The Mean Absolute Deviation (MAD) of 15 degrees indicates that the temperatures in 1900 fluctuated considerably, with the values distributed around the mean of 53.75 degrees Fahrenheit.
Mean Absolute Deviation (MAD) is a statistical metric that is used to calculate the average distance between each value in a set of data and the mean value of the dataset. It gives a better understanding of the variability of the dataset. A larger MAD indicates that the values in a dataset are more spread out, whereas a smaller MAD suggests that the data is tightly clustered around the mean.In this scenario, a MAD of 15 degrees tells us that the temperature readings from 1900 were not constant, but instead showed considerable variation over the year. The monthly temperatures ranged from 38.75°F in January to 74.5°F in July, indicating that the weather was not consistent throughout the year.
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What is the solution to this system of linear equations?
x − 3y = −2
x + 3y = 16
(7, 3)
(3, 7)
(−2, −3)
(−3, −2)
Answer:
(7,3)
Step-by-step explanation:
you can add the equations together to eliminate y and first solve for x
(x-3y = -2) + (x+3y=16) = (2x = 14)
x = 7
then plug x into one of the equations to solve for y
(7) - 3y = -2
9 = 3y
y = 3
the solution is (7,3)
Answer: (7, 3)
Step-by-step explanation:
x - 3y = -2
x + 3y = 16
Here we can add the two equations together to cancel out the y
2x = 14
divide by 2 on both sides to get
x = 7
Now that we have the X value, plug in x value into an equation to get the Y
x - 3y = -2
7 - 3y = -2
-3y = -9
y = 3
So the solution is (7, 3)
Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square roots
The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
How to determine the simplified equation?The complete question is added as an attachment
The equation is given as
[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]
Subtract (x - 10)^2 from both sides
[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]
Evaluate 4^2
[tex](y- 6)^2 =16 - (x - 10)^2[/tex]
Take the square root of both sides
[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]
Add 6 to both sides
[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
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Please help its confusing meeeeee
Answer:
p = 21.4 cm
∠P = 44°
Step-by-step explanation:
Apply the Pythagorean Theorem to solve for the length of p.
p² + 21² = 30²p² = 900 - 441p² = 459p = √459[tex]\fbox {p = 21.4 cm}[/tex]Now, take the inverse sine function to find angle P :
sin⁻¹ (opposite side / hypotenuse)sin⁻¹ (21/30)sin⁻¹ (0.7)[tex]\boxed {44^{o}}[/tex] (approximately)Answer:
a) 21.4 cm
b) 45.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
b) Angle PThe hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...
cos(P) = (21 cm)/(30 cm)
The angle value can be found using the inverse cosine function:
P = arccos(21/30)
P ≈ 45.6°
a) Side pNow, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.
tan(P) = p/21
p = 21×tan(P) = 21·tan(45.573°)
p ≈ 21.4 . . . . cm
__
Additional comment
In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.
Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.
What effect does 'h' have on the graph of a parabola?
Vertical stretch
Vertical compression
Vertical shift
Horizontal shift
The effect that 'h' have on the graph of a parabola is Horizontal shift or translation .
What is translation?A translation is the movement of a shape up, down , this can also be movement from side to side.
Even though there is movement, its appearance remains the same in any other way, hence, h values cause left or right movement with respect to the graph.
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Which x value makes this equation true? Explain how you can tell
2x^2 - x + 10 = 38
a) x=2
b) x=4
c) x=-4
d) x=6
Answer:
b) x = 4
Explanation:
[tex]2x^2 - x + 10 = 38[/tex]
collect variables
[tex]2x^2 - x + 10 - 38 = 0[/tex]
simplify
[tex]2x^2 - x - 28 = 0[/tex]
breakdown
[tex]2x^2 -8x + 7x - 28 = 0[/tex]
factor out
[tex]2x(x - 4) + 7(x - 4) = 0[/tex]
collect into groups
[tex](2x + 7)(x - 4) = 0[/tex]
set to zero
[tex]2x + 7 = 0, x - 4 = 0[/tex]
relocate variable
[tex]2x = -7, x = 4[/tex]
final solutions
[tex]x = -3.5, x = 4[/tex]
The answer is b.
