If you know a length in a scale drawing and its corresponding length in the original drawing, how can you determine the relationship between the areas of the drawings? Explain. (Lesson 13,14 & 15 of module 4)

Answer:

D. 4.12

Step-by-step explanation:

A irrational number can be a decimal, but can never be a fraction.

Answer:

45 degrees

Step-by-step explanation:

∠1 and ∠4 are on a straight line. Therefore, they are supplementary and add to 180 degrees.

∠1+∠4=180

We know that the m∠1 is 135 degrees. We can substitute 135 in for ∠1.

135+∠4=180

Now we have to solve for ∠4. To do this, we need to get ∠4 by itself. 135 is being added on to ∠4. To undo this, subtract 135 from both sides, because subtraction is the opposite of addition.

135-135+∠4=180-135

∠4=180-135

∠4=45

The measure of ∠4 is 45 degrees.

The construction worker are making more than More than 75% of teachers.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

Let us consider the construction workers  is 45000.

So 45,000 represent the third quarter which is 75% of the data.

So, the construction worker are making more than More than 75% of teachers.

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Answer:

1 solution. Solution is -3.

Step-by-step explanation:

First subtract 8 from both sides. This gives you 5x=2x-9.

Then subtract 2x from both sides. This gives you 3x= -9

Next divide both sides by 3. This would give you that x = -3.

Mark me brainliest. Hope this helps

Final answer:

The equation 5x + 8 = 2x - 1 is solved by isolating x to find that it has one solution, x = -3.

Explanation:

The equation 5x + 8 = 2x - 1 can be solved for x to determine how many solutions it has. To do this, we first rearrange the equation to bring all terms involving x on one side and the constants on the other. Subtract 2x from both sides to obtain 3x + 8 = -1. Next, subtract 8 from both sides to get 3x = -9. Finally, divide both sides by 3 to isolate x, which yields x = -3. Therefore, the equation has one solution: x = -3.

Step-by-step explanation:

Simple

The percent of bus and car is 35

So 35% x 1500 = 525

Total bus and car students are 525

Answer: 20

Step-by-step explanation:

8 times 2 = 16

16 plus 4 = 20

Answer:

2x * 4

Step-by-step explanation:

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

Explanation:

The idea is to plug in each pair of coordinates and see if you get a true equation. Choice A does not work because

y = 6x-2

20 = 6(6)-2 ... plugged in x = 6 and y = 20

20 = 36-2

20 = 34

we have a false equation. So this shows choice A does not work.

--------

However, choice D does work since...

y = 6x-2

28 = 6(5)-2 .... plug in (x,y) = (5,28)

28 = 30-2

28 = 28

Put another way, if we plugged x = 5 into the equation, then we'd get y = 28. Therefore, showing (5,28) is a point on the line y = 6x-2.

To find the ordered pair that satisfies the equation, substitute values for x and solve for y. The ordered pair for the equation y = 6x - 2 is (0, -2).

To find the ordered pair that satisfies the equation y = 6x - 2, we need to substitute different values for x and solve for y. Let's start by substituting x = 0. Plugging x = 0 into the equation, we get y = 6(0) - 2 = -2. So the ordered pair is (0, -2). Another way to find more ordered pairs is by using the slope-intercept form of the equation, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 6 and the y-intercept is -2.

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Answer:

63%

Step-by-step explanation:

Answer:

63% of the free throws.

Step-by-step explanation:

It is out of 100% so any percent from 100 is just the number in this case it would be 63 Free throws.

Answer:

2

Step-by-step explanation:

The value of z-score of an appliance that stopped working at 64 months is,

⇒ 2

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The set of life spans of an appliance is normally distributed with a mean 48 and a standard deviation 8 months.

We know that;

Z- score = (X - μ) / σ

Here, We have;

μ = 48

σ = 8 months

X = 64 months

Hence, We get;

z - score = (64 - 48) / 8

z - score = 16 / 2

z - score = 2

Thus, The value of z-score of an appliance that stopped working at 64 months is,

⇒ 2

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Answer: 17.3% of 45.94 km is 7.95 km

Final answer:

To find 17.3% of 45.94 km, convert the percentage to a decimal and multiply by the value in kilometers. The calculation gives you 7.94742 km, which rounded to two decimal places is 7.95 km.

