What is the formula for calculating the surface area of a sphere?

Answer:

Step-by-step explanation:

On a given day, a greengrocer sold 81 oranges and 43 melons. Write the ratio of oranges to melons in the form 1: n. Give any decimals in your answer to 2 d.p.

orange = 81

melons = 43

ratio 81 : 43

divide both side by 81

1 : 0.53

Answer: b

Step-by-step explanation:Remember that the Cartesian coordinates are given by the formulas

xy=rcosθ=rsinθ

We are told that r=8 and θ=11π6, so we can plug in to find that

x=rcosθ=(8)(cos11π6)=(8)(3‾√2)=4√3

Similarly, we find that

y=rsinθ=(8)(sin11π6)=(8)(−12)=−4

So the final answer is (4√3,−4).

The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

Total numbers on wheel = total possible outcomes

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Grey colored portion = {3}

White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

X = Event that wheel stops on a white slice

P(X) = number of white slices ÷ total number of slices

P(X) = 9 / 10 = 0.9

P(not X) = 1 - P(X)

P(not X) = 1 - 0.9 = 0.1

Hence the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

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Answer: 6 years

Step-by-step explanation: 32,000 divided by 25% is 24,000. 24,000 divided by 25% is 18,000. 18,000 divided by 25% is 13,500. 13,500 divided by 25% is 10,125. 10,125 divided by 25% is 7,593.75. 7,593.75 divided by 25% is 5,695.3125. so 6

The equation that represents number of hours "h" which Ezekiel spend doing "math-homework" during the next 5 days is (d) h = 5t/4.

If Ezekiel spends 1/4 of his time on math homework, then he spends 3/4 of his time on other subjects. This means that out of every 4 hours he spends on homework, he spends 1 hour on math and 3 hours on other subjects.

So, in "t" hours, he will spend "t/4" hours on math homework.

To find the number of hours he will spend on math homework during the next 5 days, we multiply the time he spends on math homework in one day by the number of days.

⇒ Number of hours spent on math homework in 1 day = t/4,

⇒ Number of hours spent on math homework in 5 days = 5 × (t/4) = 5t/4,

The required equation is h = 5t/4,

Therefore, the correct option is (d).

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The calculatd value of the model width is 11.4 m

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

Scale factor = 1/3

Actual apartment building will be 39 m wide

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

Model width = Scale factor *Actual apartment building

Substitute the known values in the above equation, so, we have the following representation

Model width = 1/3.4 * 39

Evaluate

Model width = 11.4

Hence, the model width is 11.4 m

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The length of the side of his garden can be16.6 ft

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

He has enough compost to cover an area of 276 square feet.

This means that

Area = 276 276 square feet.

The area of a square is calculated as

Area = Length^2

Substitute the known values in the above equation, so, we have the following representation

Length^2 = 276

Take the square root of both sides

Length = 16.6

Hence, the length is 16.6 ft

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Therefore, after 4 weeks, Liz will have $275 in her savings account and Fareed will have $300 in his savings account.

After 1 week

Liz will have saved $75 + $50 = $125, and

Fareed will have saved $100 + $50 = $150.

After 2 weeks,

Liz will have saved a total of $125 + $50 = $175, and

Fareed will have saved a total of $150 + $50 = $200.

After 3 weeks,

Liz will have saved a total of $175 + $50 = $225, and

Fareed will have saved a total of $200 + $50 = $250.

After 4 weeks,

Liz will have saved a total of $225 + $50 = $275, and

Fareed will have saved a total of $250 + $50 = $300.

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Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

The polynomial  (2m + 2n)6 = 12m + 12n.

For the long division, the quotient is x - 2, the remainder is 6, and the dividend can be written as (x - 2)(x² - 4x + 3) + 6.

To expand the expression (2m + 2n)6, using the distributive property of multiplication over addition:

(2m + 2n)6 = 2m(6) + 2n(6)

Simplifying further, evaluate the products:

= 12m + 12n

Therefore, (2m + 2n)6 = 12m + 12n.

