What are m 1 and m_2?
180° 115°
85
A.
21 = 30°, m 2 = 35°
B.
21 = 35°, m 2 = 30°
O
C. _1 = 65°, m_2 = 60°
=
0 D. 21 = 85°, m_2 = 80°

After 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We know the decay can be as:

[tex]\rm C = a(1-r)^t[/tex]

We have:

a = 470 grams

r = 3% = 0.03

t = 6 hours

[tex]\rm C = 470(1-0.03)^6[/tex]

C = 391.49 grams

Thus, after 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

1. You need the same denominator to subtract

2. You can do this by picking the least common multiple of both denominators or multiplying the denominators by each other. In this case, the LCM (least common multiple) and multiply 4*3 or 3*4 is the same thing: 12.

3. But, what you do to the denominator, you do to the numerator:

[tex]\frac{2*4=8}{3*4=12} \\\\\frac{2*3=6}{4*3=12}[/tex]      This leaves the fractions as [tex]\frac{8}{12} -\frac{6}{12} =\frac{2}{12}[/tex].

4. When you subtract fractions, you don't subtract the denominator.

5. You can simplify this fraction by dividing the numerator and denominator by 6: [tex]\frac{2/2}{12/2} =\frac{1}{6}[/tex]

Answer:

58 more

Step-by-step explanation:

Answer: The smallest number is 118.

Step-by-step explanation:

Let's say that the consecutive numbers are x-1, x, x+1

The sum of the three consecutive numbers is 357

(x-1) + x + (x+1) = 357

So, 3x = 357

x =  357 ÷ 3

x = 119  

The 3 consecutive numbers are: 118, 119 and 120  

The smallest out of the 3 is clearly 118.

Hope this helps!

Answer:

cylinder = 27π

cone =  9π

sphere = 36π

Step-by-step explanation:

volume of a cylinder = πr²h where r = radius and h = height

height of cylinder (h) = 3 and radius (r) = 3

so volume = π(3)²3

==> simplify exponent

volume = π9(3)

==> multiply 9 and 3

volume of cylinder = 27π

Volume of a cone = πr²(h/3) where r = radius and h = height

height of cone (h) = 3 and radius (r) = 3

so volume = π(3)²(3/3)

==> simplify exponent

volume = π9(3/3)

==> divide 3 by 3

volume = π9(1)

==> multiply 9 and 1

volume of cone = 9π

volume of a sphere = 4/3πr³ where r = radius

radius = 3

so volume = 4/3π(3)³

==> simplify exponent

volume = 4/3π27

==> multiply 4/3 and 27

volume of sphere = 36π

The mass of platinum cone is more than the mass of the gold cylinder which is 7529.76 grams.

It is defined as the ratio of mass and volume. The density gives an idea of how dense the object is, and it is denoted by the symbol ρ. The unit of the density is kilogram per cubic meter.

The volume for the cylinder = π(6/2)²(5) = 141.37 cubic cm

The density for gold = 19.3 gram/cm³

Mass of gold cylinder = 19.3×141.37 = 2728.44 grams

The volume of the cone = (π(8/2)²×21)/3 = 351.85 cubic cm

The density for platinum = 21.4 gram/cm³

Mass of platinum cone = 21.4×351.85 = 7529.76 grams

Thus, the mass of platinum cone is more than the mass of the gold cylinder which is 7529.76 grams.

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Answer:

esf

Step-by-step explanation:

Answer: b and d

Step-by-step explanation: right on edge

Answer:

The answer to this one is 0.25

Answer:

38.7

Step-by-step explanation:

Use cosine

cos = adj / hyp

adj = cos x hyp

adj = cos(49) x 59

adj = 38.7

The function that could be used to model the value of the car V after years is V(t) = 32000(1 - 0.12)^t

The given parameters are:

Initial value, a = 32000

Rate, r = 12% --- depreciation rate

Since the value of the function decreases with time, the equation of the exponential function would be:

V(t) = a(1 - r)^t

So, we have:

V(t) = 32000(1 - 12%)^t

Express as decimal

V(t) = 32000(1 - 0.12)^t

Hence, the function that could be used to model the value of the car V after years is V(t) = 32000(1 - 0.12)^t

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Answer:

Answer: 4/9 of the class are boys and 5/9 of the class are girls.

