Which of the following statements are true?
Select all that apply.
A. 4 is a perfect cube.
B. 16 is a perfect square.
C. 2,197 is both a perfect square and a perfect cube.
D. 8 is a perfect cube.
E. 18 is neither a perfect square nor a perfect cube.

The weight of each box is 450 g, 100 g and 150 g.

Given that on the table, there are three boxes.

Box 1 has a mass that is three times more than Box 3's mass.

Box 2's mass is approximately two thirds that of Box 1.

We need to determine that what is the mass of each of the other boxes if box 3 weighs 150 grams,

Since the weight of box 3 is 150 g,

So, weight of the box 1 = 3 x 150 = 450 g

Similar to this,

The weight of the box 2 = 2/3 x 150 = 100 g.

Hence the weight of each box is 450 g, 100 g and 150 g.

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Answer:

30 cm

Step-by-step explanation:

We Know

The formula for Perimeter of rectangle = 2 (L + W)

Perimeter = 90 cm

Width = 15 cm

Find the length.

We Take

90 = 2 (L + 15)

45 = L + 15

L = 30 cm

So, the length is 30 cm

The measure of angle V is,

⇒ ∠ V = 53°

We have to given that,

A parallelogram VWXY are shown in image.

Since, We know that,

Opposite angles of a parallelogram is equal.

Hence, We get;

⇒ ∠W = ∠Y

Substitute all the values, we get;

⇒ (2x + 29) = (10x - 27)

Solve for x,

⇒ 2x + 29 = 10x - 27

⇒ 29 + 27 = 10x - 2x

⇒ 56 = 8x

⇒ x = 56 / 8

⇒ x = 7

So, Measure of Angle Y is,

⇒ ∠ Y = (10x - 27)

⇒ ∠ Y = 10 x 7 - 17

⇒ ∠ Y = 70 - 17

⇒ ∠ Y = 53°

We know that,

In a parallelogram, alternate angle are equal.

⇒ ∠Y = ∠ V

⇒ ∠ V = 53°

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The value of x is equal to: (3) 12.

In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:

C = πD or C = 2πr

Where:

By substituting the given parameters into the formula for the circumference of a circle, we have the following;

Circumference of circle, C = 2 × 3.14 × 5

Circumference of circle, C = 31.4 units.

Therefore, the length of each sector is given by;

Length = 31.4/24

Length = 1.3 unit.

For the value of x, we have:

x = 12 × 1.3

x = 15.6 ≈ 16 units.

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Missing information:

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

The quadratic equation is f(x) = (x + 9)² + 37, and  the numerical values of h and k are h = - 9 and k = 37, respectively

The function is given as:

f(x) = x² + bx + 118

Start by differentiating the function,

f'(x) = 2x + b

Set to 0

2x + b = 0

Solve for x

x = -b/2

Substitute x = -b/2 in f(x) = x² + bx + 118

f(-b/2) = (-b/2)² + b(-b/2) + 118

This gives

f(-b/2) = b²/4 - b²/2 + 118

Evaluate

f(-b/2) = - b²/4 + 118

Since, The minimum of the function is 37.

So, we have:

- b²/4 + 118 = 37

Subtract 118 from both sides

- b²/4 = - 81

Multiply both sides by -4

b² = 324

Take the square root of both sides

b = 18

Substitute b = 18 in f(x) = x² + bx + 164

f(x) = x² + 18x + 118

Rewrite as:

f(x) = (x² + 18x) + 118

This gives

f(x) = (x² + 18x + (18/2)² - (18/2)²) + 118

Rewrite as:

f(x) = (x² + 18x + 9²) - 9² + 118

f(x) = (x² + 18x + 9²) + 37

Express as a perfect square expression

f(x) = (x + 9)² + 37

Thus, The function is represented as:

f(x) = (x - h)² + k

By comparison, we have:

h = - 9 and k = 37

Hence, the numerical values of h and k are h = - 9 and k = 37, respectively

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The probability of winning the jackpot is 0.000065

The number of successful outcomes is 1 because there is only one winning combination.

The total number of possible outcomes can be calculated by multiplying the number of possibilities for each event:

Number of possibilities for selecting 5 white balls out of 13:

This can be calculated using the combination formula (nCr).

