What is the word form of 602,107

Answer:

\(f(x)=\sqrt[3]{x-2} +1\)

Step-by-step explanation:

Given function for graph:  \(f(x)=1\sqrt[3]{x-h} +k\)

where (h, k) is the midpoint of the curve.

Therefore, the parent function is \(f(x)=\sqrt[3]{x}\)

\(f(x)=1\sqrt[3]{x-h} +k\) can be obtained by translating \(f(x)=\sqrt[3]{x}\) to \(h\) units to the right and \(k\) units up

The x and y intercept of \(f(x)=\sqrt[3]{x}\) is the origin

Therefore, this graph has been translated 2 units to the right and 1 unit up.

Therefore, \(h=2\) and \(k=1\)

Substituting these values into the given function:

\(\implies f(x)=\sqrt[3]{x-2} +1\)

Answer:

\(\|a\| = 5\sqrt{13}\).

\(\|b\| = 3\sqrt{29}\).

Step-by-step explanation:

Let \(m\),\(n\), and \(k\) be scalars such that:

\(\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}\).

\(\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}\).

\(\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}\).

The question states that \(\| a + b \| = 34\). In other words:

\(k\, \sqrt{8^{2} + 15^{2}} = 34\).

\(k^{2} \, (8^{2} + 15^{2}) = 34^{2}\).

\(289\, k^{2} = 34^{2}\).

Make use of the fact that \(289 = 17^{2}\) whereas \(34 = 2 \times 17\).

\(\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}\).

\(k^{2} = 2^{2}\).

The question also states that the scalar multiple here is positive. Hence, \(k = 2\).

Therefore:

\(\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}\).

\((a + b)\) could also be expressed in terms of \(m\) and \(n\):

\(\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}\).

\(\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}\).

Equate the two expressions and solve for \(m\) and \(n\):

\(\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}\).

\(\begin{cases}m = 5 \\ n = 3\end{cases}\).

Hence:

\(\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}\).

\(\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}\).

Both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

To determine the number of extraneous solutions in the given equation, let's simplify it step by step:

Step 1: Let's find the common denominator for the two fractions on the left side of the equation. The common denominator is (2m + 3)(2m - 3).

Step 2: Apply the common denominator to both fractions:

[(2m)(2m - 3)]/[(2m + 3)(2m - 3)] - [(2m)(2m + 3)]/[(2m + 3)(2m - 3)] = 1

Step 3: Simplify the numerators:

\([4m^2 - 6m - 4m^2 - 6m]/[(2m + 3)(2m - 3)] = 1\)

[-12m]/[(2m + 3)(2m - 3)] = 1

Step 4: Cancel out common factors:

-12m = (2m + 3)(2m - 3)

\(-12m = 4m^2 - 9\)

Step 5: Rearrange the equation:

\(4m^2 + 12m - 9 = 0\)

Step 6: Solve the quadratic equation using factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

\(m = (-b ± √(b^2 - 4ac))/(2a)\)

For our equation, a = 4, b = 12, and c = -9. Substituting these values:

m = (-(12) ± √((12)^2 - 4(4)(-9)))/(2(4))

m = (-12 ± √(144 + 144))/(8)

m = (-12 ± √288)/8

m = (-12 ± 12√2)/8

Simplifying further:

m = (-3 ± 3√2)/2

So, we have two potential solutions for m:

m = (-3 + 3√2)/2  and  m = (-3 - 3√2)/2

Now we need to check if these solutions satisfy the original equation. Let's substitute these values back into the equation:

For m = (-3 + 3√2)/2:

[(2(-3 + 3√2))/(2(-3 + 3√2) + 3)] - [(2(-3 + 3√2))/(2(-3 + 3√2) - 3)] = 1

Simplifying this equation, we find that it holds true.

For m = (-3 - 3√2)/2:

[(2(-3 - 3√2))/(2(-3 - 3√2) + 3)] - [(2(-3 - 3√2))/(2(-3 - 3√2) - 3)] = 1

Simplifying this equation, we also find that it holds true.

Therefore, both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

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Answer:

I think its false

Step-by-step explanation:

the car went 8 second faster

Answer:

the simplest form of 15/20 is 3/4

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

To reach your fundraising goal of $75, you can sell pencils for $0.50 and bracelets for $1.00.

1. Calculate the total amount of money needed to reach the goal:
  Goal amount = $75

2. Determine the number of pencils and bracelets you need to sell to reach the goal:
  Let's assume you sell x number of pencils and y number of bracelets.

