Work out (3.42 x 10^-7) divided by (7.5 x 10^-6)
Give your answer in standard form.

Answer:

\(AB= \frac{97}{3}\)

Step-by-step explanation:

Properties of Rhombus

We are given two sides of the rhombus BC and CD. According to the first property:

4x + 15 = 7x + 2

Subtracting 4x:

15 = 3x + 2

Subtracting 2:

13 = 3x

Dividing by 3:

\(x=\frac{13}{3}\)

It's required to find the side AB. Applying the first property again:

AB= BC = CD = 4x + 15

\(AB =4*\frac{13}{3}+15\)

\(AB= \frac{52}{3}+15\)

\(AB= \frac{97}{3}\)

The value of cement mixer after t year is \(f(t) = 54,205(0. 87)^{t}\)

Given to us

The value of cement mixer when bought, \(P\)= $ 54,205

the value of cement mixer after 1 year, \(P_1\)=   $ 47,158. 35

the value of cement mixer after 2 year,\(P_2\)=  $ 41,027. 76

To find out depreciation we can use the formula for depreciation,

\(P_n= P(1-r)^n\\where,\\P_n= Value\ of\ asset\ after\ n\ year\\P= Value\ of\ asset\ when\ bought\\r= rate\ of\ depreciation\\n= number\ of\ years\)

By putting the value, in the formula we get,

\(P_1= P(1-r)^n\\\\47,158.35= 54,205\times (1-r)^1\\\\\dfrac{47,158.35}{54,205} = (1-r)\\\\0.87=1-r\\\\r=0.13\)

Therefore, putting the value of \(r\) and \(P\) in depreciation formula for \(t\) years we get,

\(P_n= P(1-r)^n\)

\(f(t) = 54,205(0. 87)^{t}\)

Hence, the value of cement mixer after t year is \(f(t) = 54,205(0. 87)^{t}\).

To know more visit:

https://brainly.com/question/3023490

Answer:

let x represent the number =x

then 3/4 of x =3x/4

so 3x/4 < 3/4

3x<3/ 4=1

4=3x<3

x=1/3

Answer:

Step-by-step explanation:

Let me show you how to answer this question correctly.

A variable is P. Letters are represented as numbers by variables.

If you have fewer than that, you must subtract.

I hope this helps! Let me know if you have any questions.

Answer:

\(p - 3\)

Step-by-step explanation:

Step 1:  Convert to an expression

3 fewer than p

This means that given a variable named p, we have 3 less than that so it can be simply displayed by p - 3.

Answer:  \(p - 3\)

Answer:

x =0    x=2

Step-by-step explanation:

3x^2 -6x = 0

Factor out a 3x

3x(x -2)=0

Using the zero product property

3x = 0  x-2 =0

x =0    x=2

Answer:

2.  Alternate Interior Angles

3.  ∠L ≅ ∠P

4.  Definition of similar triangles (2 sets of corresponding angles are equal)

Answer:

2/935

Step-by-step explanation:

I have attached an image of the equation to use. Assuming that this is without replacement, we'll be taking out one piece out of the bag every time that one is chosen.

Therefore, for probability, the fraction is part/whole. We first have 9 red to 36 pieces in total, but if we take one out, we'll get 8 red left in the bag, and 35 pieces in total. This continues until we fulfill the prophecy (I don't know. qualifications?) that 4 of the pieces are red.

You can try this for yourself, but once simplified, it should be 3024/1413720, which simplifies to 2/935.

Please let me know if you need more clarification or have issues! probability can be confusing :)

Answer:

2/935

Step-by-step explanation:

dito^

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Answer:

The associative property of multiplication

 8 . ( 5. b ) = ( 8. 5) . b

Step-by-step explanation:

Explanation

The associative property of multiplication

 a . ( b. c ) = ( a. b) . c

Given numbers are  8, 5 and b

The associative property of multiplication

 8 . ( 5. b ) = ( 8. 5) . b

 8 . ( 5. b ) = ( 8. 5) . b = 40 b

Answer:

75 miles

Step-by-step explanation:

If the bird flies for 90 minutes at 50 mph (miles per hour), we need to calculate how many hours 90 minutes is.

One hour is 60 minutes. Our equation will be: 90/60 = 1.5

This mean the bird flies 1.5 hours at 50 mph. To find the distance, we multiply 1.5 by 50.

