According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
Find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = e−6x
The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].
The maclaurin series for f(x) is defined by the following formula:
[tex]f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}[/tex]--------------(1)
Where [tex]f^{i}[/tex] is the i - th derivative of the function
If f(x) = [tex]e^{-6x}[/tex], then the formula of the i - th derivative of the function is:
[tex]f^{i} =(-6)^{i} .e^{-6x}[/tex]----------------------(2)
Then,
[tex]f^{i}(0) = (-6)^{i}[/tex]
Lastly, the equation of the trascendental function by Maclaurin series is: [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex]---------------(3)
Hence,
The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].
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If a baseball is a sphere with a radius of 3.75 cm, what is the surface area of the baseball? use π = 3.14. a. 176.6 cm² b. 725.8 cm² c. 60.5 cm² d. 181.46 cm²
The surface area of the baseball is 176.6 cm² b.
What is meant by surface area?As a refresher, the surface area of an object is the sum of the areas of all of its faces or the exterior surfaces of its three dimensions. It is calculated in square units.The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area. This is calculated in square units and done using several area formulas.A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.To find the surface area of the baseball:
r=3.75
[tex]A=4\pi r^{2}[/tex]
[tex]A=4*\pi *3.75^{2}[/tex]
A=176.6 cm² b.
The surface area of the baseball is 176.6 cm² b.
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How do I solve this question.
Hello, the solution of the geometry problem is in this photo.
AOC = 136°
BOC = 44°
Change from rectangular to spherical coordinates. (let ≥ 0, 0 ≤ ≤ 2, and 0 ≤ ≤. ) (a) (5, 5 3 , 10 3 )
The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).
Here, the given rectangular coordinate is (5, 5.3, 10.3).
Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.
We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.
We know, ρ² = (x²+y²+z²)
Therefore, ρ
= √(x²+y²+z²)
= √[(5)²+(5.3)²+(10.3)²]
= √(25+28.09+106.09)
= √(159.18)
= 12.62
Again, tan θ = (y/x)
Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°
Similarly, cos Φ = (z/ρ)
Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°
Here, the spherical coordinate is (ρ, θ, Φ).
Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).
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Calculate angles in a triangle
HELP
Answer:
angle a = [tex]\boxed{154}^{\circ}[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠a + 13° + 13° = 180°
⇒ ∠a + 26° = 180°
⇒ ∠a = 180° - 26°
⇒ ∠a = 154°
Answer:
Angle a equals= 154°
Step-by-step explanation:
you have two angles which add up to 26°
remember that triangle always adds up to 180°
so you calculate 180-26 and you get 154
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
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olives and pineapple pizza delivered two large pizzas cut into eight slices each. james and his sister both ate 5/8 of the pizza together. how many slices are left?
if AB = 3 centimeters and AC = 2 centimeters, what is the largest possible perimeter, in centimeters, of isosceles triangle ABC?
Answer:
8
Step-by-step explanation:
AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.
P = 3 + 3 + 2 = 8.
PLEASE help me, im really struggling on this.
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:
x + y = 52 (1)
Also:
x + 2.25y = 72 (2)
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
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1/?
Which number produces a rational number when Multiplied 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number
Please Help!
The total arm and blade of a windshield wiper is 9 in. long and rotates back and forth through an angle of 92 degrees. The shaded region in the figure is the portion of the windshield cleaned by the 7-in. wiper blade. What is the area of the region cleaned?
answer with the last three decimal places
The area of the region cleaned by the 7-in wiper blade with the angle subtended being 92⁰ as described in the task content is; 39.32in².
What is the area cleaned by the 7-in wiper blade?According to the task content, it follows that the wiper blade is 7-in long and subtends an angle of 92°.
Consequently, the area swept by the blade in discuss can be determined by the Area of sector formula and hence, is;
Area = (92/360) × (22/7) × 7².
Area = 39.32 in².
Ultimately, it follows from the solving steps above that the area of the region cleaned by the 7-in wiper blade with the angle subtended being, 92⁰ is; Area = 39.32 in².
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A square has a side that measures 2.75 units. what is the area of a circle with a circumference that equals the perimeter of the square? use 3.14 for π, and round your answer to the nearest hundredth.
