step explanation:
y=2*(3+x)
y=3x-2
3x-y=2
Hurry Pleasee!! Tamara either runs or walks the same route each day. Last month, she ran half of the days and walked the other days. Which graph best represents the distance she traveled each day?
Answers
Answer:
the correct answer is c
Step-by-step explanation:
Sixteen is equal to 7 increased by the product of 3 and a number.
Answers
Answer:
number is 3
Step-by-step explanation:
let the number be n then the product of 3 and the number is 3n , so
16 = 7 + 3n ( subtract 7 from both sides )
9 = 3n ( divide both sides by 3 )
3 = n
That is the number is 3
The water slides have 1 temporary employee and 24 permanent employees. What percentage
of the employees at the water slides are temporary
Answers
Answer:
4%
Step-by-step explanation:
1/25 = 0.04 = 4%
Answer:
chu papi munanyo
Step-by-step explanation:
in the context of rm and range safety mitigation of risk is the ability
Answers
In the context of Range Safety and Risk Mitigation, the ability to detect, assess, and respond to potential hazards is essential.
Range safety and risk mitigation involve identifying and minimizing potential hazards associated with range operations, such as the launch or test of rockets, missiles, or unmanned aerial vehicles. To ensure safety, it is critical to have the ability to detect and assess potential hazards, such as debris, vehicle or equipment malfunctions, and human error. Once hazards have been identified and assessed, the next step is to develop and implement appropriate safety measures to mitigate the risk associated with those hazards. These measures may include the use of safety protocols, engineering controls, or administrative procedures to ensure that all personnel and equipment are protected. In summary, the ability to detect, assess, and respond to potential hazards is critical for effective range safety and risk mitigation. By implementing appropriate safety measures and protocols, the risks associated with range operations can be minimized, ensuring the safety of personnel and equipment.
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LeBron James was eating some Skittles. When he opened the bag there were 84 Skittles in the bag. He ate 63 of them. What PERCENTAGE of the Skittles did LeBron James eat? Explain how you solved this problem. *
Answers
help im in 6th grade
Answers
Answer:
15
Step-by-step explanation:
you were offered a job! Company A offered $10,000 initial salary with a $5,000 annual raise. Company B offered a $ 20,000 initial salary with an $3,000 annual raise. After how many years will you have the same salary? what will that salary be? PLEASE ANSWER!!!
Answers
Use the distributive property to write an equivalent expression. 2(m + 9)
Answers
Answer:
Distribute the numbers answer: 2m+18
Step-by-step explanation:
2(m+9)
MULTIPLY 2 and m, and MULTIPLY 2 and 9!
what is 5=-3+y
\(5=-3+y\)
Answers
Step-by-step explanation:
by grouping like terms, we will get;
5 + 3 = y ( when -3 goes across the equal sigh it becomes possitive and the vice versa)
8 = y
y = 8
A pack of 8 AA rechargeable batteries costs $21.20. What is the cost per battery, in dollars and cents?
Answers
Answer:
2.65
Step-by-step explanation:
21.20 ÷ 8 = 2.65
Would you also help me find the answer for this one pls
Answers
a) The variable x is the average distance of Venus from the sun.
b) The equation for the given condition,
⇒ ⇒ 57.9 = 3.8 + x/2
c) The average distance of Venus from the sun = 108.2 million kilometers.
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 average distance of Mercury from the sun = 57.9 million kilometers
And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.
Now,
Since, The average distance of Mercury from the sun = 57.9 million kilometers
And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.
Let the average distance of Venus from the sun = x
So, We can formulate;
⇒ 57.9 = 3.8 + x/2
Solve for x as;
⇒ 57.9 = 3.8 + x/2
⇒ 57.9 - 3.8 = x/2
⇒ x/2 = 54.1
⇒ x = 54.1 × 2
⇒ x = 108.2
Thus, The average distance of Venus from the sun = 108.2 million kilometers.
Therefore, a) The variable x is the average distance of Venus from the sun.
b) The equation for the given condition,
⇒ ⇒ 57.9 = 3.8 + x/2
c) The average distance of Venus from the sun = 108.2 million kilometers.
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a+3b/5 = a-2b/2 Find the ratio a:b! Please help!!!
Answers
Answer:
16 : 3
Step-by-step explanation:
(a+3b)/5=(a-b)/2 or 2 (a+3b) = 5 (a-2b) or 2a + 6b = 5a-10b or 3a. or a/b = 16/3 so a.b = 16:3
Describe how to find the surface area of a regular polygonal pyramid with an n -gon base, height h units, and an apothem of a units.
