Using the Empirical Rule, it is found that 99.7% of the data will be between 11.7 and 32.7 inches.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering the mean and the standard deviation of the data-set, the bounds between which 99.7% of the data-set are given by:
22.2 - 3 x 3.5 = 11.7 inches.22.2 + 3 x 3.5 = 32.7 inches.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Answer: 11.7 & 32.7
Step-by-step explanation:
Approximately $99.7\%$ of the snowfall amounts are between 1$$ inches and 2$$ inches.
Correct answers:
1: 11.7 2: 32.7
The Empirical Rule states that approximately 99.7% of the data is within 3 standard deviations of the mean. In terms of the sample mean x¯ and sample standard deviation s, that is between x¯−3s and x¯+3s.
The value 3 standard deviations below the mean is
x¯−3s=22.2−3(3.5)=11.7.
The value 3 standard deviations above the mean is
x¯+3s=22.2+3(3.5)=32.7.
So by the Empirical Rule, we can say that approximately 99.7% of the snowfall amounts are between 11.7 and 32.7 inches.
Solve the system of linear equations
x+y=4
-3x-y+-8
Answer:
y=3x+8
Step-by-step explanation:
Formula is L(x)=f(a)+f(a)(x-a)
This is for linearization
Lines c and d are perpendicular. The slope of line c is −1/3. What is the slope of line d?
Answer:
1/3
Step-by-step explanation:
When two lines are perpendicular, it means the lines intersect at a right angle and have opposite reciprocal slopes.The slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.
To figure out d we need to use the formula:
- 1 / m
Plug in:
- 1 / - 1/3
Solve:
1/3
[tex]~~~~~~m_c \times m_d = -1\\\\\implies -\dfrac 13 \times m_d=-1\\\\\implies m_d = 3\\\\\text{The slope of line d is 3.}[/tex]
difference of 2.4 − 1.8 = ________ by rounding each number to the nearest whole number.
Where is the function f(x)=3x^2-6x-45/x^2-5x discontinuous, and what types of discontinuities does it have?
Answer:
Below.
Step-by-step explanation:
f(x)=3x^2-6x-45/x^2-5x
= 3x^2-6x-45 / (x(x - 5))
The denominator is zero when x - 0 and x = 5.
So there will be a vertical asymptote at x = 0 and a hole at x = 5.
If we do the division we get f(x) = 3 remainder 9x - 45
so there will also be a horizontal asymptote where x = 3.
Answer:
Hole at (3, 4.8)
Asymptotes at x = 0 and y = 3
Step-by-step explanation:
[tex]f(x)=\dfrac{3x^2-6x-45}{x^2-5x}[/tex]
Factor the numerator:
[tex]\implies 3x^2-6x-45[/tex]
[tex]\implies 3(x^2-2x-15)[/tex]
[tex]\implies 3(x^2+3x-5x-15)[/tex]
[tex]\implies 3(x(x+3)-5(x+3))[/tex]
[tex]\implies 3(x-5)(x+3)[/tex]
Factor the denominator:
[tex]\implies x^2-5x[/tex]
[tex]\implies x(x-5)[/tex]
Factored form of function:
[tex]\implies f(x)=\dfrac{3(x-5)(x+3)}{x(x-5)}[/tex]
Discontinuity: a point at which the function is not continuous.
Holes
After factoring the rational function, if there is a common factor in both the numerator and denominator, there will be a hole at that point (x-value):
[tex]\implies (x-5)=0 \implies x=5[/tex]
Factor out the common factor from the function and input the found value of x into the new function to find the y-value of the hole:
[tex]\implies f(x)=\dfrac{3(x+3)}{x}[/tex]
[tex]\implies f(5)=\dfrac{3(5+3)}{5}=4.8[/tex]
Therefore, there is a hole at (5, 4.8)
Asymptotes
To find the vertical asymptotes, set the denominator of the new (factored) function to zero and solve:
⇒ Vertical Asymptote at x = 0
As the degrees of the leading terms of the numerator and denominator are equal (both x²), the horizontal asymptote is equal to the ratio of the leading coefficients.
⇒ Horizontal Asymptote at y = 3
If $1.35 is invested in an
account, find the amount of
money in the account after
10 years if it earns 1.15%
interest compounded semi-
annually.
Answer:
$1.51 is in the account after 10 years.