In this case, it is 13C5.

Number of possibilities for selecting 1 gold Mega Ball out of 12 is simply 12.

Therefore, the total number of possible outcomes is (13C5) × 12.

To calculate (13C5), we can use the combination formula: nCr = n! / (r! (n - r)!)

(13C5) = 13! / (5! × (13 - 5)!)

= 13! / (5! × 8!)

= (13 × 12 × 11 × 10 × 9) / (5 × 4 × 3 × 2 × 1)

= 1287

Now, we can calculate the total number of possible outcomes:

Total number of possible outcomes = (13C5) × 12

= 1287 × 12

= 15444

The probability of winning the jackpot by dividing the number of successful outcomes by the total number of possible outcomes:

Probability of winning the jackpot = 1 / 15444

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The correct answer is: C) The graph of f(x) is reflected over the x-axis and translated 3 units up to become g(x).

To understand how the graph of f(x) changes to become g(x), let's analyze the transformations applied.

The function f(x) = log(3x) represents a logarithmic function, where the base of the logarithm is 10. The graph of f(x) will have a vertical asymptote at x = 0 and will increase as x increases.

The function g(x) = -f(x) + 3 takes the negative of f(x) and then adds 3 to it. This means that the graph of g(x) is obtained by reflecting the graph of f(x) over the x-axis and then translating it vertically 3 units up.

The reflection over the x-axis changes the sign of the y-values, so the graph of g(x) will be below the x-axis where the graph of f(x) is above the x-axis, and vice versa.

The translation 3 units up moves the entire graph vertically, shifting it higher on the coordinate plane.

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The area of the shaded region which is the area to the left of the distribution curve is 0.9522

Given that :

Mean, μ = 100

Standard deviation, σ = 15

Score, X = 125

We obtain the Zscore of the distribution :

Zscore = (X - μ) ÷ σ

Zscore = (125 - 100) ÷ 15 = 1.667

The Area of the shaded region is the area to the left of the distribution :

P(Z < Zscore) = P(Z < 1.667)

P(Z < 1.667) = 0.9522 (rounded to 4 decimal places)

Therefore, the area of the shaded region is 0.9522 which depicts the area to the left of the distribution.

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All the solutions are,

1) Vertex = (3, 0)

2) Equation for the line of symmetry is,

⇒ x = 3

3) Coordinates of the y-intercept is,

⇒ Y - intercept = (0, 9)

4) Coordinates of the x-intercept(s) is,

⇒ Y - intercept = (3, 0)

We have to given that,

A graph of parabola is shown in image.

Now, From the graph of parabola we get;

Coordinates of the vertex is,

Vertex = (3, 0)

Equation for the line of symmetry is,

⇒ x = 3

Since, The graph at point 9 on y - axis,

Hence, Coordinates of the y-intercept is,

⇒ Y - intercept = (0, 9)

Since, The graph cut at point 3 on x - ais,

Hence, Coordinates of the x-intercept(s) is,

⇒ x - intercept = (3, 0)

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The total interest for the loan is $4,550. This means that over the course of 5 years, you will pay back the original loan amount of $13,000 plus $4,550 in interest for a total of $17,550.

To calculate the total interest for this loan, we need to use the simple interest formula:
Monthly EMI formula :
Interest = Principal x Rate x Time

In this case, the principal (amount borrowed) is $13,000, the rate is 7%, and the time is 5 years.

So,

Interest = $13,000 x 0.07 x 5

Interest = $4,550

It's important to keep in mind that this calculation assumes that the interest rate remains constant over the entire 5-year period.

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It is not possible to calculate the area accurately. If you could provide more details about the figure, such as its shape or a diagram, I would  to help you calculate the area.

Based on the information provided, it seems you are asking for the area of a figure with sides 4, 8, 4, 4, 8, and 16 meters.

However, without knowing the specific shape of the figure,  In general, calculating the area of a shape involves using formulas specific to that shape,

such as length × width for rectangles or base × height × 0.5 for triangles. Once you provide more information about the figure, I can guide you through the appropriate calculation.