Explanation:

To evaluate 17.3% of 45.94 km, you need to convert the percentage to a decimal by dividing by 100 and then multiply by the value in kilometers.

Convert the percentage to a decimal: 17.3% ÷ 100 = 0.173.

Multiply the decimal by the value in kilometers: 0.173 × 45.94 km.

Perform the multiplication to find the answer.

0.173 × 45.94 km = 7.94742 km.

Now, round the answer to two decimal places:

7.94742 km rounded to two decimal places is 7.95 km.

Answer:

Number of person use more than 15 hours per week from 800 subscribers = 448

Step-by-step explanation:

Given:

Total number of sample = 50

Result = 28 Person use more than 15 hours per week

Find:

How many people use more than 15 hours per week

Computation:

⇒ Probability of Person use internet more than 15 hours per week = 28 / 50

⇒Probability of Person use internet more than 15 hours per week = 0.56

⇒Number of person use more than 15 hours per week from 800 subscribers = 800 × Probability of Person use internet more than 15 hours per week

⇒Number of person use more than 15 hours per week from 800 subscribers = 800 × 0.56

⇒ Number of person use more than 15 hours per week from 800 subscribers = 448

Answer:

448

Step-by-step explanation:

Since 28/50 customers use the internet more than 15 hours per week. 28/50 is our fraction. So we do 28/50x800 which gives you 448.

Answer:$9.29

Step-by-step explanation:For unit rate finding the value of one is the objective. Easiest way to find it is by dividing the value (the amount of money being payed) by the amount beig sold ( the 5 shirts) so basically $46.45 ÷ 5

Answer:

9.25

Step-by-step explanation:

Answer:

18 years

Step-by-step explanation:

Formula:   V(t) = P* (1 +  r/2)^(2t)

r = 4% = 0.04

P =$1,900

V(t) = $1,900 *(1 + 0.04/2)^ (2t)

V = 1900 *(1.02)^(2t)

$3,875.79  =  1900 * 1.02^2t

3875.79/1900 =  1.02^ (2t)

2.0398894736842  = 1.02 ^(2t)

ln 2.0398894736842 =  ln (1.02^(2t) )

ln 2.0398894736842 =  2*t*ln (1.02)

ln 2.0398894736842  /(2* ln (1.02)) =  t

0.71289562682179 / (2 * 0.0198   )  = t

18.00002 years  = t

Answer: 96 students

Step-by-step explanation:

Number of students in the school= 800

Percentage of students that stays after school for Chess = 12%

To get the number of students that attend Chess Club on Wednesdays, we multiply the percentage given by 800. This can be written as:

= 12% of 800

= 12/100 × 800

= 12 × 8

= 96 students

96 students attend Chess Club on Wednesdays.

Answer:

Step-by-step explanation:

We know that the entire school

(

100

%

)

(100%)left parenthesis, 100, percent, right parenthesis has

800

800800 students. We need to find out how many students are in Chess Club, which is

12

%

12%12, percent of the school.

Hint #2

We can first divide

800

800800 by

100

100100 to see that

8

88 students make up

1

%

1%1, percent of the school, then multiply by

12

1212 to see how many students make up

12

%

12%12, percent.

12

%

of the students

=

12

⋅

1

%

of the students

=

12

⋅

8

students

=

96

students

12%of the students

​

=12⋅1%of the students

=12⋅8students

=96students

​

Hint #3

96

9696 students attend Chess Club on Wednesdays.

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

b

Answer

280

Step-by-step explanation:

Answer:

280 then 80

Step-by-step explanation:

right on edg2020

Answer:

D. 49.75 months

Step-by-step explanation:

Esme earns a net salary of $2400 per month.

In her saving account she already have a balance of $100.

She saves $100 every month after her monthly expenses.

She plans to buy a car of $20000 using a no interest loan .

She usually make a $300 payment on the loan every month.

