c) Work out the value of 8² + √100

The value of A is 3 square unit

A square number is a number multiplied by itself. This can also be called 'a number squared'. The symbol for squared is ².

Formula: s²= s x s

given that, the question is testing the concept of substitution.

A=12s^2

If s=1/2,

Substituting s with 1/2 we get;

A=12(1/2)^2

=12×1/4

=3

The answer is 3 unit squared. There is no fraction in the answer.  

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Answer:

A has a value of 3 square units.

Step-by-step explanation:

Any number multiplied by itself is a square number. This is also referred to as "a number squared." 2 represents the squared sign.

Equation: s2=s x s

As a result, the question is putting the idea of substitution to the test.

A=12s^2

If s=1/2,

Substituting s with 1/2 we get;

A=12(1/2)^2

=12×1/4

=3

The answer is 3 unit squared. There is no fraction in the answer.  

Answer:

[tex]{ \rm{rate \: of \: change = \frac{R _{2}(t) - R _{1}(t) }{t _{2} - t _{1}} }} \\ [/tex]

For 0 < t < 10; 226.6 < R(t) < 205.6

[tex]{ \rm{ = \frac{205.6 - 226.6}{10 - 0} }} \\ \\ { \rm{ = - \frac{21}{10} }} \\ \\ = { \rm{ - 2.1}} \\ \\ = 2.1[/tex]

Negative indicates an inverse proportionality, or decrease in temperature

For 30 < t < 50; 157.6 < R(t) < 119.6

[tex] = { \rm{ \frac{119.6 - 157.6}{50 - 30} }} \\ \\ = { \rm{ - \frac{38}{20} }} \\ \\ = { \rm{1.9}}[/tex]

Answer:

x = 12

Equation: 6x + 8 = 80

Step-by-step explanation:

A triangle's angles add up to 180 degrees.  Knowing this, the angle represented by the "6x + 8" must equal 80 degrees since the other two angles add to 100 degrees.

The probability that Alice, David, and Carlene are selected is 1/120.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

3 people can be chosen from 10 people in 10C3 ways and Alice, David, and Carlene can be chosen in only one way.

10C3 = 10! / (10 - 3)! 3!

= (10 [tex]*[/tex] 9 [tex]*[/tex] 8 [tex]*[/tex] 7!) / (7! [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1)

= 120

So, the number of possible outcomes is 120 and the number of favorable outcomes is 1. Therefore, the probability is 1/120.

The probability that Alice, David, and Carlene are selected is 1/120.

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Answer:

1. you can think that 289000= 17×17(=289)x100x100, so the result is √289x√100x√100=17 x 10x10=1700

2. 0.000004= 4x10^-6, so the Square root Is √4 x√10^-6= 2x 10^-3

The series that is related to a triangle with 10 cans in the bottom row can be expressed in summation notation as  [tex]\sum\limits^{10}_{n=1} {n}[/tex]

Let us consider the simpler triangle formed by stacking cans as in the attached picture.

As we can see in the picture, if the bottom row contains 3 cans, then the triangle will have 3 rows. The number of cans in each row decreases by 1. We can expand this idea for a triangle with 10 cans in the bottom row.

In this case, there will be 10 rows and the number of cans in each row  decreases by 1.

10th row : 10 cans

9th row : 9 cans

and so on.

We can express the number of all cans in this triangle as a series, starting from the top row (the first row):

1 + 2  + 3 + ... + 10

The explicit formula of the nth term is: a(n) = n.

Hence, in the summation notation, it can be written as:

[tex]\sum\limits^{10}_{n=1} {a(n)} = \sum\limits^{10}_{n=1} {n}[/tex]

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Answer:

Need to know the shape of object (cylinder, cone, etc)

We're given:

We can start by isolating one of the variables, like y:

[tex]3x-y=-6\\-y=-3x-6\\y=3x+6[/tex]

Now we can find four solutions by plugging in any number for x:

[tex]y=3x+6\\y=3(1)+6\\y=3+6\\y=9[/tex]

First solution: (1,9)

[tex]y=3x+6\\y=3(2)+6\\y=6+6\\y=12[/tex]

Second solution: (2,12)

[tex]y=3x+6\\y=3(3)+6\\y=9+6\\y=15[/tex]

Third solution: (3,15)

[tex]y=3x+6\\y=3(4)+6\\y=12+6\\y=18[/tex]

Fourth solution: (4,18)

First solution: (1,9)

Second solution: (2,12)

Third solution: (3,15)

Fourth solution: (4,18)

Answer:

D

Step-by-step explanation:

If the light build can be 50 and less, the sign needs to be ≤ because it means less than or equal to.