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i. The monthly payment is approximately $143,397.56.

ii. The company will pay approximately $2,016,763.52 in interest over the 6-year term of the loan.

i. To calculate the monthly payments for a loan, we need to use the loan term, interest rate, and loan amount with the following formula:

M =[tex]P * (r * ((1 + r)^n)) / (((1 + r)^n) - 1)[/tex]

where M is the monthly payment, P is the loan amount, r is the interest rate per month (which is the annual rate divided by 12 months), and n is the total number of payments (which is the loan term multiplied by 12 months).

Using the given values, we get:

P = $8,300,000

r = 9.2% / 12 months = 0.7667%

n = 6 years * 12 months/year = 72

M = $8,300,000 * (0.7667% * ((1 + 0.7667%)^72)) / (((1 + 0.7667%)^72) - 1)

M ≈ $143,397.56

ii. To calculate the total interest paid on a loan, we need to subtract the loan amount from the total amount paid and use the following formula:

Total interest = Total amount paid - Loan amount

The total amount paid over the 6-year term of the loan is the monthly payment multiplied by the total number of payments:

Total amount paid = M * n

Using the values we calculated in part (i), we get:

Total amount paid = $143,397.56 * 72 = $10,316,763.52

Therefore, the total interest paid on the loan is:

Total interest = $10,316,763.52 - $8,300,000 = $2,016,763.52

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There are 3 rovers does Halima make.

We have to given that,

Halima makes model rovers for a science project about space.

And, She puts 6 wheels on each rover, and she has 20 wheels.

Now, We have;

Total number of wheels = 20

Number of wheels In each rover = 6

Hence, Number of rovers Halima make is,

⇒ 20 / 6

After divide,

Quotient = 3

Remainder = 2

Thus, There are 3 rovers does Halima make.

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Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation [tex]\boxed{ax^2 + bx + c = 0}[/tex] to have exactly one real root, the value of its discriminant, [tex]\boxed{b^2 - 4ac}[/tex], must be zero.

For the given equation:

[tex]y = ax^2 - 6x + 10[/tex],

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

[tex](-6)^2 - 4(a)(10) = 0[/tex]

⇒ [tex]36 - 40a = 0[/tex]

⇒ [tex]36 = 40a[/tex]

⇒ [tex]a = \frac{36}{40}[/tex]

⇒ [tex]a = \bf 0.9[/tex]

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

[tex]x = 0, \pi[/tex]

Step-by-step explanation:

Question:

[tex]cosatanx+3tanx = 0[/tex]

Factor tanx:

[tex]tanx(cosa+3) = 0[/tex]

Split apart the equation:

[tex]tanx = 0\\cosa = -3[/tex]

Solve using the unit circle:

[tex]x = 0, \pi[/tex]

[tex]a = [NO--SOLUTION]-- [OUTSIDE--RANGE][/tex]

Answer:

x ≈ 5.4 feet

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse x is equal to the sum of the squares on the other 2 sides.

horizontal leg = 5 units = 5 feet

vertical leg = 2 units = 2 feet

Then

x² = 5² + 2² = 25 + 4 = 29 ( take square root of both sides )

x = [tex]\sqrt{29}[/tex] ≈ 5.4 feet ( to the nearest tenth of a foot )

There are 6 bundles are used to make one block of cardboard.

To determine how many bundles are used to make one block of cardboard, we first need to know how many bundles are stacked and tried together to reach a height of 1.2 metres.

Let's assume that each bundle is 0.2 metres high, so it would take six bundles stacked and tried together to make a block that is 1.2 metres high.

Therefore, we can conclude that six bundles are used to make one block of cardboard.

It's important to note that this calculation may vary depending on the dimensions of the bundles and blocks used in the cardboard manufacturing process. However, based on the information provided in the question,

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The inverse image of a set B under a function consists of all the elements in the domain of function that are mapped to elements in B.

The phrase "inverse image" refers to a concept related to functions and mappings between sets.

For example, say we have 2 sets: A and B, and a function that maps elements from set A to set B.

Given a subset of set B, called a target set, the inverse image of that set under the function, denoted as f⁻¹(B), is the subset of set A that contains all the elements in set A that map to elements in set B.

