Answer:
1178 because 31 dollars an hour for 38 hours you would multiply or times 31 and 38 and get 1178 for total money earned
If f(x)=3x^2-2x+4and g(x)=5x^2+6x-8, find (f-g)(x)
The volume of a spherical balloon is 20⅚πm³. Find the radius of the balloon.
Who can help me to answer this question? Please and thank you very much .
Answer: 2.5 meters
This value is exact without any rounding.
======================================================
Explanation:
The first task is to convert the mixed number 20⅚ into an improper fraction
I'll write 20⅚ as 20 & 5/6
The rule to use is a & b/c = (a*c + b)/c
So,
a & b/c = (a*c + b)/c
20 & 5/6 = (20*6+5)/6
20 & 5/6 = 125/6
This means the volume is exactly (125/6)pi cubic meters.
Plug this into the sphere volume formula and isolate the radius r like so
V = (4/3)*pi*r^3
(125/6)pi = (4/3)*pi*r^3
125/6 = (4/3)*r^3
(4/3)*r^3 = 125/6
4r^3 = 3*(125/6)
4r^3 = 125/2
r^3 = (125/2)*(1/4)
r^3 = 125/8
r = (125/8)^(1/3)
r = 5/2
r = 2.5
A 3 metre long piece of ribbon is cut into
two pieces in the ratio 3:2.
How long is the shorter piece?
Step-by-step explanation:
3 meters = 300 cm
anyway, the ratio tells us that the whole ribbon can be seen as the combination of 3 + 2 = 5 equally long parts.
one such part is then
3 m / 5 = 0.6 m or 60 cm
the shorter piece is 2 of these parts long :
2 × 0.6 = 1.2 m or 120 cm
Find the terms through degree four of the maclaurin series for f(x) = sin(x) 1−x.
The terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].
In this question,
The function is f(x) = [tex]\frac{sin(x)}{1-x}[/tex]
The general form of Maclaurin series is
[tex]\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......[/tex]
To find the Maclaurin series, let us split the terms as
[tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] ------- (1)
Now, consider f(x) = sin(x)
Then, the derivatives of f(x) with respect to x, we get
f'(x) = cos(x), f'(0) = 1
f''(x) = -sin(x), f'(0) = 0
f'''(x) = -cos(x), f'(0) = -1
[tex]f^{iv}(x)[/tex] = cos(x), f'(0) = 0
Maclaurin series for sin(x) becomes,
[tex]f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....[/tex]
⇒ [tex]f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....[/tex]
Now, consider [tex]f(x) = (1-x)^{-1}[/tex]
Then, the derivatives of f(x) with respect to x, we get
[tex]f'(x) = (1-x)^{-2}, f'(0) = 1[/tex]
[tex]f''(x) = 2(1-x)^{-3}, f''(0) = 2[/tex]
[tex]f'''(x) = 6(1-x)^{-4}, f'''(0) = 6[/tex]
[tex]f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24[/tex]
Maclaurin series for (1-x)^-1 becomes,
[tex]f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....[/tex]
⇒ [tex]f(x)=1+x+x^{2} +x^{3} +......[/tex]
Thus the Maclaurin series for [tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] is
⇒ [tex]f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)[/tex]
⇒ [tex]f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....[/tex]
⇒ [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex]
Hence we can conclude that the terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].
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Select all angles that have a negative measure. Someone pls help.
Answer:
First and second angles going upward
Answer: 2, 4, 6
Step-by-step explanation:
(2x² + 6x + 6) (3x - 2)
Answer:
6x³ + 14x² + 6x - 12
Step-by-step explanation:
(3x - 2)(2x² + 6x + 6)
6x³ - 4x² + 18x² - 12x + 18x - 12
6x³ + 14x² + 6x - 12
Answer: 6x³+14x²+6x-12
Step-by-step explanation:
Here, we can use the distributive property to multiply one of the factors by each term in the other. Below, I multiplied [tex]2x^2 + 6x + 6[/tex] by both 3x and -2.
[tex](2x^2+ 6x + 6) (3x - 2)\\3x(2x^2+ 6x + 6)-2(2x^2+ 6x + 6)\\6x^3+18x^2+18x-4x^2-12x-12[/tex]
Now, we can rearrange so that like terms are next to each other. Then, we can combine them to simplify.
