All digits in a dropdown number are different and one of the digits is the average of all the digits. it has at least two digits. for example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number.

Answer: w=8.5

Step-by-step explanation:

Just did it.

Question 1

Focus on the triangle on the left.

sine is the ratio of opposite over hypotenuse

sin(angle) = opposite/hypotenuse

sin(44) = w/30

w = 30*sin(44)

w = 20.839751 approximately

Now move onto the triangle on the right. We'll use cosine this time.

cos(angle) = adjacent/hypotenuse

cos(x) = w/45

cos(x) = 20.839751/45

cos(x) = 0.463106

x = arccos(0.463106) ... arccosine is the same as [tex]\cos^{-1}[/tex]

x = 62.412286

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Question 2

Focus on the triangle on the left.

sin(angle) = opposite/hypotenuse

sin(32) = w/5

w = 5*sin(32)

w = 2.649596

Now move to the triangle on the right.

sin(angle) = opposite/hypotenuse

sin(x) = w/5

sin(x) = 2.649596/5

sin(x) = 0.5299192

x = arcsin(0.5299192) .... arcsine is the same as [tex]\sin^{-1}[/tex]

x = 31.999996

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

Question 3

This time we use the tangent ratio.

Focus on the triangle that has legs of w and 16.

tan(angle) = opposite/adjacent

tan(70) = 16/w

w*tan(70) = 16

w = 16/tan(70)

w = 5.823524

Now let y = x+w and focus on the largest triangle this time.

tan(angle) = opposite/adjacent

tan(41) = 16/y

y = 16/tan(41)

y = 18.405895

This leads to:

y = x+w

x = y-w

x = 18.405895 - 5.823524

x = 12.582371

The possible values of z is an illustration of the sum operator

The sum of all possible values of z is 17

The conditions in the question are:

x <= y <= z

xyz = 2(x + y + z)

Using the trial by error method, the possible values of x, y and z are:

The sum of the z values are:

z = 8 + 5 + 4

Evaluate the sum

z = 17

Hence, the sum of all possible values of z is 17

Read more about the sum operator at:

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[tex]135 = \frac{22 + 8}{2} \times h \\ 135 = \frac{30}{2} \times h \\ 135 = 15 \times h \\ h = \frac{135}{15} \\ h = \frac{27}{3} = 9cm[/tex]

Answer:

Area of a trapezoid :

[tex]area = \frac{a + b}{2} h[/tex]

The measures given are trapezoid

Area = 135

base 1 = 22

base 2 = 8

[tex]135 = \frac{22 + 8}{2} h \\ \\135 = \frac{30}{2} h \\ 2(135) = ( 2)\frac{30}{2} h \\ 270 = 30h \\ \frac{270}{30 } = \frac{30h}{30} \\ 9 = h[/tex]

Step-by-step explanation:

We can check if the answer is right

[tex] \frac{22 + 8}{2} \times 9 \\ \frac{30}{2} \times 9 \\ 15 \times 9 = 135[/tex]

The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.

The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.

[tex]\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}[/tex]

In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.

The average of the 20 times dice rolls,

[tex]\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}[/tex]

[tex]\rm Average = \dfrac{80}{20} = 4[/tex]

Thus, the average of the 20 rolls of the dice is 4.

Now, the number of times the result of the dice roll is above 4(x>4) is 7.

Hence, the number of times Brandon rolls above the average is 7.

Learn more about Average:

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Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

Answer:

4:18

6:27

8:36

Hope this helps! :)

Answer:

[tex]\sqrt{2}[/tex] A.

Step-by-step explanation:

There's a few ways you can go about solving this, but the way I would go with is using sine law.

Sine law:

[tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]

in the equation above 'A' an angle, and 'a' would be the length of the side opposite to it. Same thing for B.

You are given the angle 90 degrees, and its opposite side length is 2.

You are also given 45 degrees from one of the corners but it doesn't tell you its side length.

There is one corner where it doesn't tell you the angle but you can figure it out using the law that the angles in a triangle must add up to 180 degrees.

So you subtract the other angles to find the angle of the bottom right angle.

180-90-45 = 45

The reason we want to find that angle, is so we can use sin law to find s.

Write down what you have so far:

[tex]\frac{sin90}{2} = \frac{sin45}{s}[/tex]

Now all you need to do is solve for s.

[tex]\frac{sin90*s}{2} = \frac{sin45}{1}[/tex]

sin 90 is 1.

[tex]\frac{1*s}{2} = sin45\\ \\s = 2*sin45\\\\[/tex]

Now since the answers available are in exact values, you can't just punch this in your calculator.

[tex]sin45 = \frac{\sqrt{2} }{2}\\ \\[/tex]

so,

[tex]s = 2*\frac{\sqrt{2} }{2} = \sqrt{2}[/tex]

Answer:

4 pepperoni pizzas

Step-by-step explanation:

3 cheese => 1 pepperoni

12cheese (3x4) => 4 (1x4) pepperoni

Answer:

sixt

Step-by-step explanation:

thats easy the sin should be six

Answer:

0.7778

Step-by-step explanation:

step 1

Address the input parameters and observe what to be found:

Input values:

The fraction = 21/27

What to be found:

Find the decimal expansion of fraction 21/27.

step 2

The numerator is smaller than the denominator of the fraction 21/27, so find how many 10s should be multiplied with both numerator and denominator. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 21/27.