Step-by-step explanation:
Step 1: Identify the Type of Problem
We can see that this is a compound interest problem due to the phrase "earns 1.15% interested compounded" in the problem.
The formula for compound interest is as follows:
[tex]A=P(1+\frac{r}{n})^{n*t}[/tex] where:
A = final amount P = principal amount (in other words, the initial or first investment)r = interest rate (as a decimal)n = number of times interest is compounded per yeart = time (in years)Step 2: Identify what we Know
Now that we have the formula we'll be working with, let's see what we know. From the problem, we can see:
A = ? (this is what we are solving for)P = $1.35r = 1.15% → 0.0115n = 2 (semi-annually means twice a year)t = 10 yearsStep 3: "Plug and Chug"
Now, all we have to do is substitute the above values into our formula. Doing so, we get:
[tex]A=1.35*(1+\frac{0.0115}{2})^{2*10} \\= \bf \$1.51[/tex]
(Note: Since the answer is an amount of money, I have rounded to the hundreths place.)
Hope this helps!
To learn more about compound interest, check out the following question:
https://brainly.com/question/21270833Correlation analysis is used to determine
Answer:
Correlation analysis is used to quantify the degree to which two variables are related.
Step-by-step explanation:
In research, correlation analysis is a statistical approach for calculating and measuring the strength of a linear relationship between two variables. Simply defined, correlation analysis determines how much one variable changes as a result of the change in the other. A high correlation indicates a strong association between two variables, whereas a low correlation indicates a weak relationship.
5. Sarah made 17 out of 25 free throws during practice. What percentage of free throws did she NOT make? A. 68% B. 58% C. 32% D. 36%
Answer:
C. 32%
Step-by-step explanation:
The percent 17 is of 25.
17 of 25 can be written as:
17/25
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
17/25 * 100/100
= (17 * 100/25) * 1/100 = 68/100
Therefore, the answer is 68%
If Sara made 68% of her free shows, that means she didn't make 32% of her free throws (100 - 68 = 32).
In a classroom, 4/6of the students are wearing
sneakers. This is 3/6more than the fraction of the
students wearing boots. What fraction of the
students are wearing boots? Write an equation
to model the problem.
The time it takes Adam to drive to Disney World varies inversely with his
average rate of speed.
If it takes Adam 10.8 hours at an average speed
of 50 miles per hour, how long would it take him at
an average speed of 60
miles per hour?
The distance will remain constant. Then the time taken by Adam with an average speed of 60 miles per hour is 9 hours.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
[tex]\rm Speed = \dfrac{Distance}{Time}\\\\\\[/tex]
The formula can be written as
Distance = Speed × Time
The time it takes Adam to drive to Disney World varies inversely with his average rate of speed.
If it takes Adam 10.8 hours at an average speed of 50 miles per hour.
If the average speed is 60 miles per hour, then the time taken will be
The distance will remain constant.
S₂ × T₂ = S₁ × T₁
60 × T₂ = 50 × 10.8
T₂ = 9 Hours
More about the speed link is given below.
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solve the quadratic formula x^2+4x-3=0
Answer:
using quadratic equation formula
-b±/b²‐4ac all over 2a
Here is a 15-by-8 rectangle divided into triangles.
8
9
6
Is the shaded triangle a right triangle?
no
The sides of the shaded triangle do not form a Pythagorean triple, therefore, it is not a right triangle.
What is a Right Triangle?A triangle is a right triangle if the square of its longest side equals the sum of the square of the other two smaller sides, based on the Pythagorean Theorem.
Using the Pythagorean Theorem, find the lengths of the legs of the shaded triangle, and find out the sum of their squares equals the length of the longest side.
First leg of the shaded triangle = √(8² + 6²) = 10
Second leg of the shaded triangle = √(8² + 9²) = 12
The third side (longest side) of the shaded triangle is 9 + 6 = 15.
15² = 10² + 12²
225 = 244 (not true)
Therefore, the shaded triangle is not a right triangle.
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Given the following set of numbers find the mean, median and mode. 6, 6, 8, 7, 10, 14, 13, 6, 5, 7, 8, 10, 13, 6, 7
Mean, median, and mode of the given data is 8.4, 7, and 6 respectively.
What is Central Tendency?A central tendency is a central or typical value for a probability distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode.
