FInd the measure of the exterior angle of a triangle if the remote interior angles are 75 degrees and 42 degrees?

Answer:

The answer is below

Step-by-step explanation:

Sumaya’s Smoothie Store is planning to sell an extra-large size. The extra-large size will have three times the volume of the small size (the small size is (8,4) ). It will cost twice as much as the small size.

Which coordinate pair represents the volume and cost of the extra-large size?

Solution:

The coordinate plane is a plane that can be used to represent the position of a point. The plane consist of x axes and y axes. The position of a point is referenced from the origin.

The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)

Since the volume of the extra-large size will have three times the volume of the small size, hence:

Volume of extra-large size = 8 * 3 = 24

The cost of extra large is twice as much as the small size, hence:

Cost of extra large = 4 * 2 = 8

Therefore the coordinate pair that represents the volume and cost of the extra-large size is:

(24, 8)

Answer:

  \(\textbf{A. }0.25^{3/2}\)

Step-by-step explanation:

Perhaps your answer choices are ...

  \(\textbf{A. }0.25^{3/2}\\\textbf{B. }(\sqrt[3]{4})^2\\\textbf{C.}\sqrt[3]{16}\\\textbf{D. }0.25^{-2/3}\)

Of these, the one that is not equivalent to 4^(2/3) is ...

  \(\boxed{\textbf{A. }0.25^{3/2}}\)

The value of this is ...

  \(\left(\dfrac{1}{4}\right)^{3/2}=\sqrt{\dfrac{1}{4^3}}=\dfrac{1}{8}\ne4^{2/3}=\sqrt[3]{16}=(\sqrt[3]{4})^2\)

\(\huge\text{Hey there!}\)

\(\mathsf{3ab - 2bc}\)

\(\mathsf{= 3(-4)(6) - 2(6)(-9)}\)

\(\mathsf{= -12(6) -12(-9)}\)

\(\mathsf{= -72 - (-108)}\)

\(\mathsf{= -72 + 108}\)

\(\mathsf{= 36}\)

\(\huge\textbf{Therefore, your answer should be:}}\)

\(\huge\boxed{\mathsf{36}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

The value is \(81\)

Step-by-step explanation:

We need to find value of \(5x+31\) when \(x=10\)

We have

\(5\times10+31=50+31\\\\=81\)

The resulting value will give you the mass of the ball of radius 3 centered at the origin with the given density function.

To find the mass of the ball with a radius of 3 centered at the origin, we need to integrate the density function over the volume of the ball.

The density function is given as f(ρ, φ, θ) = 5e^(-ρ^3), where ρ represents the radial distance, φ represents the azimuthal angle, and θ represents the polar angle.

In spherical coordinates, the volume element is given by ρ^2 sin(φ) dρ dφ dθ.

To integrate over the ball, we need to set the limits of integration as follows:

ρ: 0 to 3

φ: 0 to π

θ: 0 to 2π

The mass of the ball can be calculated using the integral:

Mass = ∫∫∫ f(ρ, φ, θ) ρ^2 sin(φ) dρ dφ dθ

Mass = ∫[0 to 2π] ∫[0 to π] ∫[0 to 3] 5e^(-ρ^3) ρ^2 sin(φ) dρ dφ dθ

This integral needs to be evaluated numerically using appropriate software or numerical techniques.

The resulting value will give you the mass of the ball of radius 3 centered at the origin with the given density function.

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The sample space for this experiment is the set of all possible outcomes of drawing 2 marbles from the box, where order matters. There are 3 choices for the first marble, and 3 choices for the second marble, so the sample space is {RR, RG, RB, GR, GG, GB, BR, BG, BB}. There are 9 possible outcomes in this sample space.

To determine the sample space for this experiment, we first list all the possible outcomes for the first marble that we could draw. There are 3 marbles in the box (red, green, and blue), so there are 3 choices for the first marble. We can represent these choices as R, G, and B.

Next, we list all the possible outcomes for the second marble that we could draw. Since the box is being replaced with the first marble before the second draw, there are still 3 marbles in the box (red, green, and blue), so there are still 3 choices for the second marble. We can represent these choices as R, G, and B.

Finally, we list all possible combinations of the first and second marble, which forms the sample space. Since order matters, we list all the possible combinations of R, G, and B as pairs. In this case, there are 3 choices for the first marble and 3 choices for the second marble, which gives us 3 * 3 = 9 possible outcomes in the sample space: {RR, RG, RB, GR, GG, GB, BR, BG, BB}.

