he point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = 1/4 (x – 8). What is the slope-intercept form of the equation for this line?

Answer:

[tex]5.03\frac{rad}{sec}[/tex]

Step-by-step explanation:

To find the angular velocity divide the revolutions by the time

so

[tex]\frac{16}{20}=0.8\frac{rev}{sec}[/tex]

Remember that

[tex]1\ rev=2\pi \ rad[/tex]

Convert rev/sec to rad/sec

[tex]0.8\frac{rev}{sec}=0.8*(2\pi)=1.6 \pi\frac{rad}{sec}[/tex]

assume [tex]\pi=3.1416[/tex]

[tex]1.6(3.1416)=5.03\frac{rad}{sec}[/tex]

Answer:

5.03

Step-by-step explanation:

After 10 hours the temperature is shown on the graph as 30 degrees.

50 degrees - 30 degrees = 20 degrees.

The temperature dropped 20 degrees in 10 hours.

Divide the change by the time:

20 degrees / 10 hours = 2 degrees per hour.

Because the temperature dropped, the change would be negative.

The answer is D. -2 degrees per hour.

Answer:

Answer: 56*pi

Step-by-step explanation:

The easiest way is to find the area of the circle and subtract the area of the sector.

Area of the circle

d = 16 cm              given

d = 2*r                   definition

16 = 2*r                  divide by 2

16/2 = 2r/2

r = 8

Area of the circle = pi * r^2

Area of the circle = pi * 8^2

Area of the circle = 64 pi

Area of the sector

Area of sector = (theta/360) * pi * r^2

Area of sector = 45/360 * pi * 64

Area of sector = 1/8 * pi * 64

Area of sector = 8 * pi

Area of the shaded area

Area of the shaded area = 64 * pi - 8*pi = 56*pi

Note: There is a shorter way, but one can never be confident of getting an angle greater than 180 correct.

360 - 45 = 315

Area of the sector = 315/360 * pi * r2

Area of the sector = 7/8 * pi * 64

Area of the sector = 7 * pi * 8

Area of the sector = 56*pi

Answer:

c)

Step-by-step explanation:

if you look at option c it would be correct because 0.75 (3/4) is bigger than 0.7. Then 11/12 is a bigger proportion then 0.75. there for your answer is correct.

The correct order of the numbers given when converted to decimals for easy comparison is 0.7, 3/4 and 11/12, which corresponds to option b: 0.7 < 3/4 < 11/12.

This is a question about comparing and ordering fractions and decimals. To answer this, we first need to convert all the numbers into the same format. We can convert the fractions 11/12 and 3/4 into decimals for easier comparison.

First, to convert 11/12 to a decimal, you'll do the division to find approximately 0.9167. Secondly, 3/4 can be converted to a decimal by performing 3 divided by 4, which equals 0.75. Now, we can easily compare these decimals to 0.7.

From this, we can see that 0.7 is less than 0.75 (3/4) and both 0.7 and 0.75 are less than 0.9167 (11/12). So the correct order of the numbers from least to greatest would be 0.7 < 3/4 < 11/12.

So the correct option is b. 0.7 < 3/4 < 11/12.

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Answer:

[tex]\large\boxed{S.A.=1,119\ in^2}[/tex]

Step-by-step explanation:

We have:

two triangles with base b = 17in and height h = 7in

two rectangles with length l = 17in and width w = 10in

two rectangles with length l =11in and width w = 10in

one rectangle with length l = 8in and width w = 11in

one rectangle with length l = 15in and width w = 11in

one rectangle with length l = 17in and width w = 11in

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

The formula of an area of a rectangle:

[tex]A_{\boxed{\ }}=lw[/tex]

l - length

w - width

Calculate:

[tex]A_\triangle=\dfrac{(17)(7)}{2}=59.5\ in^2\\\\A_1=(17)(10)=170\ in^2\\\\A_2=(11)(10)=110\ in^2\\\\A_3=(8)(11)=88\ in^2\\\\A_4=(15)(11)=165\ in^2\\\\A_5=(17)(11)=187\ in^2[/tex]