The area of a circle with a circumference that equals the perimeter of the square is 9.62 units².
What is circle ?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.the side measurements of the square is 2.75 units.
the perimeter of this square, we must multiply 2.75 by 4 because a square has four equal side measurements.
2.75 × 4 = 11
Let's use the formula for finding radius given the circumference.
[tex]Radius = \frac{circumference}{2\pi }[/tex]
the circumference because our circumference is 11 units.
Radius = [tex]\frac{11}{2pi }[/tex]
put π = 3.14 * 2
radius = 11 / 2 * 3.14
radius = 11/ 6.28 ⇒ 1.75
the area of the circle = [tex]\pi r^{2}[/tex]
area = 3.14 * (1.75)² ⇒9.61325
Lastly, we round this number to the nearest hundredth as it is asked of us in the problem.
9.61325 = 9. 62
Therefore, the area of the circle is 9.62 units².
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In circle D, which is a secant?
EF
DC
Line segment A B
Line G H
The secant of circle D is the 'line GH'. Where the line segment EF is the diameter of the circle, line segment DC is the radius, and the ray AB is the tangent of the given circle.
What is the secant of the circle?The line that passes through the circle and touches the circle at two points is said to be a secant line of the circle.
Which is the secant line in the given circle D?The given circle D has a center at D.
The radius of the circle is given by the line segment CD
The diameter (or) the longest chord of the circle is given by the line segment EF
The ray AB passes touches the circle at point B, which is called the tangent of the circle.
Where the line GH passes through the circle and touches at two points. So, this line GH is said to be the secant of the circle.
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Disclaimer: The given question is incomplete(needs a diagram). Here is the required diagram attached.
Question: In circle D, which is a secant?
a) EF
b) DC
c) Line segment AB
d) Line GH
Answer:
ray ab
Step-by-step explanation:
What is the slope of the linear equation that has the values shown in the table? Show your work
Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].
Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get
[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!
hope this helps!
A casino offers the following game: you draw one card from a standard 52-card deck. If you draw a jack, you win $1.25. If you draw a queen, you win $3.25. If you draw a king, you win $4.5 dollars. If you draw any ace except the ace of spades, you win $6.5. If you draw the ace of spades, you win $7.75. The entry fee to play this game is $1.75. Compute the expected value of this gamble (include the entry fee in your expected value).
Let [tex]W[/tex] be the random variable for the winnings from playing the game once.
• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.
• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.
• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.
• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.
• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.
• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.
So, the probability mass function for [tex]W[/tex] is
[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]
The expected winnings from playing one round of this game are
[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]
[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]
[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]
Seven is not an example of _____.
an expression
a term
a variable
a constant
Answer:
a variable.
Seven is a number and cannot be a variable.
Which of the following equations is the translation 2 units down of the graph of y = |x |?
a.) y = | x - 2|
b.) y = | x + 2|
c.) y = | x | + 2
d.) y = | x | - 2
Answer:
d
Step-by-step explanation:
up and down is outside of the x stuff so its c or d
and c is moving it up
d is moving it down
Answer:
d) y = | x | - 2
Step-by-step explanation:
In order to translate a graph downward 2 units ,we subtract 2 from the original function.
therefore,
If the Original function is y = |x|
Then the Function of the translated graph is y = | x | - 2
Three divers went scuba diving in the ocean for a couple of hours. The table shows how much oxygen they had left in their oxygen tanks.
Diver Oxygen (liters)
Alexis seventy nine over eighth
Dante 9.3
Sofia nine and eight over fifteenth
Place the divers in order from least to greatest based on the number of liters left in their oxygen tank.
Sofia, Dante, Alexis
Alexis, Sofia, Dante
Dante, Alexis, Sofia
Dante, Sofia, Alexis
The divers in order from least to greatest based on the number of liters left in their oxygen tank will be Alexis, Dante, and Sofia. The correct answer is B.
What is ascending order?In mathematics, placing numbers in ascending order refers to doing so from least to largest from left to right. When numbers are arranged in ascending order, they are done so from least to largest.