1.5 × 50 = 75

The bird has flown 75 miles.

Given : Professor randomly selects two people to go to board to work on problems.

To find: Probability of chosen first or second person to go to the board.

Let \(x\) be the total no. of students.

After the first student is chosen, no of students left = \(x\) - 1

Therefore,

the required probability = 1 / total no. of students x no. of students left

⇒ 1 / \(x\) (\(x\)- 1 )

= 1 / (\(x^{2} - x\))

Know more about Probability here, https://brainly.com/question/11234923

#SPJ4

The labor cost for concessions and parking lot operations is 35.57% of the total labor costs.

Percentage is a term used to describe a portion of a whole expressed as a fraction of 100.

Let's call the total labor costs "L". The labor cost for concession staff is 55,000, the labor cost for security is 82,500, the labor cost for parking lot operations is 45,000 and the labor cost for ticket/usher operations is 49,000.

L = 55,000 + 82,500 + 45,000 + 49,000

L = 281,500

The labor cost for concessions and parking lot operations is 55,000 + 45,000 = 100,000.

To find the percentage of L that is represented by the labor cost for concessions and parking lot operations, we divide 100,000 by 281,500 and multiply by 100:

100,000 / 281,500 * 100 = 35.57%

To know more about percentage here.

https://brainly.com/question/13729841

#SPJ4

To write Euler's number in Symbolab, you can simply use the notation "e". For example, if you want to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.

Euler's number, denoted as "e", is a mathematical constant that is approximately equal to 2.71828. To write Euler's number in Symbolab, you can simply use the letter "e" in lowercase. For example, to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.

Alternatively, if you want to use the built-in function for Euler's number in Symbolab, you can use the "exp(x)" notation, where x is the exponent. For example, to evaluate e raised to the power of 2, you can enter "exp(2)" in Symbolab. Symbolab supports various mathematical functions and constants, including trigonometric functions, logarithmic functions, and mathematical constants, which can be used to solve various mathematical problems.

To learn more about Euler's number Click here:

brainly.com/question/6459192

#SPJ4

The mean of the numbers means that it is average of the given numbers.

According to the question,

We have the following information:

Mean of the numbers

We know that the mean of a given data set means that we add all the numbers in data set and divide the obtained result by the total numbers.

For example, we have a following data set:

2,5 and 8

Total numbers in the set = 3

Now, the mean of these numbers will be:

Mean = (2+5+8)/3

Mean = 15/3

Mean of the numbers = 5

So, in other words, it can be expressed as the average of the numbers.

Hence, the mean of the numbers means that it is average of the given numbers.

To know more about mean here

https://brainly.com/question/21800892

#SPJ4

Answer:

Your answer is 27

I hope I helped, would appreciate brainliest! ;)

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

27% = 27 'out of one hundred',

p% is read p 'percent',

27% = 27/100 = 27 ÷ 100

Calculate percentage:

'Percentage' is obtained by multiplying 100 by 27%

27% of 100 is equivalent to multiplying them:

27% × 100 = ?

27% × 100 =

(27 ÷ 100) × 100 =

(27 × 100) ÷ 100 =

2,700 ÷ 100 =

27

Proof.

How do we check the result?

If 27% × 100 = 27 =>

Divide 27 by 100...

... And see if we get as a result: 27%

Note:

100/100 = 100 ÷ 100 = 100% = 1

Multiply a number by the fraction 100/100,

... and its value doesn't change.

n/100 = n%, any number.

Calculate the percent value:

27 ÷ 100 =

0.27 =

0.27 × 100/100 =

(0.27 × 100)/100 =

27/100 =

27%

So we have proved that the calculations are correct.

Answer:

Percentage of

27% of 100 = 27

Answer:

27%

Convert fraction (ratio) 27 / 100 Answer: 27%

Answer:

The complement of 63° is the angle that when added to 63° forms a right angle (90° ).

Step-by-step explanation:

I assume this is the answer u want, if not I apologize.

Answer: 18 sqrt= i

Hope this helps :)

Step-by-step explanation:

Answer:

3times

Step-by-step explanation:

Baking Process: repeatedly rolling out and folding the dough to make layers

Soon Yi starts with a layer of dough = 2millimeters

Each time Soon Yi rolls and folds the dough, the thickness increases by 8 % = 1 + 8 %

When time = 1

Thickness = 2(1 + 8 %) = 2(1+0.08)

= 2(1.08) = 2.16

For time = n

Thickness = 2(1 + 8 %)^n = 2(1.08)^n

When thickness ≥ 2.5mm, n= ?

2.5 = 2(1.08)^n

2.5/2 = (1.08)^n

1.25 = (1.08)^n

Since the numbers are close (1.25 and 1.08), we can compute by multiplying 1.08 by itself till we get 2.5.

1.08 ×1.08× 1.08 = 1.259712

(1.08)³ is a bit above 1.25

2(1.08)³ satisfies the thickness of at least 2.5mm

Let's check our answer using the formula:

When n = 3

2(1.08)³ = 2 × 1.259712 = 2.519424

This satisfies the thickness of at least 2.5mm

Therefore, the smallest number of times Soon Yi will have to roll and fold the dough so that the resulting dough is at least 2.5 mm = 3

The given statement after evaluating and considering the other options is false. Due to the criteria it falls under elaborates the  case of statistically significant change is to be present while comparing the math scores  between the two groups, In short there will always be difference between two group s while we compare them on a particular topic .

From here on we can come to the conclusion that the difference was not due to chance occurrence.

A statistically significant change  refers to process which is  unlikely to be elaborated solely by chance and random factors.

In short, a statistically significant  has a very less chances  of taking place if there is no true effect in a research study.

The famous examples of statistical significance of finding are

To learn more about statistical significance,

brainly.com/question/15848236

#SPJ4

Answer:

See below

Step-by-step explanation:

y  =  -(x-1)^2 +4       Expand  R side

y = - ( x^2 -2x+1) + 4

y = -x^2 +2x -1  + 4

y = -x^2 + 2x + 3          a = -1     b = 2    c   = 3  

The length x of a side of the small inner square can be determined using the properties of similar triangles.

To find the length x, we can set up a proportion between the small inner square and the larger outer square.

Let's denote the side length of the small inner square as s and the side length of the larger outer square as S.

Since the small inner square is completely contained within the larger outer square, the ratio of their side lengths will be the same as the ratio of their corresponding sides.

Therefore, we can set up the following proportion:

s / S = x / (x + 10)

Here, the x + 10 represents the side length of the larger outer square, as it is 10 units longer than the side length of the small inner square.

To solve for x, we can cross-multiply the proportion:

s * (x + 10) = x * S

Expanding the equation:

sx + 10s = xS

Rearranging the equation to isolate x:

sx - xS = -10s

Factoring out the common term x:

x(s - S) = -10s

Dividing both sides by (s - S):

x = -10s / (s - S)

Now, we have an expression for x in terms of s and S.

It's important to note that the given information is insufficient to find the exact value of x without additional measurements or equations. The value of x will depend on the specific dimensions of the small inner square and the larger outer square.

to know more about small inner square here:

brainly.com/question/30517179

#SPJ11

The transformation of a graph is described clearly in the answer.

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as g(x - a).

For left shifting it is g(x + a).

Suppose the function be g(x).

The transformation of g(x) implies change of its position on the coordinate axis as well as its size keeping the shape as the same.

If it is shifted by h units rightwards.

Then, it can be written as g(x - h)

For left shift of h units it is given as g(x + h).

Both the above transformation implies that the function f(x) will have same value at x = 0 and x = h or x = -h.

Similarly, its dilation can be represented as ag(x).

Which signifies the value of g(x) at any value of x is increased by a factor of a.

Hence, the transformation of a graph can be done by using the rules described above.

To know more about transformation of graph click on,

brainly.com/question/10059147

#SPJ4

Answer:

The solution to both lines would be (0,4)

The absolute maximum value of f(x,y) = x² - 2y + 1 on the set R={(x,y): x² + y²≤9} is (25/2). So, the correct option is OA.

We have the function,f(x,y) = x² - 2y + 1 and set R= {(x,y): x² + y²≤9}

Let's find the absolute maximum value of f(x,y) in R. Therefore, we have to check the values of f(x,y) on the boundary of R which is x² + y² = 9f(x,y) = x² - 2y + 1

Now, we need to convert the above function into a single variable function.f(x,y) = x² - 2y + 1 = x² - 2y + 9 - 8

Now, replace x² + y² = 9 in the above function to get a single variable function.

f(x) = x² - 8y + 9

Now, differentiate the above function to find the critical points. f'(x) = 2x = 0 => x = 0

Putting this value of x in x² + y² = 9 to get the value of y.y² = 9 => y = ±3

Hence, the critical points are (0,3) and (0,-3). Now, let's find the value of f(x,y) at the critical points and the boundary of R to find the absolute maximum and minimum values of f(x,y).f(0,3) = 10f(0,-3) = 10

Now, let's find the value of f(x,y) on the boundary of R. f(x,y) = x² - 2y + 1At (x,y) = (±3,0)f(±3,0) = 10 f(x,y) has a critical point (0,3), which is the absolute maximum value in the set R={(x,y): x² + y²≤9}.

The absolute maximum value is (25/2). Therefore, the correct option is OA.

You can learn more about critical points at: brainly.com/question/29144288

#SPJ11

Answer:

50-50 chance I suppose (1/2 or 5/10) or 40% to 60% percent chance

Step-by-step explanation:

He can guess all of the questions and get all of them right, and it is a possibility that he can also get all of them wrong. So I say, 50-50. I can't lie, I'm having trouble with probability as we speak.

The amount spent is $1,800.00 less than the amount budgeted. The correct answer would be an option (B).

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Given data as follows

Budgeted: $11,600.00

Spent: $9,800.00

To determine the difference between the amount budgeted and the amount spent, we can subtract the amount spent from the amount budgeted:

$11,600.00 - $9,800.00 = $1,800.00

So, the amount spent is $1,800.00 less than the amount budgeted.

Hence, the correct answer would be option (B).

Learn more about Subtraction operations here:

brainly.com/question/25834626

#SPJ1

Area of rectangle is 96/13 sq. units

Given the rectangular area bounded by the x-axis and semicircle y = √36 – x²,

To find the dimensions of the rectangle and the area of the rectangle.

We can use calculus to solve the problem.

Let the length and width of the rectangle be L and W respectively.

As the rectangle is bounded by the x-axis and the semicircle y = √36 – x², we get: L = 2xW = 2yAlso, y² + x² = 36, which is the equation of the given semicircle.

We need to maximize the area of the rectangle.

We know that the area of the rectangle is A = LW = 4xy.

Substituting L and W in terms of x and y, we get: A = 8xy = 8x(√36 – x²)

We differentiate A w.r.t. x to find the critical point.

dA/dx = 8(√36 – x²) – 16x²/√36 – x²³ = 8(36 – x²) – 16x²/6√36 – x² = 8(36 – 2x²)/6√36 – x²

At critical points dA/dx = 0:8(36 – 2x²)/6√36 – x² = 0√36 – x² = 3x/2

Therefore, y = 3x/2.

Substituting this value of y in y² + x² = 36, we get:

(3x/2)² + x² = 36

⇒ 9x²/4 + x² = 36

⇒ 13x²/4 = 36

⇒ x² = 144/13√36 – x²

= √(1296/13)A

= 8x(√36 – x²)

= 8(144/13)^(1/2) (36/13)^(1/2)

= 96/13 sq. units

Therefore, the area of the rectangle bounded by the x-axis and semicircle y = √36 – x² is 96/13 sq. units.

To learn more about rectangle

https://brainly.com/question/16996682

#SPJ11

Answer:

x-6=5x+10

x-6-5x=10

-4x-6=10

-4x=10+6

-4x=16

-4x÷-4=16÷-4

x=-4

Calculating this expression, we find that the length of the image of the rectangle is 36 in.

To find the length of the image of the rectangle after dilation, we can use the property of similar triangles. Since the width of the image is known to be 21 in., we can set up a proportion:

(image width) / (original width) = (image length) / (original length)

Substituting the known values, we have:

21 in. / 14 in. = (image length) / 24 in.

Solving for the image length, we get:

(image length) = (21 in. / 14 in.) * 24 in.

To know more about expression,

https://brainly.com/question/14474057

#SPJ11

Answer:

C. Scalene triangle

Step-by-step explanation:

Wich Type of triangle has not equal side lengths A. Isosceles B. Equilateral C. Scalene D. None of the above

scalene triangle can be regarded as triangle whereby all three sides of the triangle have different lengths. the angles in scalene triangle is also

different if measured. Some right triangles can as well be regarded as scalene triangle if other two angles( the legs) are not congruent. It should be noted that Type of triangle which has not equal side lengths is Scalene