The Surface Area:

[tex]S.A.=2A_triangle+2A_1+2A_2+A_3+A_4+A_5[/tex]

Substitute:

[tex]S.A.=2(59.5)+2(170)+2(110)+88+165+187=1,119\ in^2[/tex]

Answer:

38,999

Step-by-step explanation:

In your sample you have 26 out of 30. I like to get that number into a percentage, so you do 26 divided by 30

26/30 = .8666

Then you take your total amount of fans, 45,000 and multiply it by your percentage wearing team colors.

45,000 x .8666 = 38,999.97

Since you can't have .97 of a person, your round it down to 38,999.

The answer is: True.

A counterexample is a way that we can prove that something is not true about a mathematical expression or equation, it could be considered as an exception to a rule, so to check if the answer is true or false, we must prove that a counterexample of the given expression is 0°, so:

The given expression is:

[tex]sinytany=cosy[/tex]

Then,

[tex]sin(0)*\frac{sin(0)}{cos(0)}=cos(0)\\\\0*\frac{0}{1}=1\\\\0*0=1\\0=1[/tex]

We can see that the equation is not fulfilled, so 0° is a counterexample of [tex]sinytany=cosy[/tex] and the answer is true.

Have a nice day!

Answer:

That is correct

Step-by-step explanation:

When doing the math you can find that b and d are correct

Answer:

Step-by-step explanation:

Here all the statement describing the graph.

1- the cycle of the graph is 2 second.

2- mid-line of the graph is at y=0

3- amplitude is 24 i.e 12 unit + 12 unit

4- ball is traveling 24 cm in 1 sec. I.e. 12 unit in 0.5 sec and another 12 units in 0.5 sec.

The answer is C because it’s length x width x height

Answer:

C) V = (10)(5)(2)

Step-by-step explanation:

V = (10)(5)(2) To find the volume of a right rectangular prisms, multiply the length times the width times the height. -- V = lwh.

Answer:

Step-by-step explanation:

The formula for the surface area of a sphere is ...

  A = 4πr²

For a radius of 6 meters, that is ...

  A = 4π(6 m)² = 144π m²

___

The formula for the volume of a sphere is ...

  V = (4/3)πr³ = A·(r/3)

For the same sphere, this is ...

  V = (144π m²)(6 m/3) = 288π m³

Answer:

Option D. [tex]42.4\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cone (juice treats) is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=3\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(1.5)^{2}(3)=7.065\ in^{3}[/tex]

Multiply the volume of one juice treats by 6

[tex](6)7.065=42.39=42.4\ in^{3}[/tex]

Answer:

The answer is 28ft.

Step-by-step explanation:

A radius will always be exactly half of the diameter: meaning, the diameter is double the length of the radius.

To find a coterminal angle to 800 degrees within the 0 to 360-degree range, divide 800 by 360 and find the remainder, which is 80 degrees. Hence, 80 degrees is the angle that's coterminal with 800 degrees.

To find an angle that is coterminal with 800 degrees, which means an angle that shares the same terminal side as the 800-degree angle but is between 0 degrees and 360 degrees, we use the concept of coterminal angles. Since a complete circle has 360 degrees, we can subtract or add multiples of 360 degrees to any angle to find a coterminal angle.

Here’s how we find it for 800 degrees:

Therefore, 80 degrees is the angle between 0 degrees and 360 degrees that is coterminal with an angle measuring 800 degrees.