Given that three divers went scuba diving in the ocean for a couple of hours. The table for the oxygen requirement is given below:-
Diver Oxygen (liters)
Alexis Seventy nine over eighth
Dante 9.3
Sofia Nine and eight over fifteenth
The Numbers are:-
Alexis ( Seventy nine over eighth) = 79 / 9 = 8.78
Dante = 9.3
Sofia ( Nine and eight over fifteenth ) = 9(9/15} = 9.6
The arrangement from least to highest will be Alexis, Dante, and Sofia.
The correct options are given below:-
Sofia, Dante, Alexis
Alexis, Dante, and Sofia.
Dante, Alexis, Sofia
Dante, Sofia, Alexis
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Answer:
Dante, Alexis and Sofia
Step-by-step explanation:
please tell me if I'm wrong but I'm positive its Dante, Alexis and Sofia
check ple im not sure its right
Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
A 3D electron microscope magnifies objects 1 000 000 times. A water molecule has a diameter of
[tex]2 \times {10}^{ - 10} [/tex]
m.
How large will it appear in the microscope?
give your answer in milimetres.
The diameter of the water molecule is 2 * 10^-4 m or 0.2 mm.
What is a microscope?The term microscope refers to a device that is capable of increasing the size of an object. If the object is quite large, then it can be seen with the unaided eye.
Microscopes are very important in the sphere of scientific research as it was very instrumental in the study of cells and in the process of examination of other samples. There are several kinds of microscopes hay could be used for several purposes such as;
Electron microscopeCompound microscopeScanning electron microscope Light microscope etc.Each of these microscopes have a unique instance in which they could be utilized.
Given that the diameter of water is about 2 * 10^-10 m, a magnification by 1 000 000 times gives a diameter of 2 * 10^-4 m or 0.2 mm.
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What is the answer to the question: 9 to the second power times 13
Answer:
1053
Step-by-step explanation:
Find the volume of the cylinder shown using the formula in the box below. Round your answer to the nearest tenth. Show your work
Answer: 1960.2 cm
Step-by-step explanation:
v = πr^2h
v = π7.4^2(11.4)
= π54.76(11.4)
= 171.9464(11.4)
= 1960.2
The volume of the cylinder rounded to the nearest tenth is 1,960.2 cubic cm
What is the volume of the cylinder?Volume of the cylinder = πr²h
Where,
r = radius = 7.4 cm
h = height = 11.4 cm
π = 3.14
So,
Volume of the cylinder = πr²h
= 3.14 × 7.4² × 11.4
= 3.14 × 54.76 × 11.4
= 1,960.18896
Approximately to the nearest tenth
= 1,960.2 cubic cm
Therefore, 1,960.2 cubic cm is the volume of the cylinder with radius 7.4 cm and height 12.4 cm
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Find the radius of convergence, then determine the interval of convergence
By the ratio test, the series converges for
[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(x+2)^{k+1}}{\sqrt{k+1}} \cdots \frac{\sqrt k}{(x+2)^k}\right| = |x+2| \lim_{k\to\infty} \sqrt{\frac k{k+1}} = |x+2| < 1[/tex]
so that the radius of convergence is 1, and the interval of convergence is
|x + 2| < 1 ⇒ -1 < x + 2 < 1 ⇒ -3 < x < -1
The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.
Find the radius of convergence R and the interval of convergence:Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = β
If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusiveHere [tex]a_{k}[/tex] = [tex]\frac{(x+2)^{k}}{\sqrt{k} }[/tex] and [tex]a_{k+1}[/tex] = [tex]\frac{(x+2)^{k+1}}{\sqrt{k+1} }[/tex]
Now limit is taken,
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|[/tex]
= [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|[/tex]
= [tex]\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|[/tex]
= [tex]|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}[/tex]
= [tex]|{x+2 }|[/tex] < 1
- 1 < [tex]{x+2 }[/tex] < 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
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What do you get when you combine the following numbers? -4-4-4-4
Answer:
-16
Step-by-step explanation:
you just add all of them together
how do i get the method on how to solve this x+5(-2)-1
Answer:
I forgot the name but I can show you how to do it lol
Step-by-step explanation:
x+5(-2)-1
x-10-1 we multiplied 5 and -2
x-11
x=11
how I did the last one is there is a non-existent 0 with an equal sign like my teacher says so we added 11 to both sides.
