Find the greatest common factor of 7 and 7.

the upper bound for the surface area of the cube.​ is 14 m².

Volume of cube = 3.37 m³

We know the formula is:

V = a³ (where a is the side of the cube)

a³ = 3.37 m³

Cube rooting both the sides, we get that:

a = ∛3.37 m

Surface area will be:

A = 6 a²

A = 6 (∛3.37 m)²

A =6 (2.25 m²)

A = 13.5 m²

A ≈ 14 m²

Therefore, we get that, the upper bound for the surface area of the cube.​ is 14 m².

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Bo would drive 893 miles on 38 gallons of fuel.The number of miles driven by Bo is directly proportional to the number of gallons of fuel he has used.

This means that if we know how many miles Bo has driven for a certain number of gallons of fuel, we can calculate how many miles he would drive with a different number of gallons of fuel. To calculate this, we need to first determine the ratio of miles driven per gallon of fuel used. To do this, we can use the data given in the problem: Bo has driven 188 miles on 8 gallons of fuel, and 799 miles on 34 gallons of fuel.

We can calculate the ratio of miles driven per gallon of fuel used by dividing the number of miles driven by the number of gallons used. In this case, the ratio is 188/8 = 23.5 miles per gallon. We can then use this ratio to calculate the number of miles Bo would drive on 38 gallons of fuel. To do this, we simply multiply the ratio by the number of gallons used, which in this case is 38. This gives us 38 x 23.5 = 893 miles.

Therefore, Bo would drive 893 miles on 38 gallons of fuel.

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Answer:

the answer is one

Step-by-step explanation:

1.......

Answer:

A fraction like 4/4 is called an "improper fraction". An improper fraction is one in which the numerator (the top number) is greater than or equal to the denominator (the bottom number). Another example of an improper fraction is 8/7 in which the numerator, 8, is greater than the denominator, 7.

Step-by-step explanation:

Answer:

9x - 13y

Step-by-step explanation:

2(3x - 2y) + 3(x - 3y)

Use distributive law a(b + c) = ab + ac

⇒ 2·3x - 2·2y + 3·x - 3·3y

⇒ 6x - 4y + 3x - 9y

Gather like terms:

⇒ 6x + 3x - 4y - 9y

Combine like terms:

⇒ 9x - 13y

Answer:

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

40% of the total number is 6.

Find the total number x:

the point P_0(2,1,2) lies on the tangent plane, we can use it to find the equation of the normal line:

x - 2 = 2

We start by finding the characteristic equation:

r^2 + 4r + 3 = 0

Solving for r, we get:

r = -1 or r = -3

So the complementary solution is:

y_c(t) = c_1 e^{-t} + c_2 e^{-3t}

Next, we need to find the transfer function H(s):

s^2 Y(s) - s y(0) - y'(0) + 4s Y(s) - 4y(0) + 3Y(s) = 1/s + 1/(s-1)

Applying the initial conditions y(0) = 0 and y'(0) = 1, we get:

(s^2 + 4s + 3) Y(s) = 1/s + 1/(s-1) + 4

Y(s) = [1/(s+1) + 1/(s+3) + 4/(s^2 + 4s + 3)] / (s^2 + 4s + 3)

We can factor the denominator of the second term in the numerator:

Y(s) = [1/(s+1) + 1/(s+3) + 4/((s+1)(s+3))] / [(s+1)(s+3)]

Using partial fraction decomposition, we get:

Y(s) = [2/(s+1) - 1/(s+3) + 1/((s+1)(s+3))] / (s+1) + [-1/(s+1) + 2/(s+3) - 1/((s+1)(s+3))] / (s+3)

Taking the inverse Laplace transform, we get:

y(t) = 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

So the general solution is:

y(t) = y_c(t) + y_p(t) = c_1 e^{-t} + c_2 e^{-3t} + 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

To find a particular solution, we need to solve for the unknown coefficients. Using the initial conditions y(0) = 1 and y'(0) = 0, we get:

c_1 + c_2 + 3/2 = 1

-c_1 - 3c_2 - 1/2 = 0

Solving this system of equations, we get:

c_1 = -2/5

c_2 = 9/10

So the particular solution is:

y_p(t) = (-2/5) e^{-t} + (9/10) e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

Finally, the tangent plane at P_0(2,1,2) is given by the equation:

2x + 4y + 3z = 24

which corresponds to option (B) in the given choices.

To find the normal line, we first need to find the normal vector to the tangent plane, which is simply:

n = <2, 4, 3>

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The coordinates of the point that is 2/5 of the way from A to B is (-1,-2).

Given, points are A = (-4, -2) and B = (11, -2).

We want to find the coordinates of the point that is 2/5 of the way from A to B.

According to distance rule,

Now distance of A and B =

\( \sqrt{ {( - 4 - 11)}^{2} + {( - 2 + 2)}^{2} } = \sqrt{ {15}^{2} } = 15 \: unit\)

Now required co-ordinate is away 2/5 th distance

from A to B.

