A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 15 pounds each. There are 120 boxes in all. If the truck is carrying a total of 4400 pounds in boxes, how many of each type of box is it carrying?

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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The value that can be used to change to z is 65.5.

To use the normal distribution to approximate probability for a binomial distribution, we need to use the continuity correction factor. This involves adjusting the boundaries of the binomial distribution to align with the normal distribution.

To use the normal distribution to approximate the probabilities in a binomial distribution, we need to apply the continuity correction by adding or subtracting 0.5 from the value of x. In this case, to find P(X > 65), we need to calculate P(X > 65.5), since 65.5 is the midpoint between 65 and 66. Then, we can convert this value to a z-score using the standard normal distribution table. Therefore, the value to change to z is 65.5.

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Answer:

6.n/4

7.3/4time G or 0.75G

Step-by-step explanation:

6.3m+n/12-m-n/4=3m-3m+n+3n=4n/12=n/4

7.G=0.9a/1.2b G=3/4*a/b

Answer:

\( {10}^{3} \)

Answer:

2/7

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

1. Liam's initial deposit was $2694.74 and Grace's initial deposit was $1894.74. 2. The system of equations that could be used to find their initial deposits is: I = g + 800, 0.009I = 0.011g

Step-by-step explanation:

Let's first use the formula for simple interest to find the interest earned by Liam and Grace after one year:

Interest earned by Liam = I x 0.009

Interest earned by Grace = g x 0.011

We also know that both Liam and Grace earn the same amount of interest after one year, so:

I x 0.009 = g x 0.011

We also know that Liam's initial deposit was $800 more than Grace's, so:

I = g + 800

Now we can substitute I in the first equation:

(g + 800) x 0.009 = g x 0.011

Simplifying and rearranging:

0.0072g + 7.2 = 0.011g

0.0038g = 7.2

g = 1894.74

Now we can find I:

I = g + 800

I = 1894.74 + 800

I = 2694.74

Therefore, Liam's initial deposit was $2694.74 and Grace's initial deposit was $1894.74.

The system of equations that could be used to find their initial deposits is:

I = g + 800

0.009I = 0.011g

Hope this helps! If you need more help, ask me! :]

Sorry if it's wrong.

The function g( x ) is translated to the left by 9 units and down by 5 units.

Given data ,

Let the first function be represented as f ( x )

where the value of f ( x ) = | x |

Let the translated function be g ( x )

where the value of g ( x ) = | x + 9 | - 5

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

On translating to the left , f ( x + a )

So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |

Now , when the function is translated 5 units down , f ( x ) - 5

So , the translated function is g ( x ) = | x + 9 | - 5

Hence , the function is translated to the left by 9 and up by 5 units.

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Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

4/13

Step-by-step explanation:

There are 4 jacks in the deck and 13 spades. However 1 jack is a spade so we have a total of 16 cards which are either a jack or a spade. Therefore there are (13 + 4 - 1)/52 cards which are not a jack or a spade. Divided 16/52, thus the probability is 4/13.

The probability of drawing a spade or a jack from a standard deck of 52 cards is;

P(drawing either a spade or jack) = 4/13

We are told that the standard deck of cards has 52 cards.

Thus;

N = 52

Now,in a pack of cards there are usually 4 Jacks and 13 spades.

However, among the 4 Jacks, 1 of them is a spade. This means that 1 card will be both a spade and a jack. Thus,

Possible number of Jack's and spades = 13 + 4 - 1 = 16

Thus;

P(drawing either a spade or jack) = 16/52 = 4/13

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Answer:

10/12 is equal to 5/6

Step-by-step explanation:

We know that because 5 is half of 10, and 6 is half of 12

Answer:

Step-by-step explanation: the y would be 50

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Step-by-step explanation:

The last one.

-5 is notht included but 6 is.

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

check the attachment given belοw tο understand.

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We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

Answer:

  3·ln(x) -ln(1+x)

Step-by-step explanation:

You want to "solve" the expression ln(x³/(1+x)).

The relevant rules of logarithms are ...

  ln(a^b) = b·ln(a)

  ln(a/b) = ln(a) -ln(b)

The given log expression can be expanded as ...

  \(\ln{\left(\dfrac{x^3}{1+x}\right)}=\ln(x^3)-\ln(1+x)=\boxed{3\ln(x)-\ln(1+x)}\)

Answer:

I am pretty sure it's 6

Step-by-step explanation:

If am pretty sure it is 6

Answer:

2- 1/10=0.1; closest to zero

3- (25-4)/40= 21/40 (common denominator)

4- 12

5- (20-9)/24= 11/24 (common denominator)

6- (6+3/4) + (2+1/2) = 8+5/4= 9+1/4

7- 21+3/4 - 13+1/8 = (21-13)+(6/8-1/8) = 8+5/8

8- 8+5/12 - 5+3/8 = (8-5) + (10/24-9/24) = 3+1/24

9- 20

Answer:

2.) 5/10 is closest to:  1/5 is equal to 2/10 and 1/2 is equal to 5/10 and that would mean 1/5 would be closer to 0 than 1/2 or 1. So, your right.

3.) 20-21/40 (can't be more than 40 as denomanator)

4.) LCD is 12.

5 and 6 are blurry, you can comment on what they say if you want me to answer. :)

7.) You need to subtract. (c) 8 5/12- 5 3/8 (d)

3 1/24

8.) LCD = 20

I HOPE THIS HELPED.

Answer:

  Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.

Step-by-step explanation:

Logically, it makes no sense for Zoe to say, in effect, ...

  "All E are A, but A are never E."

That is incorrect on its face. At least, it means that "sometimes A are E."

__

The appropriate choice is the first one:

Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.

Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°

Answer:

(x - 3)^2 = 8

x - 3 = + 2√2

x = 3 + 2√2

The values of x when the equation (x-3)² = 8 was solved is 3±2√2.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

solve  the equation means to find the value of x in the equation (x-3)² = 8.

To find the value of x, we following the steps below

Given equation = (x-3)² = 8.

Step 1:

Note: square root and square will cancel out.

Step 2

Hence, the values of x is 3±2√2.

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

Gracias por favor

Step-by-step explanation:

Answer:

for some reason i cant see ur attachment. lo siento

(x + y)³

  use (a + b)³ = a³ + 3a²b + 3ab² + b³

x³ + 3x²y + 3xy² + y³ =

= (x + y)³

Answer:

-2

Step-by-step explanation:

Anything behind the 0 is negative. Anything in front of the 0 is positive.

-2.  Notice 10 spaces with a value of 10.  This means increments of 1.

Count backwards 1 from 0 twice to get to that arrow.

Numbers left of 0 are negative.

-2

Hope this helps,

Jeron

:- )

(p.s., maybe brainliest if I really helped??  :))))    )

Answer:

-8

Step-by-step explanation:

Answer: 212.5 square feet

Step-by-step explanation:

If we were to complete the square, the total area of the square would be \(15^2=225\) square feet.

The area of the triangle added to 'complete the square' is \(\frac{1}{2}(15-10)(15-10)=12.5\) square feet.

So, the area of the floor is \(225-12.5=212.5\) square feet.

Answer:

212.5 ft^2

Step-by-step explanation:

A=s^2

A=15^2=225 ft^2

15-10=5

5*5=25

25/2=12.5

225-12.5=212.5