[tex]6x^3+18x^2+18x-4x^2-12x-12\\6x^3+18x^2-4x^2+18x-12x-12\\6x^3+14x^2+6x-12[/tex]
Explain type i error and give an example. explain type ii error and give an example. what is the best way to reduce both kinds of error? find a current scenario that has a type i error and a type ii error. is this scenario an example of an inverse relationship? why or why not?
Type I error says that we suppose that the null hypothesis exists rejected when in reality the null hypothesis was actually true.
Type II error says that we suppose that the null hypothesis exists taken when in fact the null hypothesis stood actually false.
What is Type I error and Type II error?In statistics, a Type I error exists as a false positive conclusion, while a Type II error exists as a false negative conclusion.
Making a statistical conclusion still applies uncertainties, so the risks of creating these errors exist unavoidable in hypothesis testing.
The probability of creating a Type I error exists at the significance level, or alpha (α), while the probability of making a Type II error exists at beta (β). These risks can be minimized through careful planning in your analysis design.
Examples of Type I and Type II error
Type I error (false positive): the testing effect says you have coronavirus, but you actually don’t.Type II error (false negative): the test outcome says you don’t have coronavirus, but you actually do.To learn more about Type I and Type II error refer to:
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Determine what type of model best fits the given situation: water leaking from a local reservior at the rate of 500 gallons per hour.
The type of model that best fits the given situation is; A linear equation Model
What is the model of the equation?Right inside the local reservoir we will have an initial amount of water A.
Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.
Thus, after t hours, the amount of water in the reservoir is expressed as:
W = A - 500gal * t
This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.
The domain of this model is restricted because we can't have a negative amount of water in the reservoir, and as such the maximum value of t accepted is: W = 0 = A - 500gal*t
t = A/500 hours
Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }
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Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answer:
[tex]\dfrac{1}{2} \left(25 \arcsin \left(\dfrac{x}{5}\right) -x\sqrt{25-x^2}\right) + \text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{x^2}{\sqrt{25-x^2}}\:\:\text{d}x[/tex]
Rewrite 25 as 5²:
[tex]\implies \displaystyle \int \dfrac{x^2}{\sqrt{5^2-x^2}}\:\:\text{d}x[/tex]
Integration by substitution
[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]
[tex]\textsf{Let }x=5 \sin \theta[/tex]
[tex]\begin{aligned}\implies \sqrt{5^2-x^2} & =\sqrt{5^2-(5 \sin \theta)^2}\\ & = \sqrt{25-25 \sin^2 \theta}\\ & = \sqrt{25(1-\sin^2 \theta)}\\ & = \sqrt{25 \cos^2 \theta}\\ & = 5 \cos \theta\end{aligned}[/tex]
Find the derivative of x and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=5 \cos \theta[/tex]
[tex]\implies \text{d}x=5 \cos \theta\:\:\text{d}\theta[/tex]
Substitute everything into the original integral:
[tex]\begin{aligned}\displaystyle \int \dfrac{x^2}{\sqrt{5^2-x^2}}\:\:\text{d}x & = \int \dfrac{25 \sin^2 \theta}{5 \cos \theta}\:\:5 \cos \theta\:\:\text{d}\theta \\\\ & = \int 25 \sin^2 \theta\end{aligned}[/tex]
Take out the constant:
[tex]\implies \displaystyle 25 \int \sin^2 \theta\:\:\text{d}\theta[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \cos (2 \theta)=1 - 2 \sin^2 \theta[/tex]
[tex]\implies \displaystyle 25 \int \dfrac{1}{2}(1-\cos 2 \theta)\:\:\text{d}\theta[/tex]
[tex]\implies \displaystyle \dfrac{25}{2} \int (1-\cos 2 \theta)\:\:\text{d}\theta[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\cos kx$}\\\\$\displaystyle \int \cos kx\:\text{d}x=\dfrac{1}{k} \sin kx\:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\begin{aligned} \implies \displaystyle \dfrac{25}{2} \int (1-\cos 2 \theta)\:\:\text{d}\theta & =\dfrac{25}{2}\left[\theta-\dfrac{1}{2} \sin 2\theta \right]\:+\text{C}\\\\ & = \dfrac{25}{2} \theta-\dfrac{25}{4}\sin 2\theta + \text{C}\end{aligned}[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \sin (2 \theta)= 2 \sin \theta \cos \theta[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{25}{4}(2 \sin \theta \cos \theta) + \text{C}[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{25}{2}\sin \theta \cos \theta + \text{C}[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{5}{2}\sin \theta \cdot 5 \cos \theta + \text{C}[/tex]
[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{5} \textsf{ and }5 \cos \theta = \sqrt{25-x^2}:[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{5}{2}\cdot \dfrac{x}{5} \cdot \sqrt{25-x^2} + \text{C}[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{1}{2}x\sqrt{25-x^2} + \text{C}[/tex]
[tex]\textsf{Substitute back in } \theta=\arcsin \left(\dfrac{x}{5}\right) :[/tex]
[tex]\implies \dfrac{25}{2} \arcsin \left(\dfrac{x}{5}\right) -\dfrac{1}{2}x\sqrt{25-x^2} + \text{C}[/tex]
Take out the common factor 1/2:
[tex]\implies \dfrac{1}{2} \left(25 \arcsin \left(\dfrac{x}{5}\right) -x\sqrt{25-x^2}\right) + \text{C}[/tex]
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The lifeguards at the beach post information of surfers by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?