Rashon walked 10 miles in 4 hours. if he walked the same distance every hour, how far did he walk in one hour? write your answer in feet if 1 mile equals 5280 feet.
Answer:
Step-by-step explanation:
Miles per hour: [tex]\frac{10miles}{4hrs} = 2.5\frac{miles}{hour}[/tex]
Feet per hour:
[tex]2.5\frac{miles}{hours} (\frac{5280ft}{1mile} )[/tex]
[tex]=13,200\frac{ft\\}{hr}[/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
x ≤ -2
Step-by-step explanation:
3(x + 2) ≤ 5(-2 - x)
Distribute on both sides.
3x + 6 ≤ -10 - 5x
Add 5x to both sides.
8x + 6 ≤ -10
Subtract 6 from both sides.
8x ≤ -16
Divide both sides by 8.
x ≤ -2
Answer:
[tex]\textsf{D. }x\leq-2[/tex]
Step-by-step explanation:
Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]
Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.
[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]
[tex]\implies 3x+6\leq-10-5x[/tex]
Step 2: Subtract [tex]6[/tex] from both sides.
[tex]\implies 3x+6-6\leq-10-6-5x[/tex]
[tex]\implies 3x\leq-16-5x[/tex]
Step 3: Add [tex]5x[/tex] to both sides.
[tex]\implies 3x+5x\leq-16-5x+5x[/tex]
[tex]\implies 8x\leq-16[/tex]
Step 4: Divide both sides by [tex]8[/tex].
[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]
[tex]\implies x\leq-2[/tex]
help solve math problem
Answer:
(c) x < -5.170
Step-by-step explanation:
The given function is an exponential function with a decay factor of 0.5 and a y-intercept of 0.5^2 = 0.25. It will be larger for more negative x-values.
EstimateWe know that 2^3 = 8, so (1/2)^-3 = 8. This means the exponent of 0.5 in the given inequality will be more negative than -3:
x +2 < -3
x < -5 . . . . . . . . subtract 2
The only answer choice in this range is ...
x < -5.170
Exact solutionTaking the logarithm of both sides of the inequality, we have ...
(x +2)log(0.5) > log(9)
x +2 < log(9)/log(0.5) . . . . . . log(0.5) < 0, so the inequality reverses
x < log(9)/log(0.5) -2 . . . . . . subtract 2
x < (0.95424251)/(-0.30103000) -2 = -3.1699250 -2
x < -5.1699250 ≈ -5.170
Evaluate 5(14 – 23) + 8 ÷ 2. (1 point) 26 34 44 56
Answer:
-41
Step-by-step explanation:
5(14-23)+8 ÷ 2
=5(-9)+4
=-45+4
=-41
The solution of the given expression 5(14-23)+8 ÷ 2 is -41.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
WE have given an expression as;
5(14-23)+8 ÷ 2
Solve the bracket then division;
=5(-9) + 4
=-45+4
=-41
Therefore, the solution of the given expression is -41.
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someone help me out pleaseee
Answer:
[tex] \frac{29}{18} = 1 \frac{11}{18} [/tex]
Step-by-step explanation:
To solve this question, we definitely need to make w the subject.
[tex]w - \frac{5}{6} = \frac{7}{9} \\ w - \frac{5}{6} + \frac{5}{6} = \frac{7}{9} + \frac{5}{6} \\ w = \frac{29}{18} \\ = 1 \frac{11}{18} [/tex]
Is it possible for bruce and felicia to have used the same number of tiles? use complete sentences to explain your reasoning.
At any value of x, Bruce would have always used 3 tiles less than Felicia.
What is an expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.Calculate to explain:
Number of tiles Bruce used: 5x + 2Number of tiles Felicia used: 5x + 5On equating the two expressions:5x+2 = 5x+5So, there is no solution.
Any value of x, Bruce would have always used 3 tiles less than Felicia.
Therefore, at any value of x, Bruce would have always used 3 tiles less than Felicia.
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The complete question is given below:
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.
Number of tiles Bruce used: 5x + 2
Number of tiles Felicia used: 5x + 5