Suppose that 65% of Americans over 18 drink coffee in the morning, 25% of Americans over the age of 18 have cereal for breakfast, and 10% do both. What is the probability that a randomly selected american over the age of 18 drinks coffee in the morning or has cereal for breakfast? That is, find P(C or B).

The height and radius of the cup are 4.41 cm and 2.07 cm respectively

To minimize the amount of paper used, we need to minimize the surface area of the cup. Let h be the height and r be the radius of the cone. Then we have:
\(Volume of cone = \frac{1}{3}  πr^{2} h = 36 cm^{3}\)

Solving for h, we get:
\(h = \frac{108}{(πr^2)}\)

Now we can express the surface area of the cone as:
\(Surface area = πr^2+ πr\sqrt{r^{2}+h^{2}  }\)

Substituting the expression for h, we get:

\(Surface area = πr^2+πr \sqrt{(r^{2} +(\frac{108}{(πr^2)^{2}) } )}\)

To minimize this function, we take its derivative with respect to r and set it equal to zero:
\(\frac{d}{dx} (Surface area) =  \frac{2πr - 108r }{[(r^2+(\frac{108}{πr^2}))^{0.5}  }] - \frac{108π}{r^2 }  = 0\)

Simplifying, we get:
\(2r^3 - \frac{108^2}{π} = 0\)

Solving for r, we get:
\(r = (\frac{54}{π})^{\frac{1}{3} }\)

Substituting this value into the expression for h, we get:
\(h = \frac{108}{\frac{54}{π} ^{(\frac{2}{3}π )} }\)

Thus, the height and radius of the cup that will use the smallest amount of paper are:
height = 4.41 cm
radius = 2.07 cm (rounded to two decimal places)

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Answer:

V=I R

120= I × 20

I = 120÷20

I = 6 A

................................

Hypothesis testing is a statistical technique used to make inferences or draw conclusions about a population based on a sample. It involves formulating two competing hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).

In this scenario, the null hypothesis (H0) would typically state that there is no significant difference or effect. Since the mean time for completing the maze is given as 18 seconds, the null hypothesis would be H0: μ = 18, implying that the loud noise does not have any impact on the mice's maze completion time.

On the other hand, the alternative hypothesis (Ha) represents the claim or hypothesis that is contrary to the null hypothesis. The researcher's belief is that the loud noise will cause the mice to complete the maze faster. Therefore, the alternative hypothesis is Ha: μ < 18, indicating that the mean time for maze completion with the noise stimulus is expected to be less than 18 seconds.

To test this hypothesis, the researcher collects data from 10 mice and calculates the sample mean (x) to be 16.5 seconds. The researcher will then conduct a statistical test, such as a t-test, to determine if the observed sample mean significantly supports the alternative hypothesis.

By formulating the appropriate alternative hypothesis as Ha: μ < 18, the researcher can statistically evaluate if the loud noise stimulus has a significant effect on the mice's maze completion time.

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Answer:

54

Step-by-step explanation:

Answer:117

Step-by-step explanation:

I’m good at math

Answer:

117 Roses

Step-by-step explanation:

234 *0.5 = 117

The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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Step-by-step explanation:

\( {9}^{ \frac{ - 1}{2} } \\ {3}^{2 \times - \frac{1}{2} } \\ {3}^{ - 1} \\ \frac{1}{3} \)

Now for another

\( {27}^{ \frac{ - 2}{3} } \\ {3}^{3 \times \frac{ - 2}{3} } \\ {3}^{ - 2} \\ \frac{1}{9} \)

Hope it will help :)❤

The value that is NOT greater than [-4.2] is D. [-4.5]

The values [-4.2], [3.5], and [4.1] are all greater than [-4.5]. To determine which value is the greatest, we can use a number line or compare the numbers directly. On a number line, we can see that [-4.5] is located to the left of [-4.2], [3.5], and [4.1]. This means that [-4.2], [3.5], and [4.1] are all greater than [-4.5].

Alternatively, we can compare the values directly. We know that -4.5 is less than -4.2 since -4.5 is farther to the left on the number line. We also know that 3.5 and 4.1 are positive values, which are greater than any negative value. Therefore, the answer is [-4.5] is not greater than [-4.2]. Hence, option D is correct.

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Answer:

u

Step-by-step explanation:

it is undefined because its a vertical line.

Answer:

slope is undefined u

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, - 3 ) and (x₂, y₂ ) = (1, 0 )

m = \(\frac{0-(-3)}{1-1}\) = \(\frac{0+3}{0}\) = \(\frac{3}{0}\)

Since division by zero is undefined then the slope of the line is undefined

Answer: number 7 is 6 and number 8 is 7. I hope this helps good luck with other questions:)

Also I think number one might be 6 but Im not sure.

you know what dont listen to me i dont know what im talking about. I guess this can just be the answer if you have absolutely no other possible answer..

Answer:

1) 3/2                     2) 22/3                   3) 4/27           4) 2/45        5) 2/25             6) 5/14

Step-by-step explanation:

Answer:87 degrees

Step-by-step explanation:

113 degrees-26degrees= 87degrees.

Answer-

y=-2x+2

It starts at +2 so that is the b

And -2x is how you move so that is the m

That's how I was taught and how I remember it lol hope it helped ik it wasn't the best its 12 am here soo I be tired

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 4

The only 2 equations with a slope of 4 are

B y = 4x - 5

C y = 4x + 2

To find the one which contains the point (2, 3)

Substitute x = 2 into the equation and if y = 3 then the line contains the point

B y = 4(2) - 5 = 8 - 5 = 3 ← contains (2, 3 )

C y = 4(2) + 2 = 8 + 2 = 10 ≠ 3 ← does not contain the point

Answer:

the coordinates are  (5,3)

Step-by-step explanation:

you write it as  (x,y)

point d is on 5 of the x-axis and 3 on the y-axis

Answer:

B

Step-by-step explanation:

As n approaches infinity, the term 1/(n+1) approaches zero, and the sum of the series converges to 1/2. The series is convergent, and its sum is 1/2.

To determine the convergence and find the sum of the given series, we first observe that each term of the series can be expressed as a telescoping series. This means that most terms will cancel out, leaving only a few terms that contribute to the sum.

By expressing each term as 1/(n(n+1)(n+2)) and applying partial fraction decomposition, we find that the series can be simplified as 1/2 * [(1/1 - 1/2) + (1/2 - 1/3) + ... + (1/n - 1/(n+1))] - 1/2 * [(1/2 - 1/3) + (1/3 - 1/4) + ... + (1/(n+1) - 1/(n+2))].

The series can be expressed as:

S = 1/(1×2×3) + 1/(2×3×4) + ... + 1/(n(n+1)(n+2)) + ...

We observe that each term of the series can be written as:

1/(n(n+1)(n+2)) = 1/2 * [(1/n) - (1/(n+1))] - 1/2 * [(1/(n+1)) - (1/(n+2))]

By using partial fraction decomposition, we can simplify the series as follows:

S = 1/2 * [(1/1 - 1/2) + (1/2 - 1/3) + ... + (1/n - 1/(n+1))] - 1/2 * [(1/2 - 1/3) + (1/3 - 1/4) + ... + (1/n+1 - 1/n+2)]

Notice that many terms cancel out, and we are left with:

S = 1/2 * (1 - 1/(n+1))

Now, as n approaches infinity, the series converges to:

S = 1/2 * (1 - 1/∞) = 1/2

As n approaches infinity, the term 1/(n+1) approaches zero, and the sum of the series converges to 1/2.

Therefore, the series is convergent, and its sum is 1/2.

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The conversion of Cartesian form to polar form gives:

z = √6 [cos(7π/4)  + isin(7π/4)]

To convert Cartesian form to polar form. Use the following relations:

The cartesian form is:

z = x + iy

The polar form is:

z = r(cosθ + isinθ)

θ = tan⁻¹(y/x)

where:

r = √(x² + y²)

θ = tan⁻¹(y/x)

We have:

z= √3-√3i

Using the relations:

r = √(x² + y²)

r = √[√3)²+ (-√3)²]

r = √6

θ = tan⁻¹(y/x)

θ = tan⁻¹(-√3)/√3)

θ = tan⁻¹(-1)

θ = 315°

θ = 7π/4 (in radian)

Note: y is negative and x is positive. Thus, this is applicable to angle in the 4th quadrant. In this case, 315°.

Thus, polar form of z= √3-√3i  will be:

z = √6 [cos(7π/4)  + isin(7π/4)]

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Answer:

25%

Step-by-step explanation:

4/16 days were under 78 degress

Answer: 84 ft

Step-by-step explanation:

First, split the shape into a rectangle and triangle

Then find the dimensions for the shape

Find the area for the rectangle and triangle

formula for the rectangle would be Length(8) multiplied by Width(6) L*W

The area of the rectangle would be 48

Then find the area of the triangle

Formula for triangle would be Length(6) [14-8 is how I got this number] then multiply that by width (6) finally divide you answer by 2 L*W/2, and your answer would be 36

To finally find your final answer add 36 and 48

Answer:

Step-by-step explanation:

The dotted line shows where you can find the area of two different shapes in order to find the total area. There is a rectangle and a triangle.

Rectangle:

A= lxw

l=6

w = 8

6*8=48

Triangle:

A= (lxw)/2

l=6

w= 6 (14-8=6; Subract the total length of the shape by the given length to find whats missing)

(6*6)/2=18

Add 48 and 18 to get the combined area of both shapes.

(48+18=66 sq ft)

Answer:

45/58.4

Step-by-step explanation:

Answer: part 1: 45/54.8.

Part 2: 55.2

Step-by-step explanation:

Edge

Answer:

No, because as the x-values are increasing by a constant amount, the y-values are not being multiplied by a constant amount.

Step-by-step explanation:

We have a set of ordered pairs of the form (x, y)

If a function is exponential then the ratio between the consecutive values of y, is always equal to a constant.

This means that:

\frac{y_2}{y_1}=\frac{y_3}{y_2}=\frac{y_4}{y_3}=by1y2=y2y3=y3y4=b

This is: y_2=by_1y2=by1

Now we have this set of points {(-1, -5), (0, -3), (1, -1), (2, 1)}

Observe that:

\begin{gathered}\frac{y_2}{y_1}=\frac{-3}{-5}=\frac{3}{5}\\\\\frac{y_3}{y_2}=\frac{-1}{-3}=\frac{1}{3}\\\\\frac{3}{5}\neq \frac{1}{3}\end{gathered}y1y2=−5−3=53y2y3=−3−1=3153=31

Then the values of y are not multiplied by a constant amount "b"

Answer:

q=x-10=10

Step-by-step explanation:

add 10 10 10 to both sides

Answer:

x < 10

Step-by-step explanation:

Given: x -4 < 6​

Add four to both sides: x < 10

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The perimeter of the triangle is 4.5inches.

Equilateral Triangle : can be defined as a triangle having all three sides equal.

Perimeter of triangle is defined as the sum of the lengths of the three side.

Perimeter of triangle is denoted by 3x(side).

Given that the side of the triangle is 1.5 inches

Perimeter = 3x(1.5)

Perimeter=4.5 inches

Therefore , The Perimeter of the triangle is 4.5 inches .

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Answer:

Step-by-step explanation:

Given points

Midpoint is

The correct answer is:

\(b. \sum f^n(2)/n! (x-2)^n = -3 +16(x-2) + 20(x-2)^2 + \sum 8(x-2)^3^/^n! + \sum (x-2)^4^/^n!\)

The Maclaurin series is:

\(f(x) = \sum (-1)^n (2x)^(^4^n^+^1^)/(3^(^2^n^)^(^2^n^)!) = \sum (-1)^n (2^(^4^n^+^1^)/3^(^2^n^)^(^2^n^)!) x^(^4^n^+^1^)\)

The indefinite integral of (cos(x) - 1/x) can be expressed as an infinite series.

The correct answer for the Taylor series of f(x) = x^4 - 4x^2 + 3 centered at a = 2 is:

\(b. \sum f^n(2)/n! (x-2)^n = -3 +16(x-2) + 20(x-2)^2 + \sum 8(x-2)^3^/^n! + \sum (x-2)^4^/^n!\)

The associated radius of convergence for this series is infinity, since the power series expansion of f(x) exists for all real numbers x.

To obtain the Maclaurin series for \(f(x) = 2x cos(1/3x^2)\), we can first find the Maclaurin series for \(cos(x^2^/^3^)\) and then multiply by 2x:

\(cos(x^2/3) = \sum (-1)^n (x^2/3)^(2n)/(2n)! = \sum (-1)^n x^(^4^n^)/(3^(^2^n^)^(^2^n^)!)\)

Therefore, the Maclaurin series for \(f(x) = 2x cos(1/3x^2)\) is:

\(f(x) = \sum (-1)^n (2x)^(^4^n^+^1^)/(3^(^2^n^)^(^2^n^)!) = \sum (-1)^n (2^(^4^n^+^1^)/3^(^2^n^)^(^2^n^)!) x^(^4^n^+^1^)\)

To evaluate the indefinite integral ∫(cos(x) - 1/x) dx as an infinite series, we can use the Maclaurin series for cos(x) and the power series expansion of \(ln(x) = \sum(-1)^(^n^+^1^) (x-1)^n/n\), which converges for 0 < x ≤ 2. Thus, we have:

\(\int(cos(x) - 1/x) dx = \intcos(x) dx - \int(1/x) dx = \sum(-1)^n x^(^2^n^+^1^)/(2n+1)! - ln|x| + C\)

where C is the constant of integration. We can simplify this expression as follows:

\(\int (cos(x) - 1/x) dx = \sum (-1)^n x^(^2^n^+^1^)/(2n+1)! - ln|x| + C\)

\(= -ln|x| + \sum(-1)^n x^(^2^n^+^1^)/(2n+1)!\)

\(= -ln|x| + \sum(-1)^n (x-1)^(^2^n^+^1^)/(2n+1)x^(^2^n^+^1^)\)

Thus, the indefinite integral of (cos(x) - 1/x) can be expressed as an infinite series.

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There were 13 small boxes shipped and 6 large boxes shipped.

Let's denote the number of small boxes as 's' and the number of large boxes as 'l'.

According to the given information, the volume of each small box is 6 cubic feet, so the total volume of all small boxes can be calculated as 6s cubic feet.

Similarly, the volume of each large box is 13 cubic feet, so the total volume of all large boxes can be calculated as 13l cubic feet.

We are also given that the combined volume of all the boxes is 156 cubic feet, so we can write the equation:

6s + 13l = 156 ...(1)

Additionally, we know that a total of 19 boxes were shipped, so we can write another equation:

s + l = 19 ...(2)

Now, we have a system of equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 's' and 'l'.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here.

From equation 2, we can rewrite it as s = 19 - l.

Substituting this value of s into equation 1, we get:

6(19 - l) + 13l = 156

Simplifying the equation:

114 - 6l + 13l = 156

Combining like terms:

7l = 42

Dividing both sides by 7:

l = 6

Now, we can substitute this value of l back into equation 2 to find the value of s:

s + 6 = 19

s = 13

The number of small boxes shipped is 13, and the number of large boxes shipped is 6.

There were 13 small boxes shipped and 6 large boxes shipped.

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Given that a vehicle travels 25 miles in 2 hours, determine the average speed of the vehicle in miles per hour.

Work:

In order to find the average mph of the vehicle, you have to divide the distance the vehicle travels in a certain period of time by that amount of time.

So, in this case, the vehicle traveled 25 miles in 2 hours, so you would divide 25 by 2.

25/2 = 12.5

That means, the vehicle is traveling at a speed of 12.5 mph.

Thus, the average speed of the vehicle is 12.5 miles per hour (mph).

The expected value of y is (D.) 35.5.

The expected value of a discrete random variable is found by multiplying each value of the variable by its corresponding probability and then summing these products. In this case, the probability distribution of y is given in the table.

To find the expected value of y, we need to calculate the sum of the products of each value of y and its corresponding probability.

y * probability = y * P(y)

The expected value of y is E(y) = 100.10 + 200.25 + 300.05 + 400.30 + 500.20 + 600.10

= 2 + 5 + 1.5 + 12 + 10 + 6 = 37.

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Answer:

Incorrect measurement

Step-by-step explanation:

Given

Shape: Triangle

Length: 22in, 10in and 11in

Required: Determine if the measurements are correct

For the measurement of a triangle to be true, the sum of any 2 sides must be greater than the length of the third side.

i.e.

\(22 + 10 > 11\) --- True

\(22 + 11 > 10\) --- True

\(11 + 10 > 22\) --- False

Since all three conditions are not true, then the measurements are incorrect