Using long division to divide the polynomial x³ - 6x² + 11x - 6 by the polynomial x² - 4x + 3. The steps are as follows:

      x - 2

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

x² - 4x + 3 | x³ - 6x² + 11x - 6

- (x³ - 4x² + 3x)

      - 2x² + 8x

      - 2x² + 8x - 6

                + 6

Therefore, x³ - 6x² + 11x - 6 = (x - 2)(x² - 4x + 3) + 6.

So the quotient is x - 2, the remainder is 6, and the dividend can be written as (x - 2)(x² - 4x + 3) + 6.

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The missing side using the Pythagorean theorem is 10.2.

We have,

We see that,

Hypotenuse = 13

Base = x (say)

Height = 8

Now,

Applying the Pythagorean theorem,

Hypotenuse² = Base² + Height²

Substituting,

13² = x² + 8²

13² = 169

8² = 64

So,

169 = x² + 64

x² = 169 - 64

x² = 105

x = √105

x = 10.24

x = 10.2

Thus,

The missing side is 10.2.

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The value of the integration is -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2

We have,

∫√(2 + cos²x)/(sec x - cosec x)

We can start by simplifying the integrand by using trigonometric identities.

sec x = 1/cos x and cosec x = 1/sin x.

So,

√(2 + cos²x)/(sec x - cosec x)

= √(2 + cos²x) / [(1/cos x) - (1/sin x)]

= √(2 + cos²x) / [(sin x - cos x) / (sin x cos x)]

= √[(2 + cos²x) sin x cos x] / (sin x - cos x)

= √[2 sin x cos x + cos⁴ x] / (sin x - cos x)

= √[sin² x + cos² x + 2 sin x cos x + cos⁴ x] / (sin x - cos x)

= √[(sin x + cos² x)²] / (sin x - cos x)

= (sin x + cos² x) / |sin x - cos x|

The absolute value sign is needed because the denominator, sin x - cos x, can be negative for certain values of x.

Now we can integrate this expression:

∫√(2 + cos²x)/(sec x - cosec x) dx

= ∫(sin x + cos² x) / |sin x - cos x| dx

We can split this integral into two cases: when sin x - cos x > 0, and when sin x - cos x < 0.

Case 1:

sin x - cos x > 0 (when x is between -π/4 and π/4, or between 3π/4 and 5π/4)

In this case, we can drop the absolute value sign:

∫(sin x + cos² x) / (sin x - cos x) dx

= ∫(sin x / (sin x - cos x)) dx + ∫(cos² x / (sin x - cos x)) dx

= -ln|sin x - cos x| - ∫(1 + sin 2x) / (2sin x - 2cos x) dx

To integrate the second term, we can use the substitution u = sin x - cos x, so that du/dx = cos x + sin x and dx = du/(cos x + sin x):

∫(1 + sin 2x) / (2sin x - 2cos x) dx

= ∫(1 + 2u / √2) / (2u / √2) du

= -√2 ln|2sin x - 2cos x| - √2 ln|u| + √2 [tex]tan^{-1}[/tex] (u / √2) + C

= -√2 ln|2(sin x - cos x)| - √2 ln|sin x - cos x| + √2 [tex]tan^{-1}[/tex] [(sin x - cos x) / √2] + C

= -√2 ln|sin x - cos x| - √2 ln 2 + √2 [tex]tan^{-1}[/tex] [(sin x - cos x) / √2] + C

= -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2

Note that we have used the logarithmic identity ln(ab) = ln a + ln b and the substitution u = sin x - cos x.

Thus,

The value of the integration is -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2

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The number of cups of flour required to make 1 recipe is 8/3.

Given that, one quarter of a bread recipe calls for 2/3 cup of bread flour.

Amount of flour required per 1 recipe = Number of quarters × Number of cups of flour

= 4 × 2/3

= 8/3

Therefore, the number of cups of flour required to make 1 recipe is 8/3.

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Answer:

V = π(5^2)(11) = 275π cubic miles

= 863.9 cubic miles

The statement which is true about the end behaviour of the given quadratic function is;

As evident from the task content; the answer choice which correctly describes the end behaviour of the given quadratic function is to be determined.

By observation, the given quadratic graph opens upwards and on this note, its end behaviour is such that; As x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f (x) approaches ∞.