The number of months she will save enough money to pay off her loan completely can be calculated below.

let

x  = number of months

The amount she saved altogether every month is $300 + $100 = $400.

Recall she already has $100 in her account

Amount of loan to be repaid = 100 + 400x

20000 = 100 + 400x

20000 - 100 = 400x

19900 = 400x

divide both sides by 400

x = 19900/400

x = 49.75 months

Answer:

D.) 49.75 Months

Step-by-step explanation:

The total number of students in the 6th grade is 300.

A percentage is a number or ratio expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

For the given situation,

25% of the 6th-grade class students is 75

Let x be the total number of students, say 100%.

⇒ [tex]25\%=\frac{1}{4}[/tex]

Here, 1 part is 25% then 4 parts are 100%

Thus 1 part = 75, then

⇒ [tex]4 parts = 4(75)[/tex]

⇒ [tex]4 parts = 300[/tex]

Hence we can conclude that the total number of students in the 6th grade is 300.

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Answer:

>

Step-by-step explanation:

The correct symbol for the unit conversion is given by 2000 lb = 1 T

In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.

The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.

A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.

Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.

Given data ,

Let the symbol be represented as A

Now , the weight of the object is given by

Let the first weight be p = 2000 lb

Let the second weight be q = 1 Ton

And , from the unit conversion

2000 lb = 1 Ton

So , the value of q = p

Hence , the symbol is equal to and 2000 lb = 1 Ton

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Answer:

The angles are 26 and 64

Step-by-step explanation:

When two angles are complementary, what this means is that the add up to 90 degrees

Now, let’s say one of the angles is x, the other angle is 12 more than twice it; mathematically that would be 2x + 12

Since they add up to be 90, we have

x + 2x + 12 = 90

3x + 12 = 90

3x = 90-12

3x = 78

x = 78/3

x = 26

The other angle is 2x + 12 = 2(26) + 12 = 52 + 12 = 64

Two adjacent angles form a complementary relationship. One angle is twelve more than twice the other angle than the value of that two complementary angles are [tex]26^\circ[/tex] and [tex]64^\circ[/tex].

Given :

The sum of two complementary angles is [tex]90^\circ[/tex]. Let one of the complementary angles be 'a' then the other complementary angle is (12 + 2a) according to the given data.

The mathematical expression of the sum of complimentary angles is:

a + (2a + 12) = [tex]90^\circ[/tex]

Now, open the parenthesis and further simplify the above ex[pression.

3a + 12 = 90

Subtract both sides by 12 in the above expression.

3a + 12 - 12 = 90 - 12

3a = 78

Now, divide both sides by 3 in the above expression.

a = [tex]26^\circ[/tex]

Now, the other complementary angle is (2(26) + 12 = [tex]64^\circ[/tex]).

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Answer:-5d-6u-3

Step-by-step explanation:

-5d+(-6)u-3

-5d-6u-3

Answer:

13.90 inches

Step-by-step explanation:

The sides of rectangle are 8.5 and 11 inches.

According to question diagonal needs to calculated.

The diagonal , and two sides of rectangle will forma a right angled triangle.

Right angle as it constitute a right angle of rectangle as well.

To understand more

construct a rectangle ABCD

then one of its diagonal will be AC if we take triangle ABC.

angle ABC will be right angled at B.

for triangle ABC . diagonal AC will be hypotenuse

So diagonal can be computed using Pythagoras theorem

which states that if a and b are two sides of  right angled triangle containing the right angle then hypotenuse is given by [tex]\sqrt{a^2+b^2}[/tex].

____________________________________________

In the problem

two sides are of length 8.5 and 11 inches

So, diagonal is hypotenuse which can be calculated by [tex]\sqrt{8.5^2+11^2}\\=>\sqrt{72.25+121}\\=>\sqrt{193.25}\\=>13.90[/tex]

thus length of diagonal is 13.90 inches.

To find the minimum score required for the scholarship, we need to find the z-score that corresponds to the top 9% of the normal distribution.

To find the minimum score required for the scholarship, we need to find the z-score that corresponds to the top 9% of the normal distribution.