Here, Given data
x f xf
5 1 5
6 4 24
7 3 21
8 2 16
10 2 20
13 2 26
14 1 14
Mean = ∑xf/∑f
= 126/15
= 8.4
Median = 7
Mode = 6
Thus, Mean, median, and mode of the given data is 8.4, 7, and 6 respectively.
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The function C (t) = StartFraction 4 t Over t squared + 2 EndFraction models the cost per student of a field trip when x students go on the trip. How is the parent function On a coordinate plane, 3 curves are shown. One curve opens up and to the right in quadrant 1 and goes through (2, 4) and (4, 1). Another curve approaches x = negative 2 in quadrant 2, changes direction at (0, 0), and then decreases in quadrant 4 and approaches y = 2. The third curve opens down and to the left in quadrant 3 and goes through (negative 4, negative 1) and (negative 2, negative 4). transformed to create the function On a coordinate plane, 2 curves are shown. One curve opens up and to the left in quadrant 2 and goes through (negative 4, 8) and (negative 6, 6). Another curve opens down and to the right and goes through (negative 1, negative 3), (0, 0), and (6, 3).?
Answer:
It is vertically stretched by a factor of 200 and shifted 10 units up.
Step-by-step explanation:
cool like that
It is vertically stretched by a factor of 200 and shifted 10 units up.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
How do you write a function?You write functions with the function name followed by the dependent variable.
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how the Distributive Property can be used to solve the equation.
3(x + 4) = 36.
Answer:
3(x+4)=36
You would multiply 3 times x and 4
3x+12=36
Subtract 12 from both sides
3x=24
x=8
Step-by-step explanation:
[tex]\rule{289}{2}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
how to solve [tex]\textsc{3(x+4)=36}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First of all, multiply the number before the parentheses by the expression inside the parentheses:-
[tex]\bigstar\sc{3\times x\times4}[/tex]
Which equals
[tex]\bigstar\textsc{3x+12}[/tex]
So the equation is:-
[tex]\square[/tex] [tex]\textsc{3x+12=36}[/tex] Subtract 12 on both sides:-
[tex]\textit{3x=24}[/tex] Next, divide by 3 on both sides:-
[tex]\textit{x=8}\Huge\checkmark[/tex]
Good luck with your studies.[tex]\smile\rule{300}{2}\smile[/tex]
WILL MARK BRAINLIEST
Answer:
cot(t) = 56/33
Step-by-step explanation:
cot(t) = 56/33, because cot = adj/opp simple as that..
A correlation coefficient of -0.85 means:
As one variable increases in value the other variable decreases in value
No relationship between the variables
As one variable increases in value the other variable also increase in value
Answer:
do you got an answer key
Step-by-step explanation:
PLS HELP
Find the value of x and y
Answer: 'X' = 24 degrees
Step-by-step explanation:
5 times 'X' = 120 degrees (because the formula is base times height divided by 2).
120 divided by 5 = 'X'
= 24
'X' = 24 degrees
PLEASE HELP ME WITH THIS!!!
Answer:
B. 1
Step-by-step explanation:
imagining where 10 would be on the graph you can see that the line will cross with 1 missed shot
Answer the following.
Calculate the cost of carpet for the following room.
The room is 15 feet x 12 feet. The cost of the carpet is $2.99 per square foot and the cost of
the pad is $.50 per square foot. Installation costs are $.50 per square foot.
Answer:
I think the total is 628.20$
Step-by-step explanation:
15*12=180
180*2.99=538.2
180*.5=90
90+538.2=628.2
Hope this helped :)
Why does the shape of the moon appear to change over the course of about a month? (2 points)
Group of answer choices
The sun is always lighting up the same amount of the moon.
The sun is lighting up different amounts of the moon.
The moon changes shape over the course of a month.
The moon shrinks and grows bigger depending on the time of month.
Which one of the following statements is not true.
A. Soil is the second layer of Earth's crust.
B. Metals can be extracted from minerals.
C. Oil is made from dead plants and animals.
D. Chemical weathering can break down rocks into fragments.
Answer:
I think c sorry if wrong
Step-by-step explanation:
have a good day
The ratio of the side length of a square to the square's perimeter is always 1 to 4.
Side lenght of square (inches): 1 ,___, ___, 7
Perimeter of square (inches). : 4, 8, 16, ____
Answer:
Side length of square (inches): 1 ,2, 4, 7
Perimeter of square (inches). : 4, 8, 16, 28
Step-by-step explanation:
Ratio is 1:4 (S:P).