Step-by-step explanation:

There are 9 nine students in total in the class since 4 + 5 = 9.

Input the amount of boys and girls there are in the class in the numerator  and have 9 as the denominator. 4/9 of the class are boys and 5/9 of the class are girls.

--~Hope this helped~--

Answer:

See below

Step-by-step explanation:

Opens Downward   ( due to the  -  coefficient  of t^2 )

when t = 0    the height is = 25 meters

initial velocity = 200 m/s

Vertex = 20.41, 2065.82

Answer:

25.12 in

Step-by-step explanation:

In the given circle

Answer:

a

Step-by-step explanation:

3 feet 11 inches

hope this helps

The area of the composite figure composed of two rectangles is 217 centimetres squared

The area of the composite figure can be found as follows:

The area of the composite figure can be found by adding up the individual area of each shape in the figure.

Therefore,

area of the figure = area of rectangle + area of rectangle

area of a rectangle = lw

where

Therefore,

area of the figure =  (14 × 11) + (7 × 9)

area of the figure = 154 + 63

area of the figure = 217 cm²

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Hey ! there

Answer:

Step-by-step explanation:

In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .

And we're asked to find the length of each side of triangle.

So ,

We know that ,

[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]

Solution : -

[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]

Step 1 : Removing parenthesis and cancelling 7 with -7 :

[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]

Step 2 : Adding like terms on left side :

[tex] \longmapsto \qquad 4x = 84[/tex]

Step 3 : Dividing with 4 on both sides :

[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]

On calculating further, We get :

[tex] \longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar[/tex]

According to question ,

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Verifying : -

Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .

Therefore , our answer is correct.

Answer:

none

Step-by-step explanation:

[tex]one \: fifth = \frac{1}{5} \\ from \: the \: options \: no \: fraction \: is \: equivalent \: to \: one \: fifth \: and \: non \: of \: the \: fracrions \: can \: be \: reduced \: to \: give \: one \: fifth \\ so \: the \: answer \: is \: none[/tex]

Answer:

Not a function

Step-by-step explanation:

Since 2 different points have the same x-coordinte, the relation is not a function.

Answer:

44.6cm³

Step-by-step explanation:

V=3/4×3.14×2.2³=44.6cm³

Answer:

Option 2) 44.6 cm³ os the correct answer.

Step-by-step explanation:

SOLUTION :

Here we have given that the radius of the sphere is 2.2 cm. We have to find the volume of sphere.

Finding the volume of sphere by substituting all the given values in the formula :

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(2.2)}^{3}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 10.65}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{\cancel{3}} \times 3.14 \times \cancel{10.65}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 4 \times 3.14 \times 3.55}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 12.56 \times 3.55}}}[/tex]

[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 44.58 \: {cm}^{3}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{\underline{\underline{\pink{V_{(Sphere)} \approx 44.6 \: {cm}^{3}}}}}}}[/tex]

Hence, the volume of sphere is 44.6 cm³.

Answer:

90.75 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 ( b1+b2) *h

where b1 and b2 are the lengths of the bases and h is the height

A = 1/2(8.5+ 15.7) * 7.5

1/2 (24.2) 7.5

90.75 cm^2

Answer:

step 2

and then also in step 3 compensating the error in step 2

Step-by-step explanation:

I think I just answered this for another post.

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

so, step 1 is correct :

sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2)

but step 2 suddenly and incorrectly switched that central "-" to a "+".

yes, sin(3pi/2) = -1, but that is still an explicit factor in step 2. so it was not used to flip the central operation from subtraction to addition, and therefore this change was a mistake.

then, in step 3, another error was made by just ignoring the "-" sign of "-1" and still keeping the central "+" operation. this error compensated for the error in step 2 bringing us back by pure chance to the right result.

Answer:

2340

Step-by-step explanation:

fundamental counting principle

Answer:

87.92ft^3

Step-by-step explanation:

Formula:

       V= π*r^2 *h