An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 634" by 412" on the drawing, how large is the bedroom?

Answer:

a) √80 ≈ 9

b) √27 ≈ 5

c) √110 ≈ 10

d) √0.03 ≈ 0.2

e) √0.12 ≈ 0.3

Step-by-step explanation:

80 is close to 81

Therefore, √80 can be estimated as √81

√81 = 9

[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]

27 is close to 25

Therefore, √27 can be estimated as √25

√25 = 5

[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]

110 is close to 100

Therefore, √110 can be estimated as √100

√100 = 10

[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]

0.03 is close to 0.04

Therefore, √0.03 can be estimated as √0.04

√0.04 = 0.2

[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]

0.12 is close to 0.09

Therefore, √0.12 can be estimated as √0.09

√0.09 = 0.3

[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

174m²

Step-by-step explanation:

SA = 2(wl + hl + hw)

= 2(5m x 11m + 2m x 11m + 2m x 5m)

= 2(55m² + 22m² + 10m²)

= 2 x 87m²

=174m²//

Answer:

division

Step-by-step explanation:

ratio compares 2 numbers by dividing them

example

2 out of 3 dentists like gum

2 ÷ 3 = .67 = 67%

so you can say

67% of dentists like gum

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.

There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.

Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.

We are required to find the number of ways in which the volunteers can be assigned.

Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.

n[tex]C_{r}[/tex]=n!/r!(n-r)!

Number of ways in which the volunteers can be assigned is equal to the following:

Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.

Number of ways =14[tex]C_{12}[/tex]

=14!/12!(14-12)!

=14!/12!*2!

=14*13/2*1

=91 ways

Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.

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625 ml is the amount of smoothie is left for Ahmed to drink.

According to the statement

we have given that the

Ahmed made a 625 ml fruit smoothie in his blender and out of this he gave

320 milliliters of the smoothie to his brother and we have to find that the

How much smoothie is left for Ahmed.

So, For this purpose,

The total smoothie = 625 ml

Smoothie he gave to his brother = 320 ml

Now, we have to find the Amount of smoothie left for ahmed.

So, Smoothie left for ahmed = 625 ml - 320 ml

Smoothie left for ahmed = 305 ml

So, 625 ml is the amount of smoothie is left for Ahmed to drink.

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Question:

Ahmed made a fruit smoothie in his blender, shown below. He gave 320 milliliters of the smoothie to his brother. How much smoothie is left for Ahmed to drink? check the image below.

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The height of the triangle is 11.3 in. The correct option is C. 11.3 in

From the question, we are to determine the height of the given triangle

The height of the given triangle is x in.

Now, we will determine the value of x

In the diagram, we can observe that the height divides the triangle into two equal halves

Thus,

By the Pythagorean theorem, we can write that

12² = x² + 4²

144 = x² + 16

144 - 16 = x²

∴ x² = 144 - 16

x² = 128

x = √128

x = 11.3

Hence, the height of the triangle is 11.3 in. The correct option is C. 11.3 in

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The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

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Answer:

Step-by-step explanation:

To graph by hand I would first convert both equations into y=mx+b.

We start with:

[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]

Solve for y for 2x-2y=4

[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]

Solve for y for x+2y=8

[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]

Giving the new but equal system of equations:

[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]

From this point on you can graph the two functions to find where the two lines intersect, thats your solution.

I've gone ahead and graphed it on desmos for you

Answer:

The answer is C

Step-by-step explanation:

The five number summary can be calculated as follows:

lower quartile(Q₁) = 54 + 56 / 2 = 55

Median = 63.5

Upper quartile(Q₃) = 74

Maximum = 80

Interquartile range = Q₃ - Q₁ = 74 - 55 = 19

The five number summary can be found as follows;

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

minimum = 48

lower quartile(Q₁) = 54 + 56 / 2 = 55

The median is the middle number when the data is arranged in ascending or descending order.

Median = 63 + 64 / 2 = 127 / 2 = 63.5

Upper quartile(Q₃)= 74 + 74 / 2 = 148 / 2 = 74

Maximum = 80

Interquartile range = Q₃ - Q₁ = 74 - 55 = 19

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The value of the vector will be -53. The correct option is C.

In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.

The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.

The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-

u.v = ( 2i-9j ).( -5i+7j)

u.v = -10i² + 17 (i.j) -45(i.j) -63j²

Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.

u.v = -10 + 63

u.v = 53

Therefore, the value of the vector will be -53. The correct option is C.

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The answer is 38cm.

The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).

So,

=2×(12+7)

=2×19

=38cm

the weight of the substance after 28 years is 8 grams.

We have that the half life of a substance is defined as the time required for the substance to decrease by half

The formula for calculating the half - life of a material is given as;

[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]

Where

Substitute into the formula

N(t) = 128 × (0. 5) ^28/ 7

N (t) = 128 × ( 0. 5) ^ 4

N(t) = 128 × 0. 0625

N(t) = 8 grams

Thus, the weight of the substance after 28 years is 8 grams.

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the equation that we can solve using the given system of equations is:

3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0

Here we have the system of equations:

y = 3x^5 - 5x^3 + 2x^2 - 10x + 4

y = 4x^4 + 6x^3 - 11

Notice that both x and y should represent the same thing in both equations, then we could write:

3x^5 - 5x^3 + 2x^2 - 10x + 4 = y = 4x^4 + 6x^3 - 11

If we remove the middle part, we get:

3x^5 - 5x^3 + 2x^2 - 10x + 4  = 4x^4 + 6x^3 - 11

Now, this is an equation that only depends on x.

