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1 year ago

How much of a circle does a 100-degree angle turn through?

Mathematics

2 answers:

Anton [14]1 year ago

8 0

Answer:

$\approx 5/18$

Step-by-step explanation:

The measure of a circle is 360 $^{\circ}$ . If an angle makes a 100 degree turn through the circle then the angle has turned through $\frac{100}{360}$ of the circle: $\frac{100}{360} = \frac{10}{36} = \frac{5}{18}$

The angle turns through 5/18 of the circle.

12345 [234]1 year ago

3 0

A circle is 360 degrees so if you are turning 100 degrees... you would get 100/360 of the way around the circle.

100/360 = 5/18

answer: 5/18

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Find the P-value in a test of the claim that the mean IQ score of acupuncturists is equal to 100, given that the test statisti

klemol [59]

Answer:

P-value = 0.0455

Step-by-step explanation:

In this question, we are concerned with calculating the P- value in a test.

Mathematically we know that;

P-value = 2 * P(Z > |z|)

Please check attachment for complete solution and by step explanation

7 0

2 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

1 year ago

Carmela mixes 3/4 kilogram of walnuts, 1/2 kilogram of almonds, and 1/4 kilogram of pecans together. She divides the mixed nuts

Evgesh-ka [11]

Amount of walnuts= $\frac{3}{4} kg$

Amount of almonds= $\frac{1}{2} kg$

Amount of pecans= $\frac{1}{4} kg$

Total amount= $\frac{3}{4}+\frac{1}{2}+\frac{1}{4}$

LCM is 4 so sum is = $\frac{3+2+1}{4}=\frac{6}{4}$ = $\frac{3}{2}$

As given, Carmela divides the mixed nuts into 3/10 kilogram bags so number of bags will be:

$\frac{\frac{3}{2}}{\frac{3}{10}}$

= $\frac{3}{2}\times\frac{10}{3}$ = 5

Hence, answer is 5 bags.

5 0

2 years ago

Round off 17.2 to one significant figure

inessss [21]

The answer is 17
becoz whenever the digit after the decimal is less than 5 then it is rounded off to the same number before the decimal
But when the decimal digit is more than 5 then the number is increased by 1

5 0

2 years ago

1. Write an exponential function to represent the spread of Ben's social media post. 2. Write an exponential function to represe

Alex777 [14]

Answer:

1. y = 2(3)ˣ; 2. y = 10(4)^x; 4. Amber = 192 and 3 145 728;

Ben has 54 and 11 098; Carter = 80 and 10 249 shares;

5. Shifted up 45 shares; 6. Amber's;

7. Fewer friends. more shares.

Step-by-step explanation:

The general equation for an exponential function is

y = a(b)ˣ

1. Ben's function

The initial value a = 2.

6 = 2(b)¹ = 2b

Ben's function is

y = 2(3)^x

2. Carter's function

Carter shared his post with 10 friends on Day 0, so a= 10.

Each friend shared with 2 people each day, so b = 2.

Therefore, Carter's function is

y=10(2)ˣ

3. Graphs

$\begin{array}{cccc}& \textbf{Amber} &\textbf{Ben} & \textbf{Carter}\\\mathbf{x} & \mathbf{3(4)^{x}} &\mathbf{2(3)^{x}} & \mathbf{10(2)^{x}}\\0 & 3 & 2 & 10\\1 & 12 & 6 & 20\\2 & 48 & 18 & 40\\3 & 192 & 54 & 80\\\end{array}$

The figure below shows the graphs for each function.

4. Predictions

(a) Amber

(i) Day 3

y = 3(4)³ = 3 × 64 = 192

(ii) Day 10

y = 3(4)¹⁰ = 3 × 1 048 576 = 3 145 728

(b) Ben

(i) Day 3

y = 2(3)³ = 2 × 27 = 54

(ii) Day 10

y = 2(3)¹⁰ = 2 × 29 049 = 118 098

(c) Carter

(i) Day 3

y = 10(2)³ = 10 × 8 = 80

(ii) Day 10

y =10(2)¹⁰ = 10 × 1024 = 10 240

5. Sharing with assisted living facility

y = 3(4)ˣ + 45

The new graph will be shifted up by 45 units.

6. Fastest post

Amber's post travels the fastest.

After only two days, she already has more posts than anyone else.

By Day 10, she has more than 25 times the shares of her closest competitor.

7. Preference

It's not the number of friends you have, but the number of shares they make, that is the important factor.

Carter started with 10 friends, but they made only two shares.

Amber started with only three friends, but they made four shares. By Day 3, she had 192 shares compared to 82 for Carter and only 54 for Ben

If I had to choose, I would prefer a post with fewer friends initially but more shares, like Amber.

5 0

2 years ago