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Answer:

Step-by-step explanation:

Sum of angles of a triangle = 180

So, 56 + 58 + x = 180

      114 + x = 180

         x = 116

Now ∠ 1 + ∠x = 180      [ straight line angles]

       ∠ 1 + 66 = 180

        ∠1 = 180 - 66 = 114°

OR

You can use the rule : Exterior angle = sum of 2  interior opposite angles.

56 + 58 = ∠1

114 = ∠1

Answer:

∅=6

Step-by-step explanation:

let ∅=x

[tex]\csc(3x+15)=\frac{1}{\sin(3x+15)}\\\sin(5x+3)*(\frac{1}{\sin(3x+15)})\\\frac{\sin(5x+3)}{\sin(3x+15)}=1\\\sin(5x+3)=\sin(3x+15)\\5x+3=3x+15\\2x=12\\x=6[/tex]

Answer:

$11,321,630

Step-by-step explanation:

We solve using Exponential growth formula

A(t) = Ao (1 + r)^t

Ao = Initial worth = $94,000

r = Growth rate = 7.3% = 0.073

t = Time in years = 2020 - 1952

= 68 years

A(t) = Current worth in 2020 = After 68 years

A(t) = 94000 × ( 1 + 0.073)^68

A(t) = 94000 × 120.44286946

A(t) = 11,321,629.729

Therefore, the estimated worth of the Van Gogh painting in 2020 approximately = $11,321,630

Answer:

Step-by-step explanation:

1. The mean is calculated using below table

Marks          Frequencies       Midpoint       Product

10 to 14              18                         12                216

15 to 19               9                         17                 153

20 to 24             11                         22                242

25 to 29             25                       27                675

30 to 34              14                        32                448

35 to 39              3                         37                 111      

Sum                    80                                          1845

The mean is:

2. The mode is the midpoint of the tallest bar.

The mode is

3. The median is the middle of the data set. The number of frequencies is 80, the middle frequency is number 40, which is within the 25 to 29 bar.

Formula to calculate median:

where

Substitute values and calculate:

Answer:

10

Step-by-step explanation:

=13+ 3^3 ÷9 we can change it to:

=13+ 3^3/-9

3^3 can be changed to 27

13+ 27/9

=13+−3

=10

Answer:

B. (1,4)

Step-by-step explanation:

If you go over to the right by 1 and up by 4 the point will land inside the blue, hence it is the answer since the rest do not land inside the blue.

Answer:

Step-by-step explanation:

Answer:

surface area of the square pyramid

=(10×10)+(2×10×8)

=100+160

=260 yd²

answer is first option

Answer:

hope it helps...

have a great day!!

Answer:

Step-by-step explanation:

Set this up as a proportion with pole/building height on the top and shadow length on the bottom, using x for the unknown, which is the height of the building:

[tex]\frac{pole/building}{shadow}:\frac{3.4}{1.61}=\frac{x}{36.75}[/tex] and cross multiply to solve:

1.61x = 124.95 so

x = 78 m

Answer:

Interest = $ 2247.00

Step-by-step explanation:

principal=$6600

Amount=$8847

time=4 years

Interest=Amount - principal

=$8847 - $ 6600

=$2247 =

=$2247.00

Answer:

17000+3400 =

Step-by-step explanation:

Answer:

25,160

Step-by-step explanation:

ok if it grows 4% every year, 12 years later it will have grown 48%. so 48% of 17,000 is 8,160, so 17,000+8,160=25,160, so that is the population after 12 years.

Answer:

The number generator is not fair. In most of the experiments, considerably less than 40% of the selected are green

Step-by-step explanation:

Given

[tex]Pr(Green) = 40\%[/tex]

See attachment for plots

Required

Is the number generator fair or not

From the number line, we have the following outcomes:

[tex]0 \to 1[/tex]

[tex]1 \to 1[/tex]

[tex]2 \to 7[/tex]

[tex]3 \to 2[/tex]

[tex]8 \to 1[/tex]

Divide each outcome by 12, to get the proportion of green in each trial

[tex]0 \to 1[/tex] [tex]\to 8.33\%[/tex]

[tex]1 \to 1[/tex] [tex]\to 8.33\%[/tex]

[tex]2 \to 7[/tex] [tex]\to 58.33\%[/tex]

[tex]3 \to 2[/tex] [tex]\to 16.33\%[/tex]

[tex]8 \to 1[/tex] [tex]\to 8.33\%[/tex]

The above shows that the proportion of green in most of the trial is less than 40%

Hence, the number generator is not fair.

Answer:

D

Step-by-step explanation:

Answer:

expand the distance between the nearest two integers on your numberline. so, you can find many rational numbers such as fractions between them.

Answer: In representation of rational numbers on the number line are discussed here. We know how to represent integers on the number line.To represent the integers on the number line, we need to draw a line and take a point O on it. Call it 0 (zero).

Set of equal distances on the right as well as on the left of O. Such a distance is known as a unit length. Let A, B, C, D, etc. be the points of division on the right of 'O' and A',B', C', D', etc. be the points of division on the left of 'O'. If we take OA = 1 unit, then clearly, the point A, B, C, D, etc. represent the integers 1, 2, 3, 4, etc. respectively and the point A', B', C', D', etc. represent the integers -1, -2, -3, -4, etc. respectively.