=21

27

x10

10

step 3

Rearrange the fraction as like the below:

=10 x 21

27

x1

10

=210

27

x1

10

step 4

Simplify the above expression further:

=210

27

x1

10

=189 + 21

27

x1

10

= (189

27

+21

27

) x1

10

= (7 + 21

27

) x 1

10

step 5

Repeat the step 2 to find the decimal equivalent for the fraction 21/27 in the above expression:

= (7 + 21

27

) x 1

10

= (7 + 0.778) x1

10

step 6

Simplify the above expression further:

= (7 + 0.778) x1

10

= 7.778 x1

10

=7.778

10

21

27

= 0.7778

Hence,

21/27 as a decimal is 0.7778

Answer:

7⁵-3=7⁵x- 19

Step-by-step explanation:

16807 - 3 = 7⁵x - 19

16804 = 7⁵x - 19

16804 = 16807x - 1

adding 19 on both sides

16804 + 19 = 16807x - 19 + 19

16823 = 16807x

x = 16823 / 16807

16823 upon 16807 is the x

Answer:

7 1/3 inches

Step-by-step explanation:

2 (1 3/4 + 1 11/12)

9+11

3/4+11/12= -------------

12

20/12

=1 2/3+ 2

2(3 2/3)

= 7 1/3

Answer:

106

Step-by-step explanation:

a foot is 12 inches so 8x12 would be 96 and if you add the other 10 inches that would be 106

Answer:

2. 12

3. 1 6/8

4. 8 5/8

5. 4 4/8

6. Eli is incorrect 1 3/8 x 3 is 4 1/8 which is greater than 3 1/8

Answer:

Given equation:

[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]

27 can be written as [tex]3^3[/tex]

Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]

[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]

Therefore, we can rewrite the given equation with base 3:

[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]

To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]

[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]

[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]

[tex]\implies -3x=-4x+6[/tex]

Add [tex]4x[/tex] to both sides:

[tex]\implies x=6[/tex]

Answer:

y = - (x - 3)² + 15

Step-by-step explanation:

using the method of completing the square

y = x² + 6x + 6 ← factor out - 1 from the first 2 terms

y = - (x² - 6x) + 6

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 6x

y = - (x² + 2(- 3)x + 9 - 9) + 6

  = - (x - 3)² + 9 + 6

  = - (x - 3)² + 15

Answer:

Slope of the line is undefined

Step-by-step explanation:

(x₁, y₁) = (-1 , 3)  and (x₂, y₂) = (-1 , 8)

The line is parallel to y-axis. The slope of the line parallel to y-axis is undefined.

Answer:

[tex]A.\,\orange{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]

Step-by-step explanation:

[tex] \frac{x + 2}{ {x}^{2} + 5x + 6 } \div \frac{3x + 1}{ {x}^{2} - 9} \\ \\ = \frac{x + 2}{ {x}^{2} + 3x + 2x+ 6 } \div \frac{3x + 1}{ {x}^{2} - {(3)}^{2} } \\ \\ = \frac{\cancel{x + 2}}{ \cancel{{({x}+ 3)}} \cancel{(x+ 2) }} \times \frac{\cancel{( {x} + 3)}( {x} - {3)}}{3x + 1} \\ \\ = \purple{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]

Answer:

Step-by-step explanation:

So this is a cylinder

R= 8.75in

h=43.12in

So it will be = 3.14x8.75²x43.12

=> 3.14x76.5625x43.12

3.14x 3301.375

i think it is correct

.

stay safe

.

have a nice TIME

Sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.

" Sale price is defined as the amount on which something is sold out."

Formula used

Sale price = Cost price - Discount amount

According to the question,

Cost price of the crate of pears = $50

Discount  on sale price = 10%

Discount amount = 10% of $50

                             [tex]=\frac{10}{100}(50) \\\\= \$5[/tex]

Substitute the value in the formula of sale price we get,

Sale price = [tex]\$ ( 50 - 5)[/tex]

                 = $ 45

Hence, sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.

Learn more about sale price here

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Answer:

the answer is c

Step-by-step explanation:

45% of 1500=675

38% of 1500=570

675+570=1245

1500-1245=255

Step-by-step explanation:

so,

1cm : 4m

that means the factor is 1/400 (as 1 m = 100 cm).

also to remember : 1 m² = 100cm×100cm = 10,000 cm²

the area of a rectangle is

length × width

if both dimensions are shortened by a factor (1/400) in our case :

length×1/400 × width×1/400 =

= length × width × 1/400² = length × width × 1/160,000

that means the area of the actual tennis court is

160,000 times the area of the blueprint picture :

160,000 × 16.25 = 2,600,000 cm² = 260 m²

we now know that the actual length of the tennis court is 400 times the length of the blueprint length :

400 × 6.25 = 2,500 cm = 25 m

Answer:

its c i just got done doing the same one

Step-by-step explanation:

got it right on my real numbers test and got 100% if you need more help comment under my answer

All three are similar

In ∆SUT and ∆VWX

So by SSA they are similar

In ∆PRQ and rest two

All angles are.

So

They are similar by AAA congruence

Answer:

x = 17.9

Step-by-step explanation:

[tex]tan40^{0} =\frac{15}{x}[/tex]

[tex]x=\frac{15}{tan40^{0} } =17.88[/tex]

rounded: 17.9

Hope this helps