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A teacher has an annual income of $64,502. The income tax the teacher has to pay is 6%.

What is the amount of income tax in dollars and cents that the teacher has to pay

Answer:

the answer would be 28²

Step-by-step explanation:

I think so 28²

Triangles ΔICR and ΔISU are congruent by SAS rule of congruency, therefore; ∠CIR ≅ ∠SIU by CPCTC

Two triangles, ΔABC and ΔXYZ are said to be congruent by the Side-Angle-Side, SAS congruency rule, if the two sides and an included angle of triangle ΔABC, are congruent to two sides and an included angle of triangle ΔXYZ.

The specified measurements are;

∠1 ≅ ∠4

CU = RS

IC = IS

IC ≅ IS (Definition of congruency)

The congruency of the sides IC and IS indicates that the triangle ΔICS is an isosceles triangle

Therefore, ∠2 ≅ ∠3 by the properties of the base angles of an isosceles triangle

CU - RU = RS - RU (subtraction property)

RU ≅ RU, (reflexive property of congruency)

CU - RU = CR

RS - RU = SU

CR = SU (Substitution property)

CR ≅ SU (Definition of congruency)

ΔICR is congruent to ΔISU by Side-Angle-Side, SAS, rule of congruency.

∠CIR ≅ ∠SIU by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

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The length in feet of the longest part of the garden would be = 6ft

A garden is defined as an area that is prepared and set aside for the purpose of growing various flowers, shrubs and grasses.

The area of the given triangle = 54in²

The perimeter of the given triangle = 36 in.

Using the formula for area of a triangle ;

Area = ½ base(b) ×height(h)

where base = 9 in

54 = 1/2 × 9 × h

Make h the subject of formula;

h = 54×2/9

h = 108/9

h = 12

But the perimeter = sum of the whole sides of the triangle

perimeter = 36

side a = 9

side b = 12

side c = X

that is , 36 = 9+12+X

make X the subject of formula;

X = 36-21

X = 15in

Therefore, 15 in when converted to feet;

2 ft = 5 in

X ft = 15 in

xft = 2 × 15/5

X ft = 30/5

X ft = 6ft

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Answer:

smallest angle = 45°

Step-by-step explanation:

given ratios of angles 8 : 7 : 5 = 8x : 7x : 5x ( x is a multiplier )

the sum of the 3 angles in a triangle is 180° , then

8x + 7x + 5x = 180

20x = 180 ( divide both sides by 20 )

x = 9

smallest angle measure is 5x = 5 × 9 = 45°

Answer:

√ − 6 /√ − 6 √ − 7 = -1 + 0i

Step-by-step explanation:

The linear equation 3 · x + 4 = 7 · x - 8 has solution x = 3. (Correct choice: C)

The linear equation 2 · x = 7 · x - 5 has solution x = 1. (Correct choice: E)

The linear equation 5 · x - 8 = 5 · x + 12 has no solution. (Correct choice: D)

In this question we find three linear equations with one variable, whose corresponding solution must be determined by using algebra properties. The complete procedure is summarized below:

Now we proceed to apply the procedure for each case:

Case 1

3 · x + 4 = 7 · x - 8

7 · x - 3 · x = 8 + 4

4 · x = 12

x = 3

The linear equation has an unique solution (x = 3). (Correct choice: C)

Case 2

2 · x = 7 · x - 5

7 · x - 2 · x = 5

5 · x = 5

x = 1

The linear equation has an unique solution (x = 1). (Correct choice: E)

Case 3

5 · x - 8 = 5 · x + 12

5 · x - 5 · x = 8 + 12

0 = 20 (CRASH!)

The linear equation has no solution. (Correct choice: D)

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The square root of 2500 (√2500) is 50

-√2500 is not a reasonable solution to the problem because the number of ice cream sold by the ice cream shop would not be a negative value

The square root is the inverse of squared hence factoring the numbers to get the numbers whose when squared is 2500 is a way to solve the problem

The factorization is done as follows

factors of 2500: 2 * 2 * 5 * 5 * 5 * 5

= 2² * 5² * 5²

square root of the factors

= √(2² * 5² * 5²)

= 2 * 5 * 5

= 50

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The perimeter of rectangle B is equal to 29 centimeters.

What does a perimeter mean?

The perimeter of a shape is the space surrounding it. Space inside a shape is measured by area. Learn how to compute the area and perimeter of various forms.

Given the area of the rectangle, A is equal to the area of rectangle B.

That is 2.5(4x)=(2x-3)7

10x=14x-21

4x=21

x=5.25

The perimeter of rectangle B is the sum of all sides= 2(2x-3+7)

The perimeter of B = 4x+8=29 cm.

Therefore perimeter of rectangle B is 29 centimeters.

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a. There are 66 ways to divide 12 books between two bags.

b. There are 531,441 ways to divide 12 books between two bookshelves where order on each bookshelf matters.

c. There are 2,077 ways to divide 12 books between three bags.

d. There are 1,9,958,126 ways to divide 12 books between three bookshelves where order on each bookshelf matters.