Answers
The apothem of the pyramid can be calculated as: Apothem = √(h2 + a2). We use the Pythagorean Theorem to find the apothem.
The surface area of a regular polygonal pyramid with an n-gon base, height h units, and an apothem of a units can be determined using the formula given below.
Surface Area = [(Perimeter of base) × (Apothem)] / 2 + [Area of Base]
Where perimeter of the base can be given by the formula: Perimeter = n × s
Here, n is the number of sides of the polygonal base, and s is the length of each side.
The area of the base of the pyramid can be calculated as:
Area of Base = [Perimeter of Base × (Apothem)] / 2
The apothem of the pyramid can be calculated as: Apothem = √(h2 + a2). We use the Pythagorean Theorem to find the apothem.
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Rewrite 48 + 60 using the distributive property
Answers
Answer:
12* ( 4+5)
Step-by-step explanation:
48 = 12 * 4
60 = 12 * 5
48 + 60 = 12*4 + 12*5
= 12*( 4 + 5)
= 12* 9
= 108
Help me answer
Expand 3p(p+5)
Answers
Answer:
3p² + 15p
Step-by-step explanation:
We use distributive property to distribute 3p to each of the terms:
3p · p = 3p²
3p · 5 = 15p
3p² + 15p
Hey there!☺
\(Answer:\boxed{3p^2+15p}\)
\(Explanation:\)
\(3p(p+5)\)
Let's expand.
\(3p(p+5)\\\text{After Expanding: }3p^2+15p\)
So the answer is \(3p^2+15p\).
Hope this helps!
Nina is an artist who sells paintings online. She charges the same amount to ship each painting. When she sells 4 paintings, she charges a total of $9.96 for shipping. When she sells 8 paintings, she charges a total of $19.92 for shipping. How much more does Nina charge for shipping 20 paintings than for shipping 16 paintings?
a$2.49
b$9.96
c$19.92
d$29.96
Answers
Answer:
b. $9.96
Step-by-step explanation:
To solve this problem, let's first calculate how much Nina charges for shipping per painting. We'll divide the total shipping cost by the number of paintings sold.
When Nina sells 4 paintings and charges a total of $9.96 for shipping:
Shipping cost per painting = $9.96 / 4 = $2.49
When Nina sells 8 paintings and charges a total of $19.92 for shipping:
Shipping cost per painting = $19.92 / 8 = $2.49
We can see that regardless of the number of paintings sold, Nina charges $2.49 for shipping per painting.
Now let's calculate how much Nina charges for shipping 20 paintings and 16 paintings:
Shipping cost for 20 paintings = $2.49 * 20 = $49.80
Shipping cost for 16 paintings = $2.49 * 16 = $39.84
The difference in shipping charges for 20 paintings and 16 paintings is:
$49.80 - $39.84 = $9.96
Therefore, Nina charges $9.96 more for shipping 20 paintings than for shipping 16 paintings. The correct option is (b) $9.96.
the interquartile range (iqr) is a measure of the ____________ of the middle ____________ percent of the data.
Answers
The interquartile range (IQR) is a measure of the spread or variability of the middle 50 percent of the data.
The interquartile range (IQR) is a statistical measure that describes the spread or dispersion of the middle 50 percent of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.
The quartiles divide a dataset into four equal parts, each representing 25 percent of the data. The first quartile (Q1) represents the lower boundary of the middle 50 percent, while the third quartile (Q3) represents the upper boundary of the middle 50 percent. The IQR captures the range of values within this middle range.
By focusing on the middle 50 percent of the data and excluding the extreme values, the interquartile range provides a measure of variability that is less affected by outliers or extreme values. It is commonly used in descriptive statistics and data analysis to understand the spread and distribution of a dataset, particularly when the data is not symmetrically distributed or contains outliers.
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Q6. A colony of ants is beg please help, I don’t know this and I have to hand it in in 20 mins
increases exponentially at a rate of 10% per week. Initially there are 500
ants.
a) Show that the number of ants in the colony forms a geometric progression
b) The number of ants in week 8 is p times greater than in week 6. Find the value of p.
Answers
Answer:
a) The number of ants in week three is shown through the following geometric progression: 500*1.1*1.1*1.1
b) 1.21
Step-by-step explanation:
We know that 500 ants are increasing at a rate of 10% every week which means that we can calculate the week one ants like this
500*1.1
Week two
500*1.1*1.1
and so on.
We write the following equation
500(1.1)^n where n is the number of weeks
We plug in 8 and then 6 for n in the equation above and get
500(1.1)^8=1071.79
500(1.1)^6=885.78
Divide and get that p=1.21