We can simplify it to get:

3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0

That is the equation that we can solve using the given system of equations.

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The variable used to predict another variable in a regression analysis (usually x) is called the independent variable.

The regression analysis is used to determine the effect on the dependent variable with every one unit change in the independent variable.

The dependent variable is also known as response.

and the independent variable is also known as predictor.

In case of simple linear regression there is only one independent variable and in cases of multiple linear regression there are more than one independent variables.

The general form of simple linear regression is:

[tex]y=mx+c[/tex]

The general form of multiple linear regression is:

[tex]y=c+m_1x_1+m_2x_2+...+m_nx_n[/tex]

The dependent variable are usually denoted by the letter "y" and the independent variables are usually denoted by the letter "x".

Therefore, the variable used to predict another variable in a regression analysis (usually x) is called the independent variable.

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Answer:

Step-by-step explanation:

Comment

There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2

The graph shows that there is a peak at x = 2. That is where the maximum volume is,

Answer

x = 2

Answer:

76

Step-by-step explanation:

Formula

[tex]\sf Average=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]

Given values:

Let x be the score of the fourth test.

To find the score of the fourth test, substitute the given values into the formula and solve for x:

[tex]\begin{aligned} \sf Average & =\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}\\\\\implies \sf 80 & = \sf \dfrac{84+78+82+x}{4}\\\sf 80 & = \sf \dfrac{244+x}{4}\\\sf 80 \cdot 4 & = \sf 244 + x \\\sf 320 & = \sf 244 + x\\\implies \sf x & = \sf 320 - 244\\& = \sf 76\end{aligned}[/tex]

Therefore, John scored 76 on his fourth test.

Answer:

They are all true

Step-by-step explanation:

1. 3² +4² = 5²

3x3 + 4x4 = 5x5

  9   +  16  =  25

25 = 25

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

2. 6² + 8² = 10²

36 + 64 = 100

100 = 100

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

3. 9² + 12² = 15²

81 + 144 = 225

225 = 225

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

4. 5² +12² =13²

25 + 144 = 169

169 =169

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

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:

T(t) = A · sin (2π · t / T + C) + B       (1)

Where:

The temperature amplitude and the middle temperature can be found by the following expressions:

A = (t' - t'') / 2      (2)

B = (t' + t'') / 2      (3)

Where t' and t'' are maximum and minimum temperatures, in degrees.

Then, we proceed to find each constant of the sinusoidal model:

A = (45 - 7) / 2

A = 38 / 2

A = 19

B = (45 + 7) / 2

B = 52 / 2

B = 26

We assume a period of 24 hours (T = 24).

If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:

7 = 19 · sin [(π / 12) · 0 + C] + 26

- 19 = 19 · sin C

sin C = - 1

C = π

T(t) = 19 · sin (π · t / 12 + π) + 26

Then, the temperature at 9 AM is: (t = 4)

T(4) = 19 · sin (π · 4 / 12 + π) + 26

T(4) ≈ 9.545

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

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========================================

Work Shown:

|3x-12| ≥ 6

3x-12 ≥ 6 or 3x-12 ≤ -6  ..... see note below

3x ≥ 6+12 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ 6

x ≥ 18/3 or x ≤ 6/3

x ≥ 6 or x ≤ 2

x ≤ 2 or x ≥ 6

----

Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.

Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5

Answer:

1 is the closest to 28/31

Step-by-step explanation:

0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)

According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

[tex]k=1+log_{2} n[/tex]

Here, n is equal to 66 and by substituting the value to the equation we get:

[tex]k=1+log_{2} (66)[/tex]

k = 7.0444

k ≈ 7

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The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.

Nadia had the highest score on a test.

According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.

Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.

Additionally, the highest score by Nadia is 100 while that for Ben is; 99.

Hence, Nadia had the highest score on a test.

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Answer:

20

Step-by-step explanation:

using the arithmetic progress formula

tn=a+(n-1)d

from the series given above a which is your first term is 50

the d which is the common difference.. you minus the first term from the second term which is 45-50=-5

so the 7th term which our n=7

we have:

t7=50+(7-1)(-5)

t7=50+(6)(-5)

t7=50-30

t7=20

Answer:

a₇ = 20

Step-by-step explanation:

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 50 and d = 45 - 50 = - 5 , then

a₇ = 50 + (6 × - 5) = 50 + (- 30) = 50 - 30 = 20

Step-by-step explanation:

its 29 9x4=29 9+4=13 13+4=17

Answer:

[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]

Step-by-step explanation:

Greetings !

a. (fog)(x)= f[g(x)] = 7(x+1)

b. (gof)(x) = g[f(x)] =7x+1

c. (fog)(4)=7(4)+7=28+7=35

d. (gof)(4)= 7(4)+1=28+1=29

(fog)(x)

(gof)(x)

(fog)(4)

(gof)(4)

The value of the f(-8) from the given f(x) is 1/53.

According  to the statement

we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).

So, For this purpose,

The given value of f(x) :

The function f(x) is

f(x) = 1 / x^2 -11

Now we find the value of the f(-8) then

For this put Put x is -8 in the f(x) then the equation become

f(x) = 1 / x^2 -11

f(-8) = 1 / (-8)^2 -11

f(-8) = 1 / 64 -11

f(-8) = 1 / 53.

here the value becomes 1/53.

So, The value of the f(-8) from the given f(x) is 1/53.

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The completed table will have values filled into it accordingly from left to right and the downwards.

The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.

Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.

For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.

For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.

For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.

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