Answer:
336
Step-by-step explanation:
They can place 1 of 8 frags on the bottom.
Now they have 7 flags left.
They can place 1 of 7 flags in the middle.
Now they have 6 flags left.
The can place 1 of 6 flags on top.
8 × 7 × 6 = 336
The diameter of a circle is 8 mm. What is the circumference of the circle?
25 and 1/7mm?
50 and 2/7mm?
11/28mm?
Or
19 and 1/4mm?
Answer:
25.12 rounded.
Step-by-step explanation:
C = 2[tex]\pi[/tex]r
C=[tex]\pi[/tex]d
C = [tex]\pi[/tex](8)
C = 25.12 rounded.
Answer:
25 and 1/7 mm
Step-by-step explanation:
Diameter = circunference / π
π = 3.1416 aprox.
Then:
8 = citcunference / 3.1416
8 * 3.1416 = circunference
25.1428 = circunference
1/7 = 0.1428
Then:
25.1428 = 25 + 1/7
= 25 1/7
I am a fraction. The ratio between my numerator and denominator is 2:5. My denominator is 6 more than my numerator. What fraction am I ?
Answer:
4/10
Step-by-step explanation:
Let the numerator be 2x and the denominator is 5x. The denominator is 6 more than the numerator so if we add 6 to the numerator both numbers should be equal.
Solve:
2x+6 = 5x
6 = 3x
x = 2
2x = 4
5x = 10
Step-by-step explanation:
Let the numerator be 2x and denominator be 5x,
A.T.Q,
2x+6 = 5x
2x-5x = -6
-3x = -6
3x = 6
x = 2
So, the fraction is 4/10 = 2/5
A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes? (1 point) 0 x<9.02 or x> 9.48 because lx - 9.251 > 0.23 o x<9.25 or x > 9,48 because ix - 0.231 9.25 > 0 0 x€ 9.02 or x> 9.48 because ix - 0.231 9.25 > 0 o x< 9.25 or x> 9.48 because ix - 9.25| > 0.23
Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
What is the range?In mathematics, the range of a function can refer to one of two notions that are closely related.The function's codomain, the function's visual representation.A binary relation f between two sets X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y.To find the rejected masses:
If each pack of trail mixes is supposed to weigh 9.25 oz and must be within 0.23 oz of that weight to be accepted, then rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
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The correct question is given below:
A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?
Which expression converts 100 inches per minute to feet per minute? 100 inches/ 1 minute x 60 minutes/ 1 hour
Option ( C ) is correct for this expression . 100 inches Over 1 minute times × 1 foot Over 12 inches.
What is a basic expression?
Expressions are basically the building blocks of Statements, in that every BASIC statement is made up of keywords (like GOTO, TO, STEP) and expressions. So expressions include not just the standard arithmetic and boolean expressions (like 1 + 2), but also values (scalar variables or arrays), functions, and constants.Given that the expression 100 inches.
We need to convert 100 inches per minute to feet per minute.
Since, we know that 1ft = 12 inch
Then,
1 in = 1/12 ft
Now, we shall convert 100 inches per minute to feet per minute.
To convert in/min to ft/min, let us multiply by 1/12
Thus, we have,
[tex]\frac{100 in}{min} * \frac{1 ft }{12 in}[/tex]
Therefore, option ( c ) is correct for this expression .
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The complete question is -
Which expression converts 100 inches per minute to feet per minute?