To put it simply, the inverse image of a set B under a function consists of all the elements in the domain of function that are mapped to elements in B. It represents the pre image or the set of inputs that produce a specific set of outputs when applied to the function.

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Answer:

19.8

Step-by-step explanation:

We reduce 10% to decimal form (0.1) and add to 1 to form its reflective percentile increase. We multiply 18 by 1.1 to get 19.8

a) The relation represents the number of days each family spent camping last summer.

b) i) Jones (2) → Smith (6) → Teynor (9) → Glimler (11) → Frannot (16)

ii) Family | Number of Days: Jones (2), Smith (6), Teynor (9), Glimler (11), Frannot (16)

We have,

a)

The relation represents the number of days each family spent camping last summer.

It shows the association between each family and the corresponding number of days they spent camping.

b)

i)

Arrow Diagram:

Jones (2)   ->   Smith (6)

  |                |

  V                V

Teynor (9)  ->  Glimler (11)

  |

  V

Frannot (16)

ii)

Table Representation:

Family Number of Days

Jones 2

Smith 6

Teynor 9

Glimler 11

Frannot 16

Thus,

a) The relation represents the number of days each family spent camping last summer.

b) i) Jones (2) → Smith (6) → Teynor (9) → Glimler (11) → Frannot (16)

ii) Family | Number of Days: Jones (2), Smith (6), Teynor (9), Glimler (11), Frannot (16)

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Based on the information in the image, we can infer that the median of both graphs is 16 (brand x) and 11 (brand y).

To identify the median we must take into account the information in the graphs. In this case we must take the values of the extremes of the graphs and add them. Once we have added them we must divide the result by 2 to find the median. Based on the above, we can infer that the correct answer is:

16 brand x

11 brand and

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The values of the given expressions are,

(a) (f + g)(-1) = 12

(b) (f + g)(-1) = -4

(c) fg(-1) = 32

(d) (f/g)(-1) = 1/2

The given functions are,

f(x) = x²  - 3x

g(x) = x + 9

(a) Now to find (f + g)(-1)

Add the functions

⇒ (f + g)(x) = (x²  - 3x) + (x + 9)

                 =  x²  - 2x + 9

Now put x = -1

⇒ (f + g)(-1) =  (-1)²  - 2(-1) + 9

                  = 1 + 2 + 9

                   = 12

(b) Now to find (f - g)(-1)

Subtract the functions

⇒ (f - g)(x) = (x²  - 3x) - (x + 9)

                 =  x²  - 4x - 9

Now put x = -1

⇒ (f - g)(-1) =  (-1)²  - 4(-1) - 9

                  = 1 + 4 - 9

                   = -4

(c) To find fg(-1)

To find this multiply the functions we get,

⇒ fg(x) = (x²  - 3x)(x + 9)

           = x³ - 3x² + 9x² - 27x

           = x³ + 6x² - 27x

Now put x = -1

⇒ fg(-1) = (-1)³ + 6(-1)² - 27(-1)

            = -1 + 6 + 27

            = 32

(d) To find (f/g)(-1)

Divide the functions we get,

⇒ (f/g)(x) = (x²  - 3x)/(x + 9)

Now Put x = -1  we get,

⇒ (f/g)(-1) = ((-1)²  - 3(-1))/(-1 + 9)

               = 4/8

               = 1/2

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The true statements are:

B. f(0) = 10

D. The domain for f(x) is the set (-5, -3, 0, 2, 6, 7, 9, 10, 13).

According to the given table,

when x = 0, the corresponding value of y is 10.

So, f(0) = 10.

Now, the domain for f(x) represents all the possible x-values for which there is a corresponding y-value in the table.

From the given table, we can see that the x-values in the domain are -5, -3, 0, 2, 6, 7, 9, 10, and 13.

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The measure of CDB is 90 degrees if line AC is a tangent to circle D at point B, then DB is a radius of the circle.

If line AC is a tangent to circle D at point B, then DB is a radius of the circle.

In a circle, the radius that is perpendicular to a tangent line at the point of contact forms a right angle with the tangent line.

This means that angle CBD is a right angle, measuring 90 degrees.

Hence, if line AC is a tangent to circle D at point B, then DB is a radius of the circle then the measure of CDB is 90 degrees.