To find the value of x, we need to convert this into the form of a quadratic equation.
Subtract 38 from each side.
2x² - x + 10 - 38 = 38 - 382x² - x - 28 = 0Solve by splitting the middle term.
2x² + 7x - 8x - 28 = 0x (2x + 7) - 4 (2x + 7) = 0x = 4, x = -7/2HELP HELP HELP HELP
HELP HELP HELP
This question has two parts. Use the information to answer Part A and Part B.
Part A
Enter a number in the box to create an expression equivalent to 2-5.
Part B
Which expressions represent the distance between the two points on the
number line? Select all that apply.
A 2-5
B. 2+(-5)
c. 1-3-21
D. 12-(-3)
E. 1-3+(-2)|
OF. 1-3-(-2)
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
What is integers on number line?
Integers are represented using a number line. A straight line of numbers is shown visually as a number line. It is made up of positive integers like 1, 2, etc., negative integers like - 1, - 2, etc., and a zero that is neither positive nor negative.
Part A:
2 - 5 = -3
2 + 1 = 3
The distance on the number line between a number and 0 is its absolute value.
a. That distance is never negative.
b. The symbol for Absolute Value is “ | | ”.
Hence, by taking 1 in the box it creates an expression equivalent to 2 - 5.
Part B:
|-3 -2| = 1
This point represent distance from -3 to -2 on the number line is 1 unit.
|2-(-3)| = 5
This point represent distance from 2 to -3 on the number line is 5 units.
|-3 + (-2)| = 5
This point represent distance from -3 to -2 on the number line is 5 units.
|-3 - (-2)| = 1
This point represent distance from -3 to -2 on the number line is 1 units.
Therefore,
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
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Please help me with this polynomial based questions
Answer:
Hello,
Step-by-step explanation:
All is in the following picture:
PLS HELP IN SUPER STUCK PLEASE HELP
Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 x + 2 B. y ≥ 2 x + 2 C. y < 2 x + 2 D.
Considering the given linear function, the inequality graphed is:
B. [tex]y \geq 2x + 2[/tex].
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:
m = (4 - 2)/(2 - 1) = 2.
Thus the equation of the line is:
y = 2x + 2.
The left-side of the line is the values above the line, hence the inequality is:
B. [tex]y \geq 2x + 2[/tex].
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help me to slove this
Answer:
1. pi. 2.49-12.25pi
Step-by-step explanation:
Find the surface area of the composite solid. Round your answer to the nearest hundredth.
A. 424.11 ft²
B. 438.00 ft²
C. 449.00 ft²
D. 549.78 ft²
The surface area of the composite solid is 579.84 square feet
How to determine the surface area of the solid?The composite solid that completes the question is added as an attachment
From the attached figure, we have the following figures:
Rectangular prismCylinderThe surface area of a rectangular prism is
A = 2(lw + lh + wh)
Using the dimensions of the prism, we have:
A = 2(6 * 11 + 6 * 8 + 8 * 11)
This gives
A = 404
The surface area of a cylinder is
A = 2πr^2 + 2πrh
Using the dimensions of the cylinder, we have:
A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5
Evaluate
A = 226.08
The area of the circle between both shapes is
A = πr^2
This gives
A = 3.14 * 4^2
A = 50.24
The surface area of the composite solid is then calculated as:
Surface area = Area of rectangular prism + Area of cylinder - Area of circle
This gives
Surface area = 404 + 226.08 - 50.24
Evaluate
Surface area = 579.84
Hence, the surface area of the composite solid is 579.84 square feet
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CSN SOMEONE PLEASE HELP ASAP
If the ADA guidelines state that a
wheelchair ramps angle of elevation
must equal 4.8°. would a
ramp with the
following dimensions be up to code?
Show your work and explain. (Picture is
not drawn to scale.)
3.5 ft
e°
40 ft
The ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
How to find the angle of elevation of the ramp?The angle of elevation of the ramp can be found using trigonometric ratios.