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Answer:

7.2m

Step-by-step explanation:

24 x 6 = 14.4

14.4/2=7.2m

Answer:

X        Y

2        1

4        7

5        10

Step-by-step explanation:

Distance = 13 units

Point A: (8, -7)

Point B: (-4, -2)

\(\sqrt{(8 + 4)^{2} + (-7 + 2)^{2} }\)

\(\sqrt{(12)^{2} + (-5)^{2} }\)

\(\sqrt{144 + 25 }\)

\(\sqrt{169}\)

\(13\)

Answer:

\(\boxed {d = 13}\)

Step-by-step explanation:

Use the Distance Formula to help you find the distance between the two following points:

\(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

(where \((x_{1}, y_{1})\) represents the first point and \((x_{2}, y_{2})\) represents the second point)

-Apply the two following onto the formula:

\((x_{1}, y_{1}) = (8, -7)\)

\((x_{2}, y_{2}) = (-4, -2)\)

\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)

-Solve for the distance:

\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)

\(d = \sqrt{(-12)^{2} + 5^{2}}\)

\(d = \sqrt{144 + 25}\)

\(d = \sqrt{169}\)

\(\boxed {d = 13}\)

Therefore, the distance is \(13\).

The inverse of a function is the opposite of the function

1) y = log2 (3x)

Swap the positions of x and y

\(x = \log_2(3y)\)

Apply the exponential rule

\(2^x = 3y\)

Make y the subject

\(y = \frac{2^x}3\)

Hence, the inverse function is: \(y = \frac{2^x}3\)

2) y=log3(x-1)

Swap x and y

\(x = \log_3(y - 1)\)

Apply exponent rule

\(3^x = y - 1\)

Make y the subject

\(y = 3^x + 1\)

Hence, the inverse function is: \(y = 3^x + 1\)

3) y=-2log x

Swap x and y

\(x=-2\log y\)

Divide both sides by -2

\(-0.5x=\log y\)

Apply exponent rule

\(y = 10^{-0.5x}\)

Hence, the inverse function is: \(y = 10^{-0.5x}\)

4) y=log6(3x)

Swap x and y

\(x = \log_6(3y)\)

Apply exponent rule

\(3y = 6^x\)

Make y the subject

\(y = \frac{6^x}{3}\)

Hence, the inverse function is: \(y = \frac{6^x}{3}\)

5)y=log3(x+2)

Swap x and y

\(x = \log_3(y + 2)\)

Apply exponent rule

\(y + 2 = 3^x\)

Make y the subject

\(y = 3^x - 2\)

Hence, the inverse function is: \(y = 3^x - 2\)

6) y=log3(5^3)

Swap x and y

\(x = \log_3(5^3)\)

Hence, the inverse function is: \(x = \log_3(5^3)\)

7) y=6^x+5

Swap x and y

\(x = 6^y + 5\)

Subtract 5 from both sides

\(6^y = x - 5\)

Apply logarithm

\(y = \log_6(x - 5)\)

Hence, the inverse function is: \(y = \log_6(x - 5)\)

9) y=log3 2^x

Swap x and y

\(x = \log_3(2^y)\)

Apply exponent rule

\(2^y = 3^x\)

Apply logarithm

\(y = \log_2(3^x)\)

Hence, the inverse function is: \(y = \log_2(3^x)\)

10) y=3^x -7

Swap x and y

\(x = 3^y - 7\)

Add 7 to both sides

\(3^y = x + 7\)

Apply logarithm

\(y = \log_3(x + 7)\)

Hence, the inverse function is: \(y = \log_3(x + 7)\)

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Answer:

NOT  A or B

probably C ?

Step-by-step explanation:

The correct option is (c) h = 10sin(π15t)+35.

The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is  h = 10sin(π15t)+35.

The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.

A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.

Calculation for the equation of the model height-

Let's now review each choice individually and select the best one.

The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.

They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.

If we put t=15/2 in the options

Option (a) gives h = 25

Option (b) gives h = -10sin(15/2) + 35

Option (c) gives h = 45

Option (d) gives h = 10sin(15/2) + 35

Therefore, the correct equation is given in option c.

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The complete question is -

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

a) h = −10sin(π15t)+35  

b) h = −10sin(πt)+35

c) h = 10sin(π15t)+35

d) h = 10sin(πt)+35

Answer:

B 9/14

Step-by-step explanation:

First, we have to find the product by doing the multiplication.

9/10 x 5/7 = 45/70

We have to find the greatest common factor that both the numerator and the denominator share to divide them by which is 5.

We can simplify 45/70 by dividing both the numerator and the denominator by 5.

This will give us 9/14.

We also know that this fraction cannot be simplified anymore since we took the greatest common factor that both the numerator and the denominator shared.