A) Start Fraction #1 100 inches Over 1 minute End Fraction × Start Fraction 60 minutes Over 1 hour End Fraction
B) Start Fraction #2 100 inches Over 1 minute End Fraction × Start Fraction 1 hour Over 60 minutes End Fraction
C) 100 inches Over 1 minute times × Start Fraction 1 foot Over 12 inches End Fraction
D) 100 inches Over 1 minute times × Start Fraction 12 inches Over 1 foot End Fraction
The midpoint of K is M(-3, -1). One endpoint is J(-12, -11). What are the coordinates of endpoint K?
K=
Answer:
K(6, 9)
Step-by-step explanation:
Let the K coordinates be (x, y)
Mid-point formula:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Applying formula:
[tex]\sf (-3,\:-1) = (\:\dfrac{-12+x}{2} ,\: \dfrac{-11+y}{2} )[/tex]
Comparing expression:
[tex]\sf \dfrac{-12+x}{2} = -3 \quad and \quad \dfrac{-11+y}{2} = -1[/tex]
[tex]\sf -12+x = 2(-3) \quad and \quad -11+y = 2(-1)[/tex]
[tex]\sf x = -6 + 12 \quad and \quad y = -2 + 11[/tex]
[tex]\sf x = 6 \quad and \quad y = 9[/tex]
So, coordinates of K is (6, 9)
Word Problem On Division
1. a cup can hold 2/9 ( fraction) litres of water. how many cups of water can be filled with 3 litre bottle?
Find the product of (x − 8)2 and explain how it demonstrates the closure property of multiplication.
The product of [tex](x - 8)^2[/tex] is not a polynomial equation because a polynomial equation means a coefficient of x that has a power of two or more powers.
What is a Polynomial Equation?
The equations developed with variables, exponents, and coefficients exists named polynomial equations. It can include various exponents, where the higher one stands named the degree of the equation.
Closure property under multiplication notes that any two rational numbers' outcome will be a rational number, i.e. if a and b exist in any two rational numbers, ab will also be a rational number.
Example: (3/2) × (2/9) = 1/3.
The product of [tex]$(x - 8)^2[/tex]
Simplifying the equation as (x − 8)(x − 8)
Apply Perfect Square Formula, and we get
[tex]$(a-b)^{2}=a^{2}-2 a b+b^{2}$[/tex]
[tex]$&(x-8)^{2}=x^{2}-2 x \cdot 8+8^{2} \\[/tex]
[tex]$&=x^{2}-2 x \cdot 8+8^{2}[/tex]
Simplifying the above equation, we get
[tex]$x^{2}-2 x \cdot 8+8^{2}=x^{2}-16 x+64 \\[/tex]
[tex]$&=x^{2}-16 x+64[/tex]
This is not a polynomial equation because a polynomial equation means a coefficient of x that has a power of two or more powers.
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what is 3x+4=8 please answer quick
Hello,
[tex]3x + 4 = 8[/tex]
[tex]3x + 4 - 4 = 8 - 4[/tex]
[tex]3x = 4[/tex]
[tex] \frac{3x}{3 } = \frac{4}{3} [/tex]
[tex]x = \frac{4}{3} [/tex]
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the bird reaches Bob, it turns around immediately and starts flying toward Alice at the same speed, turning around immediately when it reaches Alice, and repeating this procedure until Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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Two circles are shown in the diagram.
Circles C 1 and C 2 are shown. The diameter of circle 1 is 1. The diameter of circle 2 is 2 r.
Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d1 = 1, C1 = π, and d2 = 2r into the proportion.
StartFraction C 1 Over d 1 EndFraction = StartFraction C 2 Over d 2 EndFraction
Which shows how to correctly solve for C2, the circumference of any circle with radius r?
Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = 2 r pi
Because StartFraction 1 Over pi EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = StartFraction 2 r Over pi EndFraction
Because StartFraction pi Over 2 r EndFraction = StartFraction C 2 Over 1 EndFraction , C 2 = StartFraction pi Over 2 r EndFraction
Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 4 r EndFraction , C 2 = 4 r pi
The correct equation is (a) because π/1 = C2/r2, [tex]C_2= 2\pi r[/tex]
How to determine the correct equation?The complete question is added as an attachment
The given parameters are:
d1 = 1
d2 = 2r
The circumferences of the circles are calculated as:
C = πd
This gives
C1 = π * 1 = π
C2 = π * 2r = 2πr
So, we have:
C1 = π
C2 = 2πr
and
d1 = 1
d2 = 2r
Divide both equations
[tex]\frac{C_2}{d_1} = \frac{C_2}{d_2}[/tex]
[tex]\frac{\pi}{1} = \frac{2\pi r}{2r}[/tex]
This gives
[tex]\frac{\pi}{1} = \frac{C_2}{2r}[/tex]
Hence, the correct equation is (a) because π/1 = C2/r2, [tex]C_2= 2\pi r[/tex]
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Answer:
Its A
Step-by-step explanation:
Can someone help me find the value of x for the triangle?
Answer:
109°
Step-by-step explanation:
The sum of angles in all triangles is equal to 180. For this given triangle, we can solve for x.
48° + 23° + x° = 180°
180° - 71° = x°
x = 109°
A track coach is gathering data on the stride length of each of her 52 team members when running a distance of 500 meters. the population mean is 62.95 inches with a standard deviation of 5.65 inches. what is the standard error of the sample mean? round your answer to the nearest hundredth.
The standard error of the sample mean to the nearest hundredth is mathematically given as
S.E=0.784
What is the standard error?The amount by which the population means deviates from a sample mean is represented by the standard error of the mean, which is more often referred to as simply the standard error.
It informs you how much the sample means would change if you were to perform an experiment using fresh samples from the same population but this time uses different samples.
The standard error is obtained by calculating the standard deviation and then dividing that number by the square root of the sample size. It determines the accuracy of a sample mean by factoring in the variation in sample means that exists from one set of data to the next.
Generally, The population's mean height is 62.95 inches, so let's use that.
Taking into account that the population has a standard deviation of 5.65 inches
The sample mean is used to calculate the standard error of the mean.
[tex]SE=\frac{SD}{\sqrt{n}}[/tex]
Therefore
[tex]SE=\frac{5.65}{ \sqrt{52}}[/tex]
S.E=0.7835
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What will be the length of the diagonal of a rectangle of sides 6 m and 8 m?
Answer:
The length of the diagonal of a rectangle is 10m
Step-by-step explanation:
There is a visual below,
The diagonal of a rectangle has formed 2 right triangles.
This diagonal is called hypotenuse side length of a triangle
To find the hypotenuse, we can use the Pythagorean Theorem
a² + b² = c²
we are given the length of a and b, where a = 6 and b = 8
(6)² + (8)² = c²
36 + 64 = c²
100 = c²
√100 = c
10 = c
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The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
The y-intercept of the linear equation that models the data indicates that:
There was 1 inch of water on the tub when the water was turned on.
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.In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:
There was 1 inch of water on the tub when the water was turned on.
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I can’t seem to find this, I’m having trouble with this question! It would be nice if someone could help! Thanks
Answer:
-456 I think but I could be wrong though
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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4/3 + -1/6 + 13/12. Please answer step by step if possible. Thanks.
Answer:
9/4
Step-by-step explanation:
We follow bodmas
4/3 +( -1/6 + 13/12)
( lcm = 12)
( -2+ 13/12)
( 11/ 12)
4/3 + ( 11/12)
4/3 + 11/12
lcm = 12 also
and that will equal to
=16 + 11/ 12
= 27/ 12
divide by 3 to simplest form
= 9/4
180 divided in the ratio of 7:3:5
Answer:
Let , the constant factor be x so 3 X + 5 x + 7 x = 180
Step-by-step explanation:
Find out the value of x
7x+3x+5x=180
15x=180
x=180/15
x=12
now,
x=3 multiplied by 12=36
x=7 multiplied by 12=84
x=5 multiplied by 12=60
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When the distribution we want to analyze is symmetrical, which of the three averages should we choose to report?
The mean, median, and mode all have the same values in a symmetrical distribution. The mean is frequently chosen as the primary indicator of central tendency in these situations.
The mean is the measure of tendency that is most strongly impacted by any outliers or skewness among the three measures of tendency. The mean, median, and mode all have the same values in a symmetrical distribution. How Does Symmetrical Distribution Work?The mean, median, and mode frequently occur at the same location in a symmetrical distribution, where the values of variables exist at regular frequencies. The graph's middle can be divided into two sides that mirror one another by drawing a line through it.
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7-3(10 divided by 2) divided by 1
Answer:
-8
Step-by-step explanation:
Remember pemdas
7 - 3*(10:2):1 =
7-3*5:1=
7-15:1=
7- 15=
-8
Answer:
-8
Step-by-step explanation:
7-3(10:2):1
We always solve what's in parenthesies first.
7 - 3*5:1
Multiplication and division have equal priority, so we solve that part from left to right:
7 - 15:1 =
= 7 - 15 =
= -8