[tex] \cos t (\sec t - \cos t) = \sin^2 t [/tex]

[tex] \cos t (\dfrac{1}{\cos t} - \cos t) = \sin^2 t [/tex]

[tex] \dfrac{\cos t}{\cos t} - \cos^2 t = \sin^2 t [/tex]

[tex] 1 - \cos^2 t = \sin^2 t [/tex]

Use the identity: [tex] \sin^2 t + \cos^2 t = 1 [/tex] and solve for [tex] \sin^2 t [/tex]. You get: [tex] \sin^2 t = 1 - \cos^2 t [/tex]

Do the substitution on the left side to get:

[tex] \sin^2 t = \sin ^2 t [/tex]

[tex] \cos \: t ( \sec \: t - \cos \: t) = \sin^{2}t \\ \\ 1. \: 1 - \frac{ \cos \: t }{ \sec \: t } = \sin^{2} t \\ 2. \: 1 - \cos \: t \cos \: t = \sin^{2} t \\ 3. \: 1 - \cos^{2} t = \sin^{2} t \\ 4. \: 1 - \cos^{2} t - \sin^{2} t = 0 \\ 5. \: 1 - 1 = 0 \\ 6. \: 0 = 0 \\ 7. \: infinitely \: many \: solutions[/tex]

Answer:

18.

Step-by-step explanation:

Mean of the values = (70+95+35+90+85) / 5

=  75.

Mean absolute deviation  :-

70 - 75 = |-5|  = 5  (absolute value is taken

95 - 75 = 20

35-75 = 40

90-75 = 15

85-75 = 10

Mean Absolute Deviation = (5 + 20 + 40 + 15 + 10) /  5

= 18.

Answer: 18

Step-by-step explanation: it was correct on ttm

Answer:

the answer is 16Ft^2

Step-by-step explanation:

Square A's area is 9 so take its square root =3

then do the same for Square c =5

then use pythagram theory which is

3^2 + 5^2 = 4^2 = 16

Answer:

area = 16 ft²

Step-by-step explanation:

The area of the green square = 9 ft²

area of the yellow square = 25 ft²

Area of the red square can be computed as follows:

area of a square = L²

Since one side of each triangle forms a part of the triangle knowing the length of sides of the green and yellow triangle can be use to get the sides of the red square and invariably the area.

Green square

L² = 9

square both sides

√L² = √9

L = 3 ft

Yellow square

L² = 25

square both sides

√L² = √25

L = 5 ft

use Pythagoras theorem to get the third side of the triangle which is the b

c² = a² + b²

b² = c²  - a²

a = 3 ft

c = 5 ft

b² =  5² - 3²

b² = 25 - 9

b² = 16

square both sides

√b² = √16

b = 4

Red square

area = L²

area = 4²

area = 16 ft²

Answer:

Step-by-step explanation:

Is a ≤ b < c are the side lengths of a right triangle, then

[tex]a^2+b^2=c^2[/tex]

A. 6cm, 8cm, 10cm.

Substitute:

[tex]6^2+8^2=10^2\\36+64=100\\100=100\to TRUE[/tex]

B. 12cm, 35cm, 37cm.

Substitute:

[tex]12^2+35^2=37^2\\144+1225=1369\\1369=1369\to TRUE[/tex]

C. 4cm, 6cm, 10cm.

It's not the side lengths of a triangle, because 4 + 6 = 10.

Without looking at it, we will check equality

[tex]4^2+6^2=10^2\\16+36=100\\52=100\to FALSE[/tex]

D. 10cm, 24cm, 26cm.

Substitute:

[tex]10^2+24^2=26^2\\100+576=676\\676=676\to TRUE[/tex]

The measurement that could not represent the side length of a right triangle is  4 cm, 6 cm, 10 cm.

A right triangle is a triangle that consists of three sides. The longest side is the hypotenuse. The other sides are the base and the length. The sum of angles in a triangle is 180 degrees.

According to this theorem, the square of the hypotenuse should be equal to the sum of the square of the other two sides.

The Pythagoras theorem: a² + b² = c²

where:

a = length

b = base

c = hypotenuse

6² + 8² = 10²

36 + 64 = 100

Option B = 12² + 35

= √144 + 1225

= √1369

= 37

Option C = 4² + 6²

16 + 36

= √52

= 7.2

Option D: 10² + 24² = 26²

100 + 576

= √676

= 26

Please find attached an image of a right triangle. To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675

The answer is 2x−5

see the image

Answer:

The daughter is 36 years old and the son is 12 years old.