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Answer: 6 feet and 2 yards are the same distance because each yard is 3 feet

Step-by-step explanation:

(-35z⁴x + 32z⁴x⁶) divided by  -4z³x⁵ gives {(35z - 32zx⁵)/ (4x⁴)} by applying simple rule of division of polynomials.

Let the given polynomial be written as,

f(z,x) = -35z⁴x + 32z⁴x⁶

g(z,x) = -4z³x⁵

Here the functions of the given polynomial are composed of two variables, namely x and z, so the functions are denotes likewise.

We can divide the polynomial f(x) by g(x) by the division method as,

[tex]\frac{f(z,x)}{g(z,x)}[/tex] = (-35z⁴x + 32z⁴x⁶) / ( -4z³x⁵)

= { (-35z⁴x)/ ( -4z³x⁵) } + {(32z⁴x⁶)/ ( -4z³x⁵)}

= [tex]\frac{35z}{4x^4}[/tex] + [tex]\frac{-8zx}{1}[/tex]

= [tex]\frac{35z - 32zx^5}{4x^4}[/tex]

or, =  {(35z - 32zx⁵)/ (4x⁴)}

Thus the required value of (-35z⁴x + 32z⁴x⁶) divided by  -4z³x⁵ is {(35z - 32zx⁵)/ (4x⁴)}

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The value of dy/dt is 4/3.

We have,

x² + 3xy - y² = 9

Now differentiating above equation w r t to 't' we get

d/dt x² + d/dt (3xy) - d/dt (-y²) = 0

d/dx (x²) . dx/dt + 3 dx/dt.  dy/dt - 2y dy dt = 0

2x (-1) + 3(-1) dy/dt - 2y dy/dt = 0

dy/dt(-3 -2y)= -4

dy/dt = -4/(-3)

dy/dt = 4/3

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The possible values of a are:

(i) A unique solution: a such that a² ≠ 5

(ii) Infinitely many solutions: a such that a² = 5

(iii) No solution: for all other values of a.

To solve this system of linear equations, use Gaussian elimination to reduce the augmented matrix to row echelon form. Then, examine the resulting matrix to determine the number of solutions.

The augmented matrix for the system is:

[1  2  -3  | 4 ]

[3  -1  5  | 2 ]

[4  1  a²-14 | a+2]

Using row operations, transform the matrix as follows:

[1  2  -3  | 4 ]

[0  -7  14 | -10]

[0  -7  a²-2 | a-6]

The third row is a linear combination of the first two rows, so we can eliminate it. This gives us:

[1  2  -3  | 4 ]

[0  -7  14 | -10]

Further simplify this matrix by dividing the second row by -7:

[1  2  -3  | 4 ]

[0  1  -2  | 10/7]

Use back-substitution to solve for the variables, start with the second row:

y - 2z = 10/7

Rearranging this equation:

y = 2z + 10/7

Substituting this into the first row:

x + 2(2z+10/7) - 3z = 4

Simplifying this equation:

x + (4/7)z = 18/7

So, the solution to the system is:

x = (18/7) - (4/7)z

y = 2z + 10/7

z is free

Now, examine the possible values of a:

(i) A unique solution: If the system has a unique solution, then there can be no free variables. From our solution above, we see that z is a free variable. Therefore, the system can have a unique solution only if a is such that the third row in the original augmented matrix does not reduce to a multiple of the first two rows. This is equivalent to the condition -7 ≠ a² - 2, or a² ≠ 5.

(ii) Infinitely many solutions: If the system has infinitely many solutions, then there must be at least one free variable. From our solution above, we see that z is a free variable. Therefore, the system can have infinitely many solutions for all values of a such that a² = 5.

(iii) No solution: If the system has no solution, then there must be a row in the reduced row echelon form that has all zeros except in the last column. However, our reduced matrix does not have this form. Therefore, the system has no solution for any value of a.

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The value of expression √6 would be,

⇒ √6 = 2.4

We have to given that;

To find the value of number √6.

Now, We get;

⇒ √6 = 2.44

⇒ √6 = 2.4

Thus, The value of expression √6 would be,

⇒ √6 = 2.4

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The price that maximizes revenue from ticket sales is  $ 11, 445.