Answer:

1 15 degrees

Step-by-step explanation:

Exterior angle is equal to sum of opposite interior angles

Answer:

d=10

d=2r=2·5=10

Answer:

Step-by-step explanation:

38 + (-17) =  21

Answer:

The answer would be 55

Step-by-step explanation:

38-(-17)

38+ +17

55

Combinations exist ways to select elements from a collection in mathematics where the order of the selection exists irrelevant. He can choose the question in 28 ways.

Combinations exist mathematical operations that count the number of potential configurations for a set of elements when the order of the selection exists is irrelevant. You can select the components of combos in any order.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Given: Number of questions in part A = 10

Number of questions in part B = 10

A student chooses 7 from part A and 4 from part B

Required number of ways = ( 10C7 × 10C4) × ( 10C3 × 10C6)

= 5040 × 24/ 6 × 720

= 28

He can choose the question in 28 ways.

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If two angles are supplementary, then one of the angles is obtuse: Never TRUE

Therefore, the statement "if two angles are supplementary, then one of the angles is obtuse" is never TRUE.

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The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004

The formula of the nth term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).

In the given problem,  a₁ =4, r=0.1, therefore:

a(n) = a₁ . r^(n-1)

a(n) = 4 . 0.1ⁿ⁻¹

To find the first five terms, replace n with 1, 2, 3, 4, and 5.

a₁ = 4

a(2) = 4 . 0.1²⁻¹

       = 4 . 0.1¹ = 0.4

a(3) = 4 . 0.1³⁻¹

       = 4 . 0.1² = 0.04

a(4) = 4 . 0.1⁴⁻¹

       = 4 . 0.1³ = 0.004

a(5) = 4 . 0.1⁵⁻¹

       = 4 . 0.1⁴ = 0.0004

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There is need of total of 9 levels to stack 285 boxes.

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

[tex]a_1,a_2,a_3,----,a_n[/tex]

where , [tex]a_n[/tex] = last term in sequence.

According to question,

Also, number of boxes at level recursively n =[tex]a_{n-1} + n^2[/tex]

The formula to find number of level for 285 boxes is :

[tex]a_n > =285[/tex]

now, find each level

[tex]a_1 = 1 , a_2 = 1 + 2^2 = 5 , a_3 = 5+3^2 = 14,\\a_4 = 14 + 4^2 = 30\\a_5 = 30 + 5^2 = 55\\a_6 = 55 + 6^2 = 91\\a_7 = 91 + 7^2 = 140\\a_8 = 140 + 8^2 = 204\\a_9 = 204 +9^2 = 285[/tex]

thus, to stack 285 boxes total numbers of level are 9.

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The complete question is :

Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.

a. How many boxes of same size would need for next lower level?

b. How many boxes of same size would need to add the 3 levels?

c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?

The correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.

Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair are always supplementary.

Now, looking at the given image, we can see a total of 8 angles formed from the transverse lines.

Angles 1 and 4 can be classified as Linear Pairs because Linear pair of angles are formed when two lines intersect each other at a single point.

Similarly, angle 4 and angle 8 are classified as corresponding angles because Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal

Thus, the correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.

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A recursive definition of the given Geometric progression is: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Now,

Given: 2, -4, 8, -16, ...

Here, [tex]r = \frac{-4}{2} = -2[/tex] and a₁ = 2.

Thus, a recursive formula for this geometric progression can be: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.

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The standard equation for the given slope is x + y = 0.

These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b using the m given in the problem and the b you just solved. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.

y = 3 and x = -3 and m = - 1

To find b, we will plug in the known parameters listed above.

3 = −1(-3) +b

To solve for b, move 3 to the other side of the equation.

3=3+b

b=0

Standard form equation:

y = -x + 0

x + y = 0

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By using angle sum property, The value of ∠ A = 40° and ∠ C = 90°

A triangle's total angle is 180°.

Using angle sum property,

∠A+∠B+∠C = 180°

assuming B = 50°

replacing in the formula

∠A+50+∠C = 180°

Due to the triangle's right angle, A+90=180-50

∠A = 130° - 90

∠ A = 40°

The angles A and C must be more than 90 degrees since the ABC is a right triangle.

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In triangle ABC, the measure of angle B is 50 degrees. Select all possible values for the measures of A and C if ABC is an right triangle. m\angle∠A= 58 degrees; m\angle∠C= 72 degrees m\angle∠A= 100 degrees; m\angle∠C= 30 degrees m\angle∠A= 80 degrees; m\angle∠C= 50 degrees m\angle∠A= 60 degrees; m\angle∠C= 70 degrees m\angle∠A= 90 degrees; m\angle∠C= 40 degrees m\angle∠A= 105 degrees; m\angle∠C= 25 degrees

Answer:

m∠A = 40°, m∠B = 75°, m∠C = 65° (A)

m∠A = 136°, m∠B = 28°, m∠C = 16° (B)

m∠A = 60°, m∠B = 60°, m∠C = 60° (E)

Step-by-step explanation:

i did the assignment and got it wrong at first then it showed me the right answers

Answer:

1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.

Therefore, they are all equal.

Step-by-step explanation:

1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.

Therefore, they are all equal.

The approximate number of fleas she should expect to remove from the cats on Day 14 is 1

The given parameters are

Function type: exponential function

Day 0 = 87

Day 6 = 14

An exponential function is represented as

y = ab^x

Where

y = a, when x = 0

This means that a = 87

So, we have

y = 87b^x

Day 6 = 14 means that

When x = 6, y = 14

So, we have

87b^6 = 14

This gives

b^6 = 0.161

Take the 6th roots of both sides

So, we have

b = 0.74

Subsitute b = 0.74 in y = 87b^x

y = 87(0.74)^x

On day 14, we have

y = 87(0.74)^14

Evaluate

y = 1.28

Approximate

y = 1

Hence, the approximate number of fleas she should expect to remove from the cats on Day 14 is 1

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The systems of equations which Tamara can use to find the dimensions of a rectangle that uses all the ribbons is;

If follows from the task content that the systems of equations which best models the situation and can be used to find the dimensions is required.

Hence, since the perimeter of a rectangle is; P = 2l +2w.

Also, the length of the rectangle is 3 inches greater than its width, we have;

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The squared root of 56 minus the squared root of 189 is -6.26 .

We have given an statement that squared root of 56 minus the squared root of 189  which can be represented in expression as

        [tex]\sqrt{56} -\sqrt{189}[/tex]                    ..(1)

Prime factorization 56 is given by

    [tex]\sqrt{56} =\sqrt{2\times2\times2\times7} \\\sqrt{56} =2\sqrt{14} \\\sqrt{56} =2\times3.74\\\sqrt{56} =7.48[/tex]

Prime factorization 189 is given by

    [tex]\sqrt{189} =\sqrt{3\times3\times3\times7} \\\sqrt{189} =3\sqrt{21} \\\sqrt{189} =3\times4.58\\\sqrt{189} =13.74[/tex]

Putting above values in equation (1) , we get

   [tex]\sqrt{56} -\sqrt{189}=7.48-13.74\\\sqrt{56} -\sqrt{189}=-6.26[/tex]

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Answer:

it will cost $32.9 for a 47 mile taxi ride

Step-by-step explanation:

Since 36 miles takes 42 minutes and Costa $25.20 then 47 miles taxi rides will take

42/36 = per minute = 1.17

1.17 × 47 = 54.83

In order to find cost per minute = $25.2/42 = 0.6

then 54.83 × 0.6 = $32.898

∴it will cost $32.9 for a 47 mile taxi ride

The recursive formula is a(n) = a(n-1) + 3 while the explicit formula is a(n) =  3n - 6.

In an arithmetic sequence, the following applies:

a(n) = a(n-1) + d  (This is the recursive formula)

a(n) = a(1) + (n-1) . d  ( This is the explicit formula)

Where:

a(n) = nth term

a(n-1) = (n-1)th term

d = common difference

a(1) = the first term

The given sequence is:

    -3, 0, 3, 6, ....

The common difference (d)  = 0 - (-3) = 3

Hence, the recursive formula is:

a(n) = a(n-1) + 3

Note that  a(1) = -3. Hence, the explicit formula is:

a(n) = a(1) + (n-1) . d

a(n) = -3 + (n-1) . 3

a(n) = -3 + 3n - 3

a(n) =  3n - 6

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Answer:

Here is your answer

Step-by-step explanation:

113/8= 14 and 1/8th

The answer is ∠1 = 113°

Linear Pair :

When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.

Now as per the question the given angle is

∠2 = 67°

It is also given that ∠1 and ∠2 form a linear pair. Therefore it means that the sum of both the angles will be 180°

∠1 + 67° = 180°

Now subtracting 67 from both sides we will get :

∠1 = 180 - 67 = 113°

Therefore, ∠1 = 113°

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