Answer

12+10+10+50+2+3+1=88

Step-by-step explanation:

Answer:

Red pens: 4 boxes

blue pens: 2 boxes

black: 3 boxes

Step-by-step explanation:

Answer:

[tex]x = 7 \: or \: x = - 7.[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 49 = 0[/tex]

Then

[tex] {x}^{2} = 49 [/tex]

So

[tex]x = 7 \: or \: x = - 7.[/tex]

Answer:

x = -7 , 7

Step-by-step explanation:

a² - b² = (a + b)(a - b)

x² - 49 = 0

x² - 7² = 0

(x + 7)(x -7) = 0

x + 7 = 0         ; x - 7 = 0

x = -7             ; x = 7

Answer:

Both 16 and 1 are squares. This suggests using the formula for the difference of squares. Answer link.

Step-by-step explanation:

Every time you have a difference in the format of

A2−B2 you can factor as (A−B)(A+B).

Then you have to identify if your quantity is the difference of two squared quantities.

It is. In fact we can write it as:

16x2−1=(4x)2−12

Then we can apply our rule

[tex] {(4x)}^{2} - {1}^{2} = (4x - 1)(4x + 1)[/tex]

Answer:

let's convert the 25 yards into feets -> 75 feet of wire.

now let's subtract the alrdy used 15 ½ feet from we that

we got 59 ½ feet left

now let's just take ⅓ of this, just by dividing by 3.

since this seems to be a mess in calculation, let's put in the effort to convert in into inches first.

59 ½ feet = 59½*12 inches = 714 feet

now we should be able to take ⅓ of it cleanly (since we just multiplied by 12)

⅓ of 714 is just as dividing 714 by 3

= 238

the time machine needs 238 inches of wire

this isn't just picking an answer tough, on the bottom of the exercises are the unit conversations

Answer:

x = 0 , y = 0

Step-by-step explanation:

given:

  [tex]4x = y \\\\2x - y = 0\\\\Substitute \ y\ =\ 4x\ in \ second \ equation :\\2x - 4x = 0\\\\-2x = 0\\\\x = 0, \\y = 0[/tex]

Answer:

Step-by-step explanation:

The relationship between x and y is called a linear relationship because the points so plotted all lie on a single straight line. The number 95 in the equation y=95x+32 is the slope of the line, and measures its steepness.

Answer:

She is an undergraduate because more undergraduates are enrolled

Step-by-step explanation:

From the question, we understand that:

Undergraduate > Graduate

This represents the base rate

So, when taking a guess using the base rate, your guess will be that: the woman is an undergraduate.

The reason for this is that you know that there are more undergraduates than graduates enrolled in the course.

Answer:

The answer is "A 10 units down traduction, following by 8 pieces right traduction".

Step-by-step explanation:

Even as the changed image is similar to the original picture in rotation, reflections, and translations, so every point would be modified so that the examination of each point will provide several changes performed.

Consideration of paragraph A(-6, 4).

When a point (x, y) k is transferred down, it becomes (x, y-k).

So when 10 units are converted to A, it becomes (-6, -6).

When the point (x, y) k units are translated, it becomes (x+k and y)

This manner, it gets 8 units (-6, -6) to the right point (2, -6)

These are the A' coordinates.

Thus, quadrilateral ABCD was subjected to 10 further units of translation and 8 to the left. translations .

Answer:

x = 16 and y = 121

Yes, its a long process.

Step-by-step explanation:

vertical angles are congruent given that: we do this

(4x-5)+(4x-5)+y+y=360

or

2(4x-5)+2y=360

divide both sides by 2

(4x-5)+y=180

distribute (there is an invisible 1 beside the parentheses of 4x-5)

4x-5+y=180

add 5 to both sides

4x+y = 185

subtract y from both sides

4x = 185-y

divide both sides by 4

x = (185-y)/4

note that (4x-5) is also EQUAL to (3x+11)

4x-5=3x+11

subtract 3x from both sides

x-5=11

add 5 to both sides

x = 16

Now that we know what x is, we can substitute it in the equation we got from 2(4x-5)+2y=360

Our equation was

x = (185-y)/4

16 = (185-y)/4

Multiply both sides by 4

64 = 185-y

Subtract 185 from both sides

-121=-y

multiply both sides by -1

121 = y

Answer:

Width of the box = 2 inches

Step-by-step explanation:

Volume of a box = length × width × height

Volume of the box = 240 cubic inches

Length of the box = (x + 8) inches

Width of the box = x inches

Height of the box = 12 inches

Volume of a box = length × width × height

240 = (x + 8) * x * 12

240 = (x² + 8x) * 12

240 = 12x² + 96x

12x² + 96x - 240 = 0

x² + 8x - 20 = 0

Solve quadratic equation using factorization method

x² + 10x - 2x - 20 = 0

x(x + 10) -2(x + 10) = 0

(x + 10) (x - 2) = 0

x + 10 = 0 OR x - 2 = 0

x = -10 OR x = 2

Width of the box can not be a negative value

Therefore,

Width of the box = 2 inches

Answer:

if the formela right

so this is the answer

Answer:

x = {-5, 2}

Step-by-step explanation:

unfamiliar with the notation 7;2

will solve for |2x + 3| = 7

Solution I -  the quanity inside the absolute value is 7

2x + 3 = 7

2x = 4

x = 2

Solution II -  the quanity inside the absolute value is –7

2x + 3 = –7

2x = -10

x = -5

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

x = {-5, 2}