Step 1: Convert the top 9% to a z-score using the standard normal distribution table.

Step 2: Use the z-score formula to find the corresponding ACT Reading score.

Step 3: Round the answer to the nearest tenth.

The minimum score required for the scholarship is the score that corresponds to the z-score found in Step 1.

To be in the top 9% for ACT Reading scores, a student needs a minimum score of approximately 29.3.

To determine the minimum ACT Reading score required for the top 9%, we need to find the z-score that corresponds to the 91st percentile in a standard normal distribution. According to z-tables, the z-score for the 91st percentile is approximately 1.34.

⇒ Z = (X - μ) ÷ σ

⇒ Mean (μ) = 21.4,

⇒ Standard Deviation (σ) = 5.9,

⇒ Z = 1.34

⇒ X = Z × σ + μ

⇒ 1.34 × 5.9 + 21.4 = 7.906 + 21.4

≈ 29.3

Therefore, to be in the top 9%, the minimum ACT Reading score required is approximately 29.3.

Answer:

Yes there is a loss of area

The loss is 5,858 ft²

Step-by-step explanation:

Kindly find attached rough sketch of the problem for your reference.

This problem bothers on the mensuration of flat shapes, rectangle and parallelogram

Firstly let us calculate initial area of the map, the rectangle

Area = length x width

Area = 200*100

Area = 20,000ft²

Now let us calculate the area of the new zoning map, parallelogram

Area = Base x height

But from the sketch we can solve for the height Applying

SOH CAH TOA

Using SOH

Sinθ= opposite/hypotenuse

Sin θ= h/100

h= sinθ*100

h= sin(45)*100

h= 0.7071*100

h= 70.71ft

We can now solve for the area of the new zoning map

A= 200*70.71

A= 14142ft²

Loss in square feet is

Area of initial map - area of New map

= 20,000-14,142

= 5,858 ft²

9514 1404 393

Answer:

Step-by-step explanation:

Let n represent the number of nickels Ryan has. Then the number of pennies is n-3, and his coins have a value (in cents) of ...

  5n +1(n -3) = 75

  6n = 78 . . . . . . . . . collect terms, add 3

  n = 13 . . . . . . . . . .  number of nickels Ryan has

  n-3 = 10 . . . . . . . .  number of pennies Ryan has

Ryan has 10 pennies and 13 nickels.

Ryan has 10 pennies and 13 nickels.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

Ryan has $0.75 worth of pennies and nickels.

Let x be the number of nickels Ryan has.

So, the number of pennies be x-3,

Then,

 5x +1(x -3) = 75

 6x = 78

  x = 13

 and, x-3 = 10

Hence, Ryan has 10 pennies and 13 nickels.

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Answer:

A. log Subscript 4 Baseline (3 x + 4) = 2

Step-by-step explanation:

I graphed it.

The equation [tex]\log_4(3x + 4) = 2[/tex] has a solution of x = 4

An equation is an algebraic expression that is represented by the equality "=" sign

For an equation to have a solution of x = 4, the equation must be true at x = 4

From the options, we have:

[tex]\log_4(3x + 4) = 2[/tex]

Substitute 4 for x

[tex]\log_4(3*4 + 4) = 2[/tex]

[tex]\log_4(16) = 2[/tex]

Express 16 as 4^2

[tex]\log_4(4^2) = 2[/tex]

Apply the law of logarithm

[tex]2\log_4(4) = 2[/tex]

Apply the law of logarithm

[tex]2*1 = 2[/tex]

[tex]2= 2[/tex]

The value of x = 4 is true for [tex]\log_4(3x + 4) = 2[/tex].

Hence, the equation [tex]\log_4(3x + 4) = 2[/tex] has a solution of x = 4

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Answer:

81pi meter squared

Answer:

81π m²

Step-by-step explanation:

Formula: C=2πr

The circumference of the column is 18π meters so therefore: 18π=2πr

Divide the both sides by 2π:

r= 9 meters

Now find the area:

Formula for Area: A=πr²

Therefore: A= π · 9² = 81π meters²