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After the translation vertically downward by 7 units, we get the function g(x) is g(x)=x².

The given function is h(x)=x²+7.

The graph of h is translated vertically downward by 7 units, it becomes the graph of a function g.

The new graph of g(x) will have the same shape as the graph of h(x), but it will be shifted down by 7 units. This means that the equation for g(x) can be obtained by subtracting 7 from h(x):

g(x) = x² + 7 -7 = x²

Therefore, after the translation vertically downward by 7 units, we get the function g(x) is g(x)=x².

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Yes, it is possible to find whole Number .In general, if we let n be any whole number from 1 to 14, we will get a corresponding whole number value for m that satisfies the equation.

values of m and n that fit the equation 3m+6n=87. First, we can simplify the equation by factoring out 3 to get 3(m+2n)=87. Then, we can divide both sides by 3 to get m+2n=29.

Since we want whole number values for m and n, we can try different values of n and see if we get a whole number value for m.

For example, if we let n=1, then m+2=29, so m=27. This gives us one possible solution of m=27 and n=1.

We can continue this process by trying different values of n until we find another solution.

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Using equations;

a. The total pages to read is 5

b. Marco has to read 20 pages

a. To find the total number of pages Marco has read, we need to sum up the number of pages he reads each day. Since he reads 4 pages every day, we can find the total number of pages read by multiplying 4 by the number of days he has been reading.

Let's say Marco takes x days to finish reading the book. Then the total number of pages he has read can be calculated as:

Total pages read = 4x

To find the total number of days it will take him to finish reading the book, we need to determine the value of x. In the given information, it is mentioned that the number of pages left to read each day (y) can be modeled by the equation y = 20 - 4x, where x ≥ 0.

Since y represents the number of pages left to read, we can set it equal to zero to determine when Marco will finish reading the book:

20 - 4x = 0

Now, let's solve this equation for x:

20 - 4x = 0

4x = 20

x = 20/4

x = 5

Therefore, it will take Marco 5 days to finish reading the book.

b. To find the total number of pages he has read, we substitute the value of x into the equation for total pages read:

Total pages read = 4 * x

Total pages read = 4 * 5

Total pages read = 20

Therefore, Marco has read a total of 20 pages.

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Option b. 0.48 would be the closest representation for the logarithm value of log10 3 among the given options.

To determine the value of log10 3 among the given options, we need to understand that the logarithm of a number represents the exponent to which the base must be raised to obtain that number. In this case, we are looking for the logarithm of 3 with base 10.

Among the given options (0.30, 0.48, 1.10, 2.10), none of them exactly represents the value of log10 3. However, we can make an estimation based on the given options.

The value of log10 3 is approximately 0.48. This can be inferred from the fact that log10 1 is 0 and log10 10 is 1, so the logarithm of numbers between 1 and 10 should be between 0 and 1. Since 3 is closer to 1 than 10, we can estimate its logarithm to be closer to 0.48 than 1.10 or 2.10.

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Answer:

answer is here!!

Step-by-step explanation:

To find the next digit in the quotient using the standard algorithm, you follow these steps:

First, divide the largest possible multiple of the divisor (13) into the dividend (543) without exceeding it. In this case, 13 goes into 54 four times (4 × 13 = 52).

Subtract the product obtained in step 1 (52) from the dividend (543), resulting in a remainder of 543 - 52 = 491.

Bring down the next digit of the dividend (3) next to the remainder (491), creating the new number 4913.

Repeat step 1 by dividing the largest possible multiple of the divisor (13) into the new number (4913) without exceeding it. The largest multiple of 13 that fits into 491 is 37 (37 × 13 = 481).

Subtract the product obtained in step 4 (481) from the new number (4913), resulting in a remainder of 4913 - 481 = 4432.

At this point, you have obtained the next digit in the quotient. It is the result of dividing the new number (4432) by the divisor (13).

The percentage of the goal that has been sold is 16%

Here we know that a local charity sold 8 tickets with the goal of selling 50 tickets.

To find the percentage of the goal that has been sold, we need ot use the formula:

Percentage = 100%*(number of tickets sold)/(number of the goal)

Replacing these values we will get:

Percentage = 100%*(8/50)

Percentage = 16%

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