Therefore, the angle of elevation must be equal to 4.8 degrees to obey the ADA guidelines .
Hence,
tan ∅ = opposite / adjacent
opposite side = 3.5 ft
adjacent side = 40 ft
Therefore,
tan ∅ = 3.5 / 40
∅ = tan ⁻¹ 0.0875
∅ = 5.00064459756
∅ = 5 degrees
Therefore, the ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
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A music store owner noted that cd sales had dropped 23% from one quarter to the next. if the owner sold 715 units in the first quarter, how many did she sell in the next quarter?
round your answer to the nearest whole unit of cds. do not include units with your answer.
help please what's the correct answer
If the sales had dropped 23% then music store had sold 551 units in the second quarter.
Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.
We are required to determine the sales in the second quarter.
Percentage is the number or ratio expressed in terms of 100. It is expressed as %.
Sales in first quarter=715 units
Decrease in sales=23%
In units ,decrease=715*23%
=715*23/100
=164.45
Sales of second quarter=715-164.45
=550.55
After rounding we will get 551.
Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.
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PLEASE HELP ASAP
Determine the number of terms in the sequence. Your work must be shown with fractions not decimals.
2/81, 4/27, 8/9,…,6912
we conclude that the sequence has 8 terms.
How to get the number of terms in the sequence?
Here we have the geometric sequence:
2/81, 4/27, 8/9, ..., 6912
Notice that each term is equal to 6 times the previous term, such that:
2/81*6 = 4/27
4/27*6 = 8/9
Then the n-th term is equal to:
[tex]a_n = a_1*r^{n-1}[/tex]
Where in this case:
[tex]a_1 = 2/81\\\\r = 6[/tex]
Now we need to find the value of n such that:
[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]
If we apply the natural logarithm to both sides, then:
[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]
Then we conclude that the sequence has 8 terms.
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help me please please please
The area and circumference of a circle are 12.56square feet and 12.56ft respectively
Area and circumference of a circleThe formula for calculating the area and circumference of a circle is expressed as:
A = πr²
C = πd
where
r is the radius and d is the diameter
Area = 3.14 * (2)²
Area = 12.56ft²
For the circumference
C = 3.14(4)
C = 12.54ft
Hence the area and circumference of a circle are 12.56square feet and 12.56ft respectively
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9. The half-life of aspirin in your bloodstream is 12 hours. Use exponential model to
estimate how long for the 500 mg dosage to decay to 70% in your bloodstream.
after 6.2 hours the dose will decay to 70% in your bloodstream.
How long you must wait for the dosage to decay to 70% in your bloodstream?We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:
[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]
If the dosage needs to decay to a 70% of the initial dosage, then we must have:
[tex]e^{-t*ln(2)/12h} = 0.7[/tex]
Now we need to solve that for t:
If we apply the natural logarithm in both sides, we get:
[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]
So after 6.2 hours the dose will decay to 70% in your bloodstream.
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The inequality |2x - 5 > 8 can be written as which two inequalities?
Answer:
2x - 5 < -8 or 2x - 5 > 8
Step-by-step explanation:
|2x - 5| > 8
2x - 5 < -8 or 2x - 5 > 8
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
We have,
To split the inequality |2x - 5| > 8 into two separate inequalities, we consider both the positive and negative cases for the absolute value expression.
Positive case:
When 2x - 5 is positive, we have:
2x - 5 > 8 _____(1)
Negative case:
When 2x - 5 is negative, we have:
-(2x - 5) > 8
Simplifying the negative case:
-2x + 5 > 8 ______(2)
Now, we have two inequalities:
2x - 5 > 8
-2x + 5 > 8
These are the two inequalities resulting from the given inequality
|2x - 5| > 8.
Thus,
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
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A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Find the width of the freezer.
Step-by-step explanation:
volume = length • width • height
by making width subject
V=LWH
W=V/LH
W= 54/8×3
W=54/24
W=9/4
W=2.25
OA=
What Is OA=
Help me please!!! Thanksss
The length of side OA in the given rhombus is: 5 units.
What is a Rhombus?A rhombus is a quadrilateral that has four sides that are all of the same length. Therefore, in the image given, the length of AB equals the length of OA.
Given the following:
A(3, 4)B(8, 4)Length of AB = |8 - 3}
Length of AB = 5 units.
AB = OA = 5 units.
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1. What is the value of the 4th iterate of
f(x) = 3x-1/x2 if x0 = -2? Round to three decimal places.
The value of the 4th iterate of the given function f(x) is -2.096
2nd option is correct.
A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.
Any function taken on its own is regarded as the first iteration.
A function is said to have an identity function at iteration zero.
According to the question,
f(x) = (3x-1)/[tex]x^{2}[/tex]
[tex]x_{o}[/tex] = -2
The first iterate is calculated by finding f(-2).
f(-2) = (3(-2)-1)/4
f(-2) = -1.75
Similarly, the next iterates are calculated as follows:
f(-1.75) = -2.048
f(-2.048) = -1.71
f(-1.71) = -2.096
Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096
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show the height of the pyramid is 9 cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let us assume that the pyramid has a volume of 75 cm³ and square base area of 25 cm², hence:
Volume = (1/3) * area of base * height
75 = (1/3) * 25 * height
height = 9cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
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A man spends 1/4 of his salary on food and 1/8 on transportation. His salary is Rs. 50,000
i) Find his total expenses as a fraction of the salary
ii) Find the amount of salary he spent
iii) Find the remaining balance of the salary
total expenses= 1/4 + 1/8
the denominators should be equal to add the values.
1/4×2(divide both the numerator and denominator by two)
=2/8
=2/8+1/8
3/8//
3/8(fraction of the salary he spent)
3/8 of the salary
3/8×50,000
R.s 6250
balance = 50,000-6,250
= R.s 43,750//
The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t
At the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
How to describe the initial condition of this experiment?First of all, we would derive an expression for the position with respect to the angle (phase shift) under the appropriate conditions:
Asin(ωt + ø) = c₂sinωt + c₁cosωt.
At t = 0, we have:
y = c₂sin(0) + c₁cos(0).
y = 0 + c₁
y = 0 + 5
y = 5 units.
Therefore, we can logically deduce that at the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
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Complete Question:
The angle Φ represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then Φ = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then Φ = π. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then Φ = π/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Okay can someone explain this?
Answer:
see below
Step-by-step explanation:
90 degree clockwise will change x, y coordinates to y, -x
point D 1,3 becomes 3,-1
point E 4, 4 becomes 4,-4
point F 4, -2 becomes -2,-4
point G 1,-1 becomes -1, -1
Can someone help me please
EXTRA POINTS HELP ASAP!
x + x/3 = 4/9
solve for x
Answer:
x=1
Step-by-step explanation:
1 + 1/3 = 4/9
1/3 also equals 3/9
hope this helped :)
Answer :
Value of x is 1 / 3Step-by-step explanation :
>> (3 × x + x / 3) = 4 / 9
>> (3x + x / 3) = 4 / 9
>> (4x / 3) = 4 / 9
>> 4x × 9 = 3 × 4
>> 36x = 12
>> x = 12 / 36
>> x = 6 / 18
>> x = 3 / 9
>> x = 1 / 3
Write down the mathematical name of the shape made by each net.
a)
b)
How do I do the picture
Answer:
1. Cube
2. Square-based pyramid
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
a) Cube
b Pyramid
Which answer best describes the complex zeros of the polynomial function? f(x)=x3+x2+10x+10
"The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location."
Polynomial functions are equations such as quadratic and cubic equations that take only the non-negative integer power of a variable or a positive integer exponent. For example, 2x + 5 is a polynomial with an exponent equal to 1.
A polynomial function is an expression that is a combination of variables of different degrees, non-zero coefficients, positive exponents (of variables), and constants. For example, f (b) = 4b2 – 6 is a polynomial of'b'and has a degree of 2.
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A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies cost $64.00, how much will it cost to print 1500 copies?
Answer:
88.5
Step-by-step explanation:
3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:
64-28 = 36.
Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get
88.5