Probability is the measure of the likelihood that an event will occur in a given set of circumstances. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. In probability theory, events are often represented by sets of outcomes, called sample spaces, and the probability of an event is defined as the ratio of the number of outcomes in the event to the total number of possible outcomes in the sample space.

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Answer:

c = 6p

Step-by-step explanation:

6 times the number of pounds that she buys will be the total cost.

Based on the graph of logarithmic function log6(x – 1) = log2(2x + 2), the statement true about the graph is that the curves do not intersect. (Option A)

In the given case, two logarithmic functions are given: log6(x – 1) and log2(2x + 2). The graph of inverse function of any function is the reflection of the graph of the function about the line y=x . All logarithmic graphs in the form f(x)=logb(x) will have a vertical asymptote on the y-axis and an x-intercept at (1, 0) and will pass through (b , 1). Graphing the given function which is attached, it can be seen that the two curves do not intercept and indicates that the equation has no solution.

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Answer:

Step-by-step explanation:

105 divided by 7 =15 so if 15 times 7=105 then 15 times 5 is 75. so susan has 75 stamps. please mark me brainliest.

The joint density of  the proportion of the capacity of the tank that is stocked & sold during the week is 1/8 and 1/2. ( a and b)

Let y1 be the percentage of the tank's capacity that is stocked at the start of the week.

y2, the percentage of the weekly capacity sold

The formula for the joint probability density function of y1,y2 is

f(y1 , y2)=  { 3y^1  ;0≤ y2≤ y1 ≤1

0, elsewhere.          

a)F(1/2,1/3)=P(Y1<=1/2,Y2<=1/3
=∫^1/2 ∫^y1 3y1 d y2 d y1
=∫^1/2 3Y1 ⎥y^2⎥y^1 dy1
=∫ ^1/2 3y1 y1 dy1
=∫ ⎥y^3/3 ⎥^1/2        
=1/8            
               

b)P(Y2<=Y1/2)=P(0<=Y1<=1,0<=Y2<=Y1/2
=∫^1 ∫^y1/2 3y1 dy1 dy2
=∫^1 3y1 ⎥ y2 ⎥ ^y1/2 dy1
=∫^1 3y1 y1/2 dy1
=∫^1 3/2y^2 dy1

=3/2 ⎥ y^3/3⎥ ^1^ 0
=1/2

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The new price of product can be estimated as $34.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The original price is given as $19.99.

And, the expression for new price is  t + 0.07t.

Where t is the original price.

Plug t = 19.99 to obtain,

⇒ 19.99 + 0.7 × 19.99 = 33.983

Which is approximately $34.

Hence, the new price is obtained as $34.

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The quartic function with only two real zeros of x=0 and x=4 is x² - 4x = 0

A quartic function is a quartic polynomial, that is, a polynomial with integer coefficients whose highest degree is four. The coefficient of the variable to the fourth degree cannot be zero. Examples of quartic functions include

From the roots;

a = 0 ; b = 4

From the polynomial expressions

x² - (a +b)x + ab = 0

x² - (0 +4 )x + 0*4 = 0

x² - 4x = 0

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Answer:

0.071 is your answer.

Step-by-step explanation:

Or you can write 11/1540. First divide 11/44 and divide 35 by your answer. You will get your answer 0.071 and if you want to have this answer in divide form than your answer is 11/1540.

When the short leg of a right triangle is 10 meters long and the sharp angles are present, the right triangle's longer leg has a measurement of 21.45 meters.

Right angles are created when two straight lines cross at a 90° angle or are perpendicular to one another at the intersection. The sign stands for a right angle. Different right angle formations can be seen in the above image. The proper angles can be found in shapes. Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees.

given

x / sin 65° = 10 / sin 25°

x = 10 sin 65°/ sin 25°

x = 21 .45 meters

as law of sine

a / sinA = b / sinB = c / sinC

When the short leg of a right triangle is 10 meters long and the sharp angles are present, the right triangle's longer leg has a measurement of 21.45 meters.

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The required solution of the differential equation is given as; y = x⁴/4 + c₁x²/2 + c₁².

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

We are Given the differential equation,

y' = 2 √y . x

y' = dy/dx so,

Therefore, we have

dy/dx = 2√y.x

dy/√y = 2x dx

y = [1/2(x² + c₁)]²

y = x⁴/4 + c₁x²/2 + c₁²  

Thus, the solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁² .

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The x-intercept of the function is where y=0 and x = -1 or x=5

You should be aware that the x-coordinate of a point where a line, curve, or surface intersects the x-axis. Also, The x-intercept for any curve is the value of x coordinate of the point where the graph cuts x-axis

Considering the table

i                P(i)

-1                0

2               -9

5                0

6                7

7                16

The factored form would be

P(i) = (i+1)(i-5)

The standard form would also be

P(i) = i²-5i+i-5

= i²-7i-5

Therefore the factored and standard forms are  (i+1)(i-5) and  i²-7i-5 respectively

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The sum of all nine integers in the subtraction square is equal to 9 times the number in the top left unit square, which is k.