Therefore the answer is B 9/14

(sorry if this is confusing but I hope it helped anyway)

Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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☃ \( \: \: \: \: \: \: \: \: \red{ \underline{ \large{ \blue{ \tt{ ꧁ \: A \: N \: S \: W \: E \:R ꧂}}}}}\)

✧ \( \large\tt{Step \: - \: By \: - \: Step \: Explanation} : \)

Let the total number of students who failed in SLC be n ( U ) , number of students failed in science only be n ( only S ) , number of students failed in mathematics only be n ( only M ) , number of students who failed in both subjects be n ( M ∩ S ) and number of students who failed in other subjects be \( \tt{n( \overline{s \: ∪ \: m})}\).

❀ \( \underline{ \underline{ \large{ \tt{ \: G \: I\: V \: E \: N}}}} : \)

↳ \( \large{ \tt{n(u) = 20 \: \% \:of \: 115000 = \red{ \underline{23000}}}}\)

↳ \( \large{ \tt{ n_{0}(s) = 40\% \: of \: 23000 = \red{ \underline{9200}}}} \)

↳ \( \large{ \tt{ n_{o}(m) = 35\% \: of \: 23000 = \red {\underline{8050}}}}\)

↳ \( \large{ \tt{n( \overline{s \:∪ \: m) }= 5\% \: of \: 23000 = \red{ \underline{1150}}}}\)

✎ \( \underline{ \underline{ \large{ \tt{ \: S \: O \:L\: V \: I \: N\: G}}}} ..... \)

\( \large {\tt{i. \: n(u) = n_{o}(s) + n_{o}(m) + n(s ∩ \: m) \: + n( \overline{s \:∪ \: m)} }}\)

⟶ \( \large{ \tt{23000 = 9200 + 8050 + n(s∩m) + 1150}}\)

⟶ \( \large \tt \: 23000 = 18400 + n(s ∩ m)\)

⟶ \( \large \tt \: 23000 - 18400 = n(s \:  ∩  \: m \: )\)

⟶ \( \large \boxed{ \tt {4600} = n(s ∩ m)}\)

Therefore , 4600 students failed in both subjects.

\( \large{ \sf{ii. \: Please \:see \: the \: attached \: picture \: for \: venn - diagram!}}\)

☪ Hope I helped! ♡

♕ Have a wonderful day / night ! ツ

☆ \( \underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}\) !

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The number of dark chocolate AJ sold is 75

Simultaneous equations are two or more algebraic equations that share variables e.g. m and d . They are called simultaneous equations because the equations are solved at the same time.

If the number of Milk chocolate candy is m and the number of dark chocolate candy is d, then

m+d= 200 equation 1

3m+4d= 675 equation 2

to eliminate m we multiply both equations by 3

3m+3d= 600 equation 3

3m+ 4d=675 equation 4

subtract equation 3 from 4

d = 675-600

d= 75

Therefore the number of dark chocolate candy AJ sold is 75.

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An appropriate assignment of digits to carry out the simulation to estimate the number of packages that would need to be randomly selected in order to find a package that was not delivered on time when a shipping company claims that 95% of packages are delivered on time is

01 - 05 = Packages delivered not on time

06 - 100 = Packages delivered on time

Random numbers are numbers selected from a set of limited or unlimited numbers without a particular pattern for prediction. In this case the student can generate random numbers from a limited pool of digits from 1 to 100 using any random number generator like excel.

Given that 95% of packages are delivered on time. Based on this statement we can assign that 95% of these generated random numbers represent packages delivered on time, here that is 06 - 100.

Hence random numbers from 01 - 05, the 5% of generated random numbers represents the packages not delivered on time.

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The requried factor of the given expression aⁿ +aⁿ⁺¹ is given as aⁿ and (1 + a)

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,
Given expression,
= aⁿ +aⁿ⁺¹

In order to factor the above expression we are using the property,
x²  = x¹ (x¹)

So,
= aⁿ + a.aⁿ

Now, taking aⁿ common,

= aⁿ(1 + a)

So, aⁿ and (1 + a) are the requried factors.

Thus, the requried factor of the given expression aⁿ +aⁿ⁺¹ is given as aⁿ and (1 + a)

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Answer:

$26.65

Step-by-step explanation:

41 decrease 35% =

41 × (1 - 35%) = 41 × (1 - 0.35) = 26.65

Answer:

32 is 40% of 80.

Step-by-step explanation:

80×4÷10=320÷10=32

Answer:

119.4 cm^2

Step-by-step explanation:

Area of a circle is \(\pi\) x radius^2, and the area of a rectangle is length * width. 11 cm x 12 cm = 132 cm^2 (rectangle's area). The circle's area would be \(\pi\) x 2^2 which would equal 12.56637061 cm^2 (left unrounded until the end). Then subtract 12.56637061 from 132 cm^2 and that would equal 119.4 cm^2 rounded to the tenth.

The value of h is 3

The line that includes the point (h, 3) and (9, -3) has a slope of -1.

Using the slope intercept equation,

y = mx + b

where

Therefore,

y = mx + b

y = -x + b

using (9, - 3)

-3 = - 9 + b

b = -3 + 9

b = 6

Therefore, the equation is as follows:

y = -x + 6

using (h, 3)

y = -(h) + 6

3 = -h + 6

-h = 3 - 6

-h = -3

h = 3

Therefore, the value of h is 3.

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The function g(x) = 4x⁸ - 3x⁶ can be rewritten as a difference of two terms, and its derivative, g'(x), is 32x⁷ - 18x⁵.

To rewrite the function g(x) as a sum or difference, we can split it into two terms: 4x⁸ and -3x⁶. Thus, g(x) = 4x⁸ - 3x⁶.

To find the derivative of g(x), g'(x), we apply the power rule of differentiation. For each term, we multiply the coefficient by the power of x and decrease the power by 1. Therefore, the derivative of 4x⁸ is 32x⁷, and the derivative of -3x⁶ is -18x⁵.

Combining the derivatives of both terms, we obtain the derivative of g(x) as g'(x) = 32x⁷ - 18x⁵.

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Step-by-step explanation:

Divided both side 2Z^2 -Y Then you will get J

Hermite interpolation uses not only function values but also their derivatives to construct the interpolating polynomial, while ordinary interpolation only uses function values.

A cubic spline interpolant is a piecewise polynomial function consisting of several cubic polynomials, while a Hermite cubic interpolant is a single polynomial of degree 3 that interpolates function and their derivatives.

Hermite interpolation is a type of interpolation that not only matches the function values but also its derivatives at the given data points. This means that Hermite interpolation provides a more accurate and smooth approximation of the underlying function than ordinary interpolation, which only matches the function values at the given points.

Hermite interpolation is particularly useful when the function being approximated is expected to be smooth and differentiable.

A cubic spline interpolant, on the other hand, is a piecewise function that consists of multiple cubic polynomials, each defined over a subinterval of the data points.

The cubic spline interpolant is designed to be smoother than the Hermite cubic interpolant. In contrast to the Hermite cubic interpolant, the cubic spline interpolant matches the function values at the data points and also ensures that the first and second derivatives are continuous across the subintervals.

This results in a smoother and more natural-looking approximation of the function. Overall, both Hermite interpolation and cubic spline interpolation provide powerful tools for approximating functions with a high degree of accuracy and smoothness.

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A 1x25 Playfair matrix results in a substitution system called the "Playfair Cipher."

This cipher is a digraph substitution cipher, where pairs of letters are encrypted using a 5x5 matrix created from a keyword. The matrix is filled with unique letters of the alphabet, and "I" and "J" are typically combined into one slot. The Playfair Cipher encrypts pairs of letters by following specific rules: if the letters are in the same row or column, they're replaced by the letters to their immediate right or below, and if they form a rectangle, they're replaced by the letters on the same row but in the opposite corners. This cipher provides a more secure encryption compared to simple substitution ciphers, as it encrypts pairs of letters instead of single characters.

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Hence, the volume of the solid described above is (8/3)π cubic units.

The region R bounded by the graphs of x = 0, y = 2x, and y = 2 is revolved about the line y = 2.

The volume of the solid described above is 8 cubic units.Here's how to solve for the volume of the solid generated in the following situation:

Step 1: Draw the graphThe region R is a triangle with the vertices (0,0), (1,2), and (2,2). To revolve the region around y = 2, the radius is 2 - y. Therefore, the cross-section of the region is a washer.

Step 2: Find the radius of the washerThe distance between the line of revolution and the curve y = 2x is 2 - y = 2 - 2x, and the distance between the line of revolution and the horizontal line y = 2 is 0. Therefore, the radius of the washer is R - r = 2 - (2 - 2x) = 2x.

Step 3: Find the area of the washer The area of the washer is given by π(R² - r²). In this case, R = 2 and r = 2x. Thus, the area of the washer is π(2² - (2x)²) = 4π - 4πx².

Step 4: Find the volume of the solid. To find the volume of the solid, integrate the area of the washer from x = 0 to x = 1:V = ∫₀¹ [4π - 4πx²] dx= 4πx - (4π/3)x³ [from 0 to 1]= 4π - (4π/3)= (8/3)π

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The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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