  The amount raised from selling pencils = x * $0.50
  The amount raised from selling bracelets = y * $1.00

  The total amount raised from both items should be equal to the goal amount:
  x * $0.50 + y * $1.00 = $75

3. Simplify the equation:
  0.50x + 1.00y = 75

4. Solve for one variable in terms of the other:
  Let's solve for x in terms of y:
  0.50x = 75 - 1.00y
  x = (75 - 1.00y) / 0.50

5. Substitute the value of x into the equation:
  (75 - 1.00y) / 0.50 * 0.50 + y * $1.00 = $75
  75 - 2y + y = 75
  -y = 0
  y = 0

6. Find the value of x:
  x = (75 - 1.00 * 0) / 0.50
  x = 75 / 0.50
  x = 150

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

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Hey there! I'm happy to help!

How many times does 30 minutes go into 60 minutes?

60/30=2

This means we are traveling 32 miles two times!

32(2)=64

Therefore, Kathryn and her mom drive 64 miles in an hour.

Have a wonderful day! :D

Answer:

-140C

Step-by-step explanation:

∆T = T2-T1

∆T = -50-90= -140C

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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The amounts for the other three partners are $25000, $100000, and $200000.

The amount that the other people will share will be:

= $400000 - $50000

= $350000

Therefore this will be divided as follows:

A = 2/(2+4+8) × $350000

= 2/14 × $350000

= $25000

B = 4/14 × $350000

= $100000

C = 8/14 × $350000

= $200000

Therefore, the amounts for the other three partners are $25000, $100000, and $200000.

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Answer:

12%.

Step-by-step explanation:

Entonces 6 seria el doble: 12%.

The function in vertex form that models the path of the stream is:

\(y = (-5/9)(x - 3)^2 + 5\)

A location where two or more straight lines or curves intersect is referred to as a vertex . A vertex in geometry is sometimes referred to as a corner or an intersection point. The phrase is frequently used to refer to the highest or lowest point on a curve or surface, the place where two lines intersect to make an angle, and the point where two sides of a polygon meet.

The vertex form of the equation of a parabola is given by:

\(y = a(x - h)^2 + k\)

where (h, k) represents the vertex of the parabola.

Using the given vertex and the point (6,0), we can find the value of "a" and plug it into the vertex form to get the equation of the parabolic path of the water stream.

Step 1: Find the value of "a"

Since the vertex is (3,5), we know that:

h = 3

k = 5

Using the point (6,0), we can find the value of "a" as follows:

\(0 = a(6 - 3)^2 + 5\)

\(0 = 9a + 5\)

\(9a = -5\)

\(a = -5/9\)

Step 2: Plug in the values of h, k, and a into the vertex form:

\(y = (-5/9)(x - 3)^2 + 5\)

Therefore, the function in vertex form that models the path of the stream is:

\(y = (-5/9)(x - 3)^2 + 5\)

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Answer:

r = 2

Step-by-step explanation:

nth term of a geometric sequence = \( ar^{n - 1} \).

Where,

a = first term, r = common ratio,

We are given that, the 11th term is 32 times larger than the 6th term of the geometric sequence. Thus:

the 6th term can be expressed as \( ar^{n - 1} = ar^{6 - 1} \)

\( a_6 = ar^{5} \)

The 11th term is expressed as \( a_11 = ar^{10} \)

Since the 11th term is 32 times larger than the 6th term, therefore, the following equation can be derived to find the common ratio, r, of the sequence:

\( a_11 = 32*a_6 \)

\( a_11 = ar^{10} \)

\( a_6 = ar^{5} \), therefore:

\( ar^{10} = 32*ar^{5} \)

Divide both sides by ar⁵

\( \frac{ar^{10}}{ar^5} = \frac{32*ar^{5}}{ar^5} \)

\( r^5 = 32 \)

\( r^5 = 2^5 \)

\( r = 2 \)

Common ratio = 2

Here is the same rectangle. It has some unit squares inside. The area of the rectangle is 10 Square unit.

Area of Rectangle:

The area of ​​a rectangle is the area occupied within the bounds of the rectangle. In other words, the area bounded by a rectangle is called the area of ​​the rectangle. It can be calculated using the area of ​​a rectangle formula and using various methods, depending on the given dimensions.

According to the Question:

Area of each small square = 1 sq cm

Area of rectangle in figure 2 by counting the squares = 10 sq. cm

Area = 10 square cm

Length of rectangle = 5 cm

Breadth of rectangle = 2 cm

Area = 5 × 2 = 10 sq. cm

Hence, area of rectangle = length × breadth

A = l × b where, A is the area, l and b are length and breadth of a rectangle.

Complete Question:

You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square is outside the rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle?

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Given data:

The given amount of equipment purchased by the Sandra is A=$1,200.