1.  Fill in the subtraction square with three rows and three columns.

2.  In each row from left to right, and in each column from top to bottom, the first integer minus the second integer equals the third integer.

3.  The sum of all nine integers is equal to the sum of the numbers in each row plus the sum of the numbers in each column.

4.  The sum of the numbers in each row is equal to k + (k - k) + (k - (k - k)) = 3k

5.  The sum of the numbers in each column is equal to k + (k - (k - k)) + (k - (k - (k - k))) = 3k

6.  So the sum of all nine integers is 9k.

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Just plug in numbers.

This grid works

k k 0k k 00 0 0

so the answer is 4k.

The property shown is an example of commutative property of addition.

A binary operation is commutative if changing the order of the operands does not change the result.

Given that, what property is (6+5)+3=3+(6+5)

The given example is of commutative property,

a+b = b+a, here a = (6+5) and b = 3

In commutative property, the commutative property of addition says that changing the order of addends does not change the sum. Here's an example: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+4.

The commutative property of addition states that a change in the order of the numbers being added does not affect the sum.

Hence, the property shown is an example of commutative property of addition.

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Answer:

5/2 liters, which is equal to 2 1/2 liters per 1 bottle

Step-by-step explanation:

I see that this problem works with fractions, so I will assume that the final answer must be as such.

1 1/5 is the same as saying 6/5, so how many bottles would 1 liter fill?

(6/5 bottles)/(3 liters) = 2/5 bottles per liter

So two liters would fill a single bottle only 4/5 of the way. What about the last 1/5?

Keep in mind that 1/5 is half of 2/5, so (1 liter)/2 = 1/2 liter

So therefore, you can either add 1/2 a liter to 2 liters, or subtract a liter from 3 liters to get 2 1/2 liters per bottle.

Another way to do this problem is as follows:

The ratio we’re looking at is 3 liters for every 6/5 of a bottle

(3 liters) / (6/5 bottles)

We can invert 6/5 before multiplying out the fraction making this process easier

3 * 5/6 = (3*5)/6

Remember that 6/3=2

So we get 5/2 liters, which is equal to 2 1/2 liters per 1 bottle

The solution is Option A.

The slope of the equation is given by Slope m = -1/12

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the first point be P = P ( -2 , -7/2 )

Let the second point be Q = Q ( 4 , -4 )

The slope of the line between the points is given by the equation ,

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -4 - ( -7/2 ) ) / 4 - ( -2 )

On simplifying the equation , we get

Slope m = ( -4 + 7/2 ) / 6

Slope m = ( -8 + 7 ) / ( 2 x 6 )

Slope m = -1/12

Therefore , the value of m is -1/12

Hence , the slope of the line is m = -1/12

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The graph of the arithmetic sequence is added as an attachment

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

Sequence: 4, 12, 20, 28....

The above sequence is an arithmetic sequence with the following parameters

First term, a = 4

Common difference, d = 8

So, the x-th term is

f(x) = a + (x - 1) * d

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

f(x) = 4 + (x - 1) * 8

This gives

f(x) = 8x - 4

So, the equation to plot is f(x) = 8x - 4

See attachment for the graph

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The next three numbers of sequence is,

⇒ 2.8, 8.4, 8.2

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The sequence is,

⇒ 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0, .., .., ...,

Now,

Since, The sequence is,

⇒ 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0, .., .., ...,

Clearly, The pattern of the sequence is,

⇒ 0.4 - 0.2 = 0.2

⇒ 0.2 × 3 = 0.6

⇒ 0.6 - 0.2 - 0.4

⇒ 0.4 × 3 = 1.2

⇒ 1.2 - 0.2 = 1.0

⇒ 1.0 × 3 = 3.0

⇒ 3.0 - 0.2 = 2.8

⇒ 2.8 × 3 = 8.4

⇒ 8.4 - 0.2 = 8.2

Thus, Next three terms of the sequence is,

⇒ 2.8, 8.4, 8.2

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Answer:

To find the cut-off lengths for nails to be discarded, you can use the fact that the mean of the nail lengths is 3 inches, and the standard deviation is 0.03 inches.

The bottom 2.87% of the nails are the shortest 2.87% of the nails, and the top 3.59% of the nails are the longest 3.59% of the nails. You can use the normal distribution to find the number of standard deviations from the mean that the cut-off lengths are.

Since the manufacturer intends to discard the bottom 2.87% and the top 3.59% of nails, you can use the standard normal table to find that the cut-off lengths are -1.28 standard deviations from the mean for the bottom 2.87% and 1.28 standard deviations from the mean for the top 3.59%.

To find the cut-off lengths in inches, you can multiply the number of standard deviations by the standard deviation in inches:

Low-end: -1.28 * 0.03 inches/standard deviation = -0.0384 inches

High-end: 1.28 * 0.03 inches/standard deviation = 0.0384 inches

Rounded to two decimal places, the cut-off lengths are:

Low-end: -0.04 inches

High-end: 0.04 inches

So the manufacturer should discard nails that are shorter than

3 inches - 0.04 inches = 2.96