So:
#:8, #=2. This is because 2/8 and 1/4 both = 0.25.
#:16, #=4. 4/16=0.25
7:#, #=28. 4x7=28, 7/28=0.25
Hope that helps
PLEASEE HELP ME WITH !!!!!
Answer:
C = 101
Step-by-step explanation:
A triangle has 180 degrees, so just minus 28 and 51 by that and you get 101... it's pretty simple
WHICH ONE?? NEED HELP ASAP
Answer:
DD
Step-by-step explanation:
If you distribute the 2 you get 12.2x + 14 so D
Please help me do this mathematics assignment
Answer:
dy = -3
dx
equation of normal=
y=1/3x+1
Step-by-step explanation:
dy/dx=10x-3
=10(0)-3
= -3
equation of normal:
grad=1/3
y-1 =1/3
x-0
3y-3=x
y= 1/3x+1
[tex]\underline{\textbf{First part:}} \\\\\text{Given that,}\\\\~~~~~~y= 5x^2-3x+6\\\\\\\implies \dfrac{dy}{dx} = \dfrac{dy}{dx} (5x^2 -3x +6)\\ \\\\~~~~~~~~~~~=5\dfrac{d}{dx} x^2-3\dfrac{d}{dx} x + \dfrac{d}{dx} (6)\\\\\\~~~~~~~~~~~=5\cdot 2x-3+0\\\\\\~~~~~~~~~~~=10x-3\\\\\text{At (0,1)}\\\\\dfrac{dy}{dx} = 10(0) -3 \\\\~~~~~=0-3\\\\~~~~~=-3[/tex]
[tex]\underline{\textbf{Second part:}}\\\\[/tex]
[tex]\text{Equation of normal,}\\\\~~~~~~y-y_1 = -\dfrac{1}{\tfrac{dy}{dx}} (x-x_1)\\\\\\\implies y - 1 = -\dfrac 1{-3 }(x-0)\\\\\\\implies y-1 = \dfrac 13 x\\\\\\\implies y= \dfrac 13 x +1[/tex]
Find the total surface area of the triangular prism
shown below.
5 cm.
5 cm.
11 cm.
6 cm.
Answer:
Answer:
124.84
Step-by-step explanation:
A = ah + bh + ch + 1 /2×√( ﹣a^4 ﹣ b^4 ﹣ c^4+ 2(ab)² + 2(ac)² + 2(bc)² ) =4×7+5×7+6×7+ 1 /2×√(-4^4 - 5^4 - 6^4 + 2(4×5)² + 2(4×6)² + 2(5×6)² )
≈ 124.84313
Step-by-step explanation:
PLEASE HELP ASAP A can has a radius of 1.3
inches and a height of 3.8 inches. What is the
volume of the can? (The volume of a cylinder
is V = Tr? where 7 ~ 3.14, r is the radius,
and / is the height.)
Answer:
V=20.17
Step-by-step explanation:
V=πr²h
=π1.3²×3.8
=20.17
Given: sin = 4/5 and cos x = -5/13 ; evaluate the following expression.
cos( ∅ - x )
Answer:
[tex]\cos(\theta - x)=\dfrac{33}{65}[/tex]
Step-by-step explanation:
Given:
[tex]\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}[/tex]
[tex]\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}[/tex]
Using the trig identity:
[tex]\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B[/tex]
[tex]\begin{aligned}\implies \cos(\theta - x) &=\cos \theta \cos x + \sin \theta \sin x\\\\&=\dfrac{3}{5} \cdot -\dfrac{5}{13} + \dfrac{4}{5} \cdot \dfrac{12}{13}\\\\&=-\dfrac{15}{65} + \dfrac{48}{65}\\\\&=\dfrac{33}{65}\end{aligned}[/tex]
sinø=4/5
so
cosø=3/5And
cosx=-5/13
so
sinx=12/13cos(ø-x)
sinøsinx+cosøcosx(4/5)(12/13)+(3/5)(-5/13)(48/65)-(15/65)48-15/6533/65Amna multiplies 38 by 4.
Should her answer be greater than or less than 4?
It should be greater not lesser
On a coordinate plane, the pre-image is shifted 2 units to the right and 1 unit up. It is rotated 90 degrees counterclockwise.
Which sequence of transformations produced the image?
Answer:B.
Step-by-step explanation:
B.a translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin