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If Katya drives 224 miles during one week of commuting to school and work, how many gallons of gas would she use?

Background information:

Constant: 28

X value: Number of Gallons

Y value: Number of miles driven

Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.

The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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Answer:

B. 6 cm

Step-by-step explanation:

\(\text{Take the volume of a sphere and solve for r.}\\V=\frac{4}{3}\pi r^3\\\text{We already know that the volume is 113, so substitute that value.}\\113=\frac{4}{3}\pi r^3\\\text{Divide both sides by 4/3 pi.}\\\frac{113}{\frac{4}{3}\pi}=r^3\\\text{Divide 113 by 4/3 pi.}\\r^3=26.98\\\text{For a more accessible value, round up.}\\r^3 \approx27\\\text{Take the cube root of both sides.}\\r=3\)

Now that the radius is known, all we have to do is multiply it by 2 to get the diameter. Here the answer is simply 3 * 2, or 6.

Answer:

B. 6 cm

Step-by-step explanation:

You can use the formulas \(d=(\frac{6V}{\pi } )^{\frac{1}{3} }\) or \(d = \sqrt[3]{\frac{6V}{\pi } }\) to solve for diameter using volume. I will use the first forumla for this problem.

1. Substitute 113 for "V":

\(d=(\frac{6(113)}{\pi }) ^{\frac{1}{3} }\)

2. Multiply in the parenthesis:

\(d=(\frac{678}{\pi } )^{\frac{1}{3} }\)

3. Divide by pi (3.14):

678 ÷ 3.14 = 215.923567

\(d=215.9^{\frac{1}{3} }\)

4. Apply the exponent:

d = 5.99907...

d = 6 cm

hope this helps!

Answer:

Polynomial Expression.

Step-by-step explanation:

The radius r that produces the minimum surface area is 1.06 cm and the height h is 1.41 cm.

Let r be the radius of the cylinder and h be the height. You can find the equation for the volume of a solid by adding the volumes of the two hemispheres and the cylinder.

Volume = \((2/3)πr^3 + πr^2h\) = 10 cubic centimeters

Now let's find the values ​​of r and h that minimize the surface area of ​​the solid. This area consists of three parts:

Curved surfaces of two hemispheres and sides of a cylinder. This can be expressed as:

surface area = \(2πr^2 + 2πrh\)

To find the values ​​of r and h that minimize this expression, we can use the Lagrangian multiplier method. Given that the volume of the solid is 10 cubic centimeters, we want to minimize the surface area. So it looks like this:

\(f(r, h) = 2πr^2 + 2πrh + λ[(2/3)πr^3 + πr^2h - 10]\)

Taking the partial derivatives for r, h, and λ and setting them to zero gives

\(4πr + 2πh = 2πr^2λ + (4/3)πr^3λ\)

\(2πr = πr^2λ + πrhλ\)

Solving these equations simultaneously gives:

h = 4r/3

λ = 2/(3r)

Substituting these values ​​into the volume equation gives:

\(r^2h = 5/3\)

Substituting h = 4r/3 from above, we get:

\(r^3 = 15/8pi\)

Taking the cube root of both sides gives:

r=1.06cm

Substituting this value for r into the formula for h yields:

h=1.41cm

Therefore, the radius r that produces the minimum surface area is about 1.06 cm and the height h is about 1.41 cm.

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Answer:

what Will You do there? locate fractions?

(a) A = 1/2 (bh)

(b) b = P/R

(c) 8?

Answer:

- 4 < x ( or ) x > - 4

Step-by-step explanation:

- 10 < - 6 + x

Add 6 on both the sides,

- 10 + 6 < x

- 4 < x

===========================================================

Explanation:

Your teacher shows that minor arc BD is 129 degrees. Recall that any minor arc is always less than 180 degrees.

Let's say that we had point A at the center of the circle. This would mean angle DAB is 129 degrees. This central angle subtends or cuts off minor arc BD.

Now focus entirely on quadrilateral DABC. The goal is to find the unknown angle C. The angle A was found earlier at 129 degrees. The angles B and D are 90 degrees each since tangents are perpendicular to the radius at the point of tangency.

We have this so far

Adding all four angles of any quadrilateral will always get us 360 degrees. It's similar to how adding the angles of a triangle gets us 180 degrees. In fact, any quadrilateral can be cut into two triangles (aka the process of triangulation). So adding two triangles gets us 180+180 = 360 more or less.

--------------

Anyways, the four angles A,B,C,D must add to 360. So,

A+B+C+D = 360

129+90+C+90 = 360

C+309 = 360

C = 360-309

C = 51

--------------

As a shortcut, note how B+D = 90+90 = 180

Also note that A+C = 360-(B+D) which becomes A+C = 180

So, C = 180-A = 180-129 = 51

use graph calculator (attachment)
or you can solve it by equation:
y+2.3=0.45x (eq 1)

-2y=4.2x-7.8
-y=2.1x-3.9

y=-2.1x+3.9 (eq 2)

eg 2 ⇒ eq 1
\(\tt -2.1x+3.9+2.3=0.45x\\\\-2.1x-0.45x=-6.2\\\\x=2.43\\\\y=-2.1(2.43)+3.9=-1.2\)

Answer:

≈ 5.6 (or) 5 R 34

Step-by-step explanation:

The answer will go on forever if you keep going. I would suggest round to the nearest 10th, or whatever your teacher wants you to round to.

Another way to do this is by showing the remainder, or R.

304 ÷ 54 will be 5 rounded to the nearest whole number. Then you find the remainder, which is 34.

To set up a triple integral to find the volume of the solid bounded by the given cone and sphere, we need to express the limits of integration for each variable.

Let's consider the given equations: z = √√x² + y² (equation of the cone) and x² + y² + z² = 8 (equation of the sphere). We can rewrite the equation of the cone as z = (x² + y²)^(1/4). Notice that the cone is symmetric with respect to the z-axis, so we can focus on the region where z ≥ 0.

Now, let's determine the limits of integration for each variable. Since the cone is symmetric, we can consider only the region where x ≥ 0 and y ≥ 0. For the sphere, we can use spherical coordinates to simplify the calculation.In spherical coordinates, the equation of the sphere becomes r² = 8. We can set up the following limits: 0 ≤ r ≤ 2√2 (from the equation of the sphere), 0 ≤ θ ≤ π/2 (to cover the region where x ≥ 0), and 0 ≤ φ ≤ π/4 (to cover the region where y ≥ 0).Now, we can set up the triple integral to find the volume:V = ∫∫∫ f(x, y, z) dV= ∫∫∫ 1 dV= ∫₀^(π/4) ∫₀^(π/2) ∫₀^(2√2) r² sin φ dr dθ dφ

Integrating with respect to r, θ, and φ over their respective limits will give us the volume of the solid bounded by the cone and sphere.In summary, the triple integral to find the volume of the solid is V = ∫₀^(π/4) ∫₀^(π/2) ∫₀^(2√2) r² sin φ dr dθ dφ. By evaluating this integral, we can determine the volume of the solid.

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The transitivity of divisibility theorem says that for all integers a, b, and c, if a divides b and b divides c, then a divides c. In other words, if a is a factor of b and b is a factor of c, then a is also a factor of c.

This theorem can be written as follows: If a | b and b | c, then a | c. For example, if a = 2, b = 6, and c = 12, we know that 2 | 6 and 6 | 12, so by the transitivity of divisibility theorem, we can conclude that 2 | 12.

The transitivity of divisibility is an important property of integers and is often used in number theory and other mathematical areas. It allows us to make inferences about the factors of numbers and the properties of divisibility, and is a useful tool in proofs involving divisibility and prime numbers.

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Answer:

Constant.

Step-by-step explanation:

If a graph of a function is flat, it means there is no increase or decrease, meaning it has no changes.

The maximum and minimum values of f(x,y,z) = 2xyz are \(\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }\)

The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function.

f(x,y,z)=2xyz

Computation:

Differentiating the given equation up to second order

\(\begin{gathered}f_x=2yz\Rightarrow 2yz=0 either y=0 or z=0\\f_y=0\Rightarrow 2xz=0 either x=0 or z=0\\f_z=0\Rightarrow 2xy=0 either x=0 or y=0\end{gathered}\)

So, the critical point is (0,0,0)

Now, using the Lagrange's on the boundary,

\(\begin{gathered}g(x,y,z)=x^2+y^2+z^2-1=0\\g_x=2x\\g_y=2y\\g_z=2z\end{gathered}\)

\(So, \bigtriangledown f=\lambda \bigtriangledown g\left < 5yz,5xz,5xy \right > =\lambda \left < 2x,2y,2z )\)

By solving we get,

\(x^2=y^2=z^2\) then,

\(\begin{gathered}x^2+y^2+z^2=1\\3z^2=1\\z=\pm \frac{1}{\sqrt{3} } \\y=\pm \frac{1}{\sqrt{3} } \\\\x=\pm \frac{1}{\sqrt{3} } \\\end{gathered} x 2+y 2+z 2=13z 2=1z=± 31\)

\(So, the critical points are (0,0,0),(\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } )and (\frac{-1}{\sqrt{3} }, \frac{-1}{\sqrt{3} },\frac{-1}{\sqrt{3} })\)

So, by substituting the critical points we get,

\(\begin{gathered}f(0,0,0)=0\\f(\frac{1}{\sqrt{3} }, \frac{1}{\sqrt{3} },\frac{1}{\sqrt{3} })=2(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })\\=\frac{2}{3\sqrt{3} } \\f(-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} })=2(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })\\=-\frac{2}{3\sqrt{3} }\end{gathered}\)

Hence the maximum and minimum values of f(x,y,z) are \(\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }\)

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Answer:

36 people joined the radio control club.

Step-by-step explanation:

15-3= 12

12*3=36

Answer:

D

Step-by-step explanation:

Answer:

1885

Step-by-step explanation:

Volume = Base x Height

The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Domain = \((-\infty,6)\;\cup\;(6,\infty)\)

Range = \((-\infty,1)\;\cup\;(1,\infty)\)

vertical asymptote is at \(x=6\)

Step-by-step explanation:

Domain is all the x values, with an asymptote, it is just a line that approaches a number but never reaches it. The vertical asymptote if you look at x, the lines look like the come from infinity on the left and right, try to reach 6 but can't.

Range is all the y values, with an asymptote, it approaches a number but never reaches it. The horizontal asymptote if you look at y, the lines look like the come from infinity on the top and bottom, try to reach 1 but can't.

The correlation coefficient between weight and height for these 9 individuals is approximately -0.73. So  the answer is (a) -0.73.

The correlation coefficient between weight and height can be estimated by using a statistical software or a calculator. Using a calculator, the correlation coefficient is calculated as follows:

- Enter the weight and height data into two separate lists (e.g. L1 and L2).
- Press the STAT button, then select CALC, and then select option 4: LinReg(ax+b).
- Enter L1 and L2 as the Xlist and Ylist, respectively.
- Make sure that the option "Calculate" is set to "r", which stands for the correlation coefficient.
- Press ENTER to calculate the correlation coefficient.

Using this method, the correlation coefficient between weight and height for these 9 individuals is approximately -0.73. Therefore, the answer is (a) -0.73.

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The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.

Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:

1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0

where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.

We can see that if we set base = 2, then the equation becomes:

1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0

Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

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a. The inequality that represents the additional number of passengers, p, that can board the plane will be D. 15+p≤44 15 plus p is less than or equal to 44

b. The option that represents the people who can board the plane is A. 30 more passengers cannot board the plane. Only 29 more passengers can board the plane.

From the information, the small airplane can hold 44 passengers. Fifteen passengers board the plane.

Let P = those that can board the plane.

P + 15 ≤ 44

Collect like terms

P ≤ 44 - 15

P ≤ 29

The highest number of passengers that can enter the plane is 29.

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a. In this case, the most appropriate research test is a t-test..

b. The most suitable research test for this scenario is a correlation coefficient.

c. A single-sample t-test is the most appropriate research test for this situation.

d. A one-way ANOVA is the most appropriate research test for this situation.

e. A dependent samples t-test is the most appropriate research test for this situation.

Given below are the research tests that are most likely to be used in practice:

a. In this case, the most appropriate research test is a t-test..

b. The most suitable research test for this scenario is a correlation coefficient.

c. A single-sample t-test is the most appropriate research test for this situation.

d. To analyze the differences in self-reported well-being among individuals subscribed to different streaming services, an analysis of variance (ANOVA) test would be appropriate.

Specifically, a one-way ANOVA could be used to compare the means of the three groups (Netflix, HBO Max, and Disney Plus) on the well-being scale.

e. A paired samples t-test would be suitable for this experiment.

By measuring participants' happiness levels before and after watching the funny video, the test would assess whether there is a significant difference in happiness scores pre- and post-video.

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Question:

QS and TV are parallel lines.



What angles are alternate exterior angles?



Options:

a) b) c) d)

Solution:

Remember that the alternate exterior angles are the exterior angles found on either side of the secant. Then, in our case we have that the alternate exterior angles are:

QRP and SRP



Answer:

Where's the grid?

Step-by-step explanation:

The correct option is A) 9∕8, evaluating the exponent expression with a = -2 and b = 3, we find that the value is -8.

We are given the expression a^b, where a = -2 and b = 3. Substituting these values into the expression, we have (-2)^3.

To evaluate this expression, we raise -2 to the power of 3. When we raise a negative number to an odd power, the result will be a negative number.

So, (-2)^3 will yield a negative value.

Calculating (-2)^3, we multiply -2 by itself three times: (-2) × (-2) × (-2). This equals -8.

Therefore, the correct option is A) 9∕8 and the value of the exponent expression (-2)^3 is -8.

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Answer:

34.5

Step-by-step explanation:

You have to add all the kittens up.

Answer:

-290

Step-by-step explanation:

Just times -10 by 52

the percentage increase of members at the skating club is 28%

"relative change = (final value - initial value)/ initial value"

percent change = relative change × 100

For given example,

There were 200 members at a skating club. After some new members went in, there were 256 members altogether at the skating club.

initial value (a) = 200

final value (b) = 256

So, relative increase is,

⇒ R = (b - a)/a

⇒ R = (256 - 200)/200

⇒ R = 56/200

⇒ R = 0.28

So, the percent increase is,

⇒ P = R × 100

⇒ P = 0.28 × 100

⇒ P = 28%

Therefore, the percentage increase of members at the skating club is 28%

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Answer:

1/2048 or 4.8828125*10^(-4)

Step-by-step explanation:

First, figure out the thickness of 1 sheet of paper in number format:

[(8*10)]^(-3)=(80)^(-3) or (1/(80)^(3))=1/512000

Now, multiply 1/512000 by 250 to find the thickness of 250 sheets of paper:

250(1/512000)=1/2048

In scientific notation, this is written as 4.8828125*10^(-4).

The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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