Answer:

-15

Step-by-step explanation:

Multiply the whole equation by the inverse of the multiplier of the blank. Then you get ...

___ × 1 = (-27)×(5/9) = -15

The blank filled with -15 will make the equation true.

Fine the average rate of change by the difference in N over the difference in T:

3000 - 500 / 4-0 = 2500 / 4 = 625

This means for every 1 T, N = 625.

Now multiply 625 by 8:

625 x 8 = 5000

When T = 8 N = 5,000

The decay rate can be found by dividing -ln(2) by the half life.

Decay rate = -ln(2) / 5715 = -0.00012

Answer:

bro whats the question

Step-by-step explanation:

chur answer is gonna be 63787 km

Both lines are dotted so no equation should include equal to in it.

The shaded area is on the left side .

The correct answer would be y>2x+1 and x+y = -2

The 3rd answer is correct.

Answer:

y>2x+1 and x+y < -2 represent the graph line.

Step-by-step explanation:

Given : graph .

To find : Which system of linear inequalities is graphed

Solution : We have given graph with two line both lines are dotted line and shaded down.

Equation of line form  : y = mx + b.

Where, m = slope ,  b= y intercept.

Line x+y < -2 less than sign for shaded down and y intercept -2.

and y>2x+1.

Therefore, y>2x+1 and x+y < -2 represent the graph line.

Answer:

The total number of digits required in numbering the pages of a book that has 53 pages would be: 97.

Step-by-step explanation:

This answer would be 97 due to the first nine digits being singular.

The next 44 digits are double, so therefore, you multiply 44 by 2, and you end up with 88.

After that, you take 88 and add the 9, which, is 97 digits in total that you would need to number a 53 page book.

Answer:

P (S∩LC) = 0.03

Step-by-step explanation:

We are given that the probability that someone is a smoker is P(S)=0.19 and the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158.

Given the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).

P (LC|S) = P (S∩LC) / P (S)

Substituting the given values to get:

0.158 = P(S∩LC) / 0.19

P (S∩LC) = 0.158 × 0.19 = 0.03

Answer:Michelle paid $56.15 for her shoes

Step-by-step explanation:

Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.

$3.89+$52.25= $56.15

Final answer:

Michelle paid $56.15 for her shoes, which is $3.89 more than the $52.26 that Conrad paid for his.

Explanation:

The question involves a simple arithmetic calculation to determine how much Michelle paid for her shoes. To find the answer, we will add $3.89, which is the additional amount Michelle paid, to $52.26, which is the amount Conrad paid for his shoes.

Step-by-step calculation:

Therefore, Michelle paid $56.15 for her shoes.

Final answer:

The explicit formula for the salary increases represented as a geometric sequence is a_n= 38,000(1.035)^(n-1), and the recursive formula is a_1= $38,000 and a_n= a_(n-1) × 1.035 for n > 1, reflecting an annual raise of 3.5%.

Explanation:

The starting salary at a company is $38,000 per year with an annual raise of 3.5%. To represent the salary increases as a geometric sequence, we need both explicit and recursive formulas.

The explicit formula for a geometric sequence is an= a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, a1= $38,000 and r = 1.035 (since the salary increase is 3.5%, or 0.035 in decimal form, plus the original amount, hence 1 + 0.035). Therefore, the explicit formula is an= 38,000(1.035)(n-1).

The recursive formula defines each term based on the previous term. It can be written as a1= $38,000, an= a(n-1) × 1.035, for n > 1. This means that starting from the second year (when n > 1), the salary is obtained by multiplying the previous year's salary by 1.035.

Since the sides are equal the angels have to be equal too

5x-20=2x+37

3x=57

X=19