Answer:

D. 52

Step-by-step explanation:

105/2=52

The middle of 110 and 100 is 105. When you divide that by 2 you get 52.5 or 52. The answer is D

Answer:

D 52 is the answer

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The length of each side of the base is 3 inches. Thus, the correct option is D.

In terms of geometry, a pyramid is a polygon that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. If the base of the pyramid is a rectangle then the pyramid is known as a rectangular pyramid.

The lateral area of a regular pentagonal pyramid is 75 square inches and the slant height is 10 inches.

The length of each side of the base is calculated as,

75 = 5 x 1/2 x a x 10

75 = 25a

a = 3 inches

Thus, the correct option is D.

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Answer:

4.79

Step-by-step explanation:

4.79 is reasonable for the problem

The price of one paint set before the sale is $4.79

We are expected to determine the price of one paint set before the sale.

From the information given:

∴

The amount at which Yuri bought 1 paint set is:

\(\mathbf{= \dfrac{\$6.88}{2.0}}\)

= $3.44

Recall that during the sale, the store reduce the price of each paint set by $1.35

Therefore, the price of one paint set before the sale is = $3.44 + $1.35 = $4.79

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Answer:

30%

Step-by-step explanation:

Purchases:

Coat £20

Hat £15

Gloves for £5

Total amount of purchases: £20 + £15 + £5 = £40

Sales:

Coat at 50% profit: 150% × £20 = 1.5 × £20 = £30

Hat: £18

Gloves at a 20% loss: 80% of £5 = £4

Total amount of sales: £30 + £18 + £4 = £52

Amount of profit: £52 - £40 = £12

Percent of profit: £12 / £40 × 100% = 30%

The quadrilateral WXYZ is not a square using the distance formula

From the question, we have the following parameters that can be used in our computation:

W(-1,1),X(3,4),Y(6,0) and Z(2,3)

The lengths of the sides can be calculated using the following distance formula

Length = √[Change in x² + Change in y²]

Using the above as a guide, we have the following:

WX = √[(-1 - 3)² + (1 - 4)²] = 5

XY = √[(3 - 6)² + (4 - 0)²] = 5

YZ = √[(6 - 2)² + (0 - 3)²] = 5

ZW = √[(2 + 1)² + (3 - 1)²] = 13

The sides that are congruent are WX, XY and YZ

This means that WXYZ is not a square

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

5⁸ + 4⁶ + 2¹⁵ = 427489

Step-by-step explanation:

(5⁴)² + (4²)³ + (2³)⁵ = 5⁸ + 4⁶ + 2¹⁵

= 390625 + 4096 + 32768

= 427489

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

In this problem we need to find a sinusoidal expression that models the curve seen in the picture. The most typical sinusoidal model is described below:

f(x) = a · sin (b · x + c) + d    (1)

Where:

Now we proceed to find the value of each variable:

Amplitude

a = - 2 - (-6.5)

a = 4.5

Angular frequency

b = 2π / T, where T is the period.

0.25 · T = 4 - 3

T = 4

b = 2π / 4

b = π / 2

Midpoint

d = - 6.5

Angular phase

- 2 = 4.5 · sin (π · 4/2 + c) - 6.5

4.5 = 4.5 · sin (π · 4/2 + c)

1 = sin (2π + c)

π = 2π + c

c = - π

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

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Answer:180 degrees

Step-by-step explanation:

(a) Using Lagrange polynomial, P_{3}(0.4) is calculated.

(b) Least Square fitting method is used to find the RMSE and f(0.4).

(a) To find P_{3} (0.4) using Lagrange polynomial, we consider four data points (x, f(x)) and calculate the interpolating polynomial P_{3} (x) that passes through these points. Then, we evaluate P_{3} (0.4) to find the desired value.

(b) Using the least square fitting method, we approximate the function f(x) by fitting it to a polynomial of degree 3. We calculate the coefficients of the polynomial that minimize the sum of squared errors (RMSE). Then, we use the obtained polynomial to find f(0.4) by substituting x=0.4 into the polynomial.

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Answer:

The vertex translates 4 units to the right and 1 unit upward

Step-by-step explanation:

Suppose we have a function f(x).

To translate the function a units to the left, we need to find f(x + a).

To translate the function a units to the right, we need to find f(x - a).

To translate the function a units upward, we need to find f(x) + a

To translate the function a units downwards, we need to find f(x) - a.

In this question.

We start with:

f(x) = x²

First, we look at changes in x. We have

f(x-4) = (x - 4)². So a translation of 4 units to the right.

Then

f(x - 4) + 1 = (x-4)² + 1

One unit upwards.

The correct answer is:

The vertex translates 4 units to the right and 1 unit upward