So, the distance

\( = 15 \times \frac{2}{5} = 3 \: unit\)

Let, required co-ordinate be (x,y)

Now, distance between (x,y) and (-4,-2) = 3

\( \sqrt{ {(x + 4)}^{2} + {(y + 2)}^{2} } = 3....(1)\)

We are putting first point (5,0) in equation (1) and get \( \sqrt{ {(5 + 2)}^{2} + {(0 + 2)}^{2} } \ne3\)

Again putting (-1,-2) in equation (1), and get \( \sqrt{ {( - 1 + 4)}^{2} + {( - 2 + 2)}^{2} } = 3\)

Therefore, it is clear that required co-ordinate is (-1,-2).

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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Answer:

The equivalent expression for 2 (x+2) is 2x+4

Step-by-step explanation:

i did this and got it right

Answer:

1/2

Step-by-step explanation:

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

Answer:

3780

Step-by-step explanation:

84 = 2^2 * 3 * 7

27 = 3^3

35 = 5 * 7

45 = 3^2 * 5

lcm = 2^2 * 3^3 * 5 * 7 = 3780

The side that is opposite the 95-degree angle should be the longest, followed by the 53-degree angle and finally the 32-degree angle, which will be the shortest. The answer is (b).

How do you tell which angle is larger: The largest angle is located across from the longest side, just like with the sides. Theorem: If and only if angle A (= angle CAB) is greater than angle B (= angle ABC), then side BC of a triangle ABC will be longer than side CA. To put it another way, larger sides are in opposition to larger angles.

If you have an angle and its opposite side, you may calculate the hypotenuse by dividing the length of the opposing side by sin(). To find the length of the side next to the angle, you can also divide the length by tan(). Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Hint: There are two fundamental units used to measure angles from one of the two fundamental units, radians () or degrees ().

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Correct Question:

The standard form of the number  \((1.5*10^(13))^2\)  is  2.25×\(10^(26)\) .

What is standard form of a number ?

 An equation, an expression, or a set of integers can all be written in standard form using the standard form approach. It is possible to express a number in a way that adheres to certain standards by writing it in its standard form. Standard form refers to any number between 1.0 and 10.0 that may be expressed as a decimal number and multiplied by a power of 10. The term "standard form" in this context refers to the act of condensing a particularly big expanded form of a number.

Here given is ,

=> \((1.5*10^(13))^2\)

=> \(1.5^2\) × \(10^(13)^2\)

=> 2.25×\(10^(26)\)

Therefore standard form of the number is  2.25×\(10^(26)\).

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Answer:

What do you mean?

Step-by-step explanation:

Give full explanation please

Answer:  54° or 40°, depending on my interpretation of the problem.

Step-by-step explanation:

I do not understand the drawing. I see a right angle with a line bisecting it at 36 degrees.  A right angle is 90°, so the other angle should be (90 - 36) or 54°.  But what's shown is (14 - 1)°, and I don't know how to interpret that.  Is the "1" supposed to be an "x"?  If so, x = 40°

Answer:

(6 + x)(6 + x) = (6 + x)²

Step-by-step explanation:

Given

36 + 12x + x²

Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (+ 12)

The factors are + 6 and + 6, since

6 × 6 = 36 and 6 + 6 = 12, thus

36 + 12x + x² = (6 + x)(6 + x) = (6 + x)²

Answer:

2.56 kgs

Step-by-step explanation:

76.8kg ÷ 30 days = 2.56 kgs

Amount of sugar used - 76.8 kg

No. Of Days in Month of April - 30 days

∴ Sugar used each day is = 76.8 ÷ 30

\(76.8 \div 30 \\ \\ = \frac{76.8}{30} \\ \\ = \frac{768}{30 \times 10} \\ \\ = \frac{ \cancel{768}}{ \cancel{30} \times 10} \fbox{cancelling by 3} \\ \\ = \frac{256}{10 \times 10} \\ \\ = \frac{256}{100} \\ \\ = 2.56 \: kg\)

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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To eliminate the cross-product terms we can perform an orthogonal change of variables. We can determine the orthogonal transformation.

The quadratic form f(x, y) = \(x^2\) + 2xy + \(y^2\) can be represented by the matrix A = [[1, 1], [1, 1]]. To eliminate the cross product terms, we need to find the eigenvectors of A. By solving the eigenvalue problem, we find the eigenvalues λ_1 = 0 and λ_2 = 2. Corresponding to λ_1 = 0, we obtain the eigenvector v_1 = [-1, 1]. For λ_2 = 2, we find the eigenvector v_2 = [1, 1]. These eigenvectors form an orthogonal basis.

The change of variables can be expressed as x = v_1 · [x', y'] and y = v_2 · [x', y'], where · denotes the dot product. Substituting these expressions into the quadratic form, we obtain f(x', y') = λ_1(\(x'^2\)) + λ_2(\(y'^2\)). This new form has eliminated the cross product terms.

Now, considering the equation \(x^2\) + 2xy + \(y^2\) + 3x + y - 1 = 0, we can apply the change of variables. After substituting x = v_1 · [x', y'] and y = v_2 · [x', y'], the equation transforms into λ_1\((x'^2)\) + λ_2(\(y'^2\)) + (3\(V_{1}\) + \(V_{2}\)) · [x', y'] - 1 = 0. Simplifying further, we have 2\(y'^2\) + (3\(\sqrt{2x'}\) + \(\sqrt{2y'}\)) - 1 = 0. This equation represents a parabola, as the coefficient of the x'^2 term is zero. To sketch the graph of this parabola, we can determine its vertex and axis of symmetry. The vertex is given by the point (-3/4, 1/4), and the axis of symmetry is parallel to the y-axis. By plotting this information and a few additional points, we can sketch the graph of the parabola.

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It takes approximately 26.56 seconds for the ferris wheel to make one revolution.

so, the correct option is: e) 26.56 seconds

Here, we have,

The ferris wheel makes one complete revolution when the distance of the person above the ground returns to the original value after completing a full circle.

This occurs when the sine function returns to its maximum value, which is 1.

Thus, we have the following equation:

20 * sin(π/30 * t) + 10 = 20

Solving for t,

we will get:

sin(π/30 * t) = 0.5

Taking the inverse sine of both sides:

(π/30 * t) = sin^-1(0.5)

Multiplying both sides by 30/π,

we will get the following:

t = (30/π) * sin^-1(0.5)

Now solving the value of t

We will get it as: t ≈ 26.56 seconds.

so, the correct option is: e) 26.56 seconds

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complete question:

the distance from the ground of a person riding on a ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. how long will it take for the ferris wheel to make one revolution?

a) 10 seconds

b) 20 seconds

c) 30 seconds

d) 60 seconds

e) 26.56 seconds

The larger the group of answer choices, the less likely our data represent the model due to larger differences between the expected frequencies.

Based on the terms provided, we want to know the relationship between the size of a group of answer choices, differences between expected frequencies, and how likely the data represents a model.

The larger the group of answer choices, the larger the differences between the expected frequencies, and the less likely our data represent the model.

This is because a larger group of answer choices increases the complexity of the dataset, which may lead to more significant deviations from the expected frequencies, ultimately making it less likely that the data represents the given model.

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Answer: 25

Step-by-step explanation: 50 divided by 2 is 25

Answer: 1/3=n

Step-by-step explanation:

-1/2(2n + 4) + 6 = –9 + 4(2n + 1)

Distribute:

-1n-2+6=-9+8n+4

Combine like terms:

-1n-2+6=-9+8n+4

-1n+4=-5+8n

Add 1n on both sides:

-1n+4=-5+8n

-1n+1n+4=-5+8n+1n

4=-5+9n

Add 5 on both sides:

4+5=-5+5+9n

9=9n

Divide 9 on both sides:

9/9=9n/9

1=n

Answer:

7

Step-by-step explanation:

The number of triangles in the figure is given as 15 triangles.

Given that,
To determine the number of triangles inside the triangles.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

here,
here in the figure inside the parent figure, there are 6 segments that contribute two triangles in the figure,
Number of triangle  = 6C2
Number of triangle = 15

Thus, the number of triangles in the figure is given as 15 triangles.

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The problem can be expressed in the form

The cost per kg for the potatoes and onions is

15 kg of potatoes and 10 kg of onions will cost

From the question it can be deduced

let the price of potatoes be x and the price of onions be y

The total cost of 4 kg of potatoes and 2 kg of onions is Rs. 350

4x + 2y = 350

If the cost of 3 kg of potatoes is same as the cost of 2 kg of onions

3x = 2y

substituting 2y for 3x in 4x + 2y = 350

4x + 3x = 350

7x = 350

x = 50

solving for y in 3x = 2y

3 * 50 = 2y

2y = 150

y = 75

c. 15x + 10y will cost

= 15 * 50 + 10 * 75

= 1500

the cost will be 1500

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The value of x that satisfies the equation is x = 15/8, which is equivalent to 1.875.

To solve the equation (2/3)x - (1/5)x = x - 1 and find the value of x, we can follow these steps:

Combine like terms on the left side of the equation:

(2/3 - 1/5)x = x - 1

Find a common denominator for the fractions on the left side. The common denominator for 3 and 5 is 15, so we rewrite the equation as:

(10/15 - 3/15)x = x - 1

Simplify the left side of the equation:

(7/15)x = x - 1

To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is 15:

15 * (7/15)x = 15 * (x - 1)

This simplifies to:

7x = 15x - 15

Subtract 15x from both sides of the equation to isolate the x term:

7x - 15x = -15

Simplifying further:

-8x = -15

Divide both sides of the equation by -8 to solve for x:

x = (-15) / (-8)

Simplifying the division:

x = 15/8

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