We have,

Ticket price = $47

Let x the decreasing number of the ticket price.

So, The revenue is

R =  ticket price x numbers of spectator

R(x) =  ( 47 - x )  ( 640 + 20x)

= 30,800 + 940x - 640x -20x²

= -20x² + 300x + 30,800

Now, Taking derivatives on both sides

R'(x) = -40x + 300

and, R'(x) = 0

-40x = -300

x = 7.5

So, the price per ticket is

= 47- 7.5

= $ 39.5

and, R(max) = -20(39.5)² + 300(39.5) + 30,800

R(max) = -31205 + 42650

R(max) = $ 11, 445

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Answer:

$39.50

Step-by-step explanation:

The account will have $7240 after the last deposit.

Given that, $2960 is being deposited at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually,

So,

When the amount is compounded biannually,

[tex]A = P(1+r/2)^{2t[/tex]

A = final amount, P = initial amount, r = rate and t = time,

[tex]A = 2960(1+0.07/2)^{2(13)[/tex]

[tex]A = 2960(1.035)^{26[/tex]

[tex]A = 7240[/tex]

Hence, the account will have $7240 after the last deposit.

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Answer:

all triangle angle measures should add up to 180.  So given that,

40+60+80=180

Therefore it can be done

Answer:

We know that point A(5, 1) maps to A'(6, -2) in the translation. To find the translation vector, we can subtract the coordinates of A from the coordinates of A':

Translation vector = A' - A = (6, -2) - (5, 1) = (1, -3)

This means that every point in the preimage moves 1 unit to the right and 3 units down to reach its corresponding point in the image.

We also know that point B'(−1, 0) is the image of a point B in the preimage. To find the coordinates of point B, we can apply the translation vector to B':

B = B' - Translation vector = (-1, 0) - (1, -3) = (-2, 3)

Therefore, the coordinates of point B in the preimage are (-2, 3).

The hypothesis test is left-tailed, and we are testing the population standard deviation.

If a hypothesis test has an equal hypothesis versus a not equal hypothesis, then it is a two-tailed test.

If it has an equal hypothesis versus a less than hypothesis, then it is a left-tailed test.

Finally, if it has an equal hypothesis versus a greater than hypothesis, then it is a right-tailed test.

This is an equal hypothesis versus a 'less than', so this is left-tailed.

Recall that is the population mean, a is the population standard deviation, and p is a population proportion.

Since the hypotheses refer to σ we are testing the population standard deviation.

Hence, the hypothesis test is left-tailed, and we are testing the population standard deviation.

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The shape generated by the cross-section is a rectangle. So the correct option is D.

Notice that the cross-section goes through two opposite sides of the cube.

Then the shape that we will get will also be a quadrilateral of parallel sides. Notice that if the plane was parallel to the square, the cross-section would be also a cube, but because it is slanted, one of the sides will be larger, then we will get a rectangle, thus, the correct option is the last one.

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The expression What is 2.00x + 1.50y = cannot be added/evaluated because 2.00x and 1.50y are not like terms

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

What is 2.00x + 1.50y =

The above statement is an addition expression that adds the values of 2.00x and 1.50y

However, the terms of the expression are not like terms

i.e. 2.00x and 1.50y are not like terms

This means that the expression cannot be added/evaluated

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Answer:

When rolling two number cubes, the possible outcomes of the sum of the numbers on the top faces are from 2 (1+1) to 12 (6+6). Since we want to know how many times we can expect the sum to be 7, we need to count the number of ways to get a sum of 7.

The pairs of numbers that add up to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, there are 6 ways to get a sum of 7.

Each time we roll the two number cubes, the probability of getting a sum of 7 is 6/36 or 1/6, since there are 6 possible outcomes that result in a sum of 7 out of a total of 36 possible outcomes.

Therefore, if we repeat this process 300 times, we can expect to get a sum of 7 approximately (1/6) x 300 = 50 times.

So we can expect the two cubes to add to exactly 7 about 50 times when rolled 300 times.

Step-by-step explanation: