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2 years ago

Given: circle O with tangent AB mBC= 2x -16; mCD = x+40; mDE = x; mEB = 60 find the x

Mathematics

1 answer:

murzikaleks [220]2 years ago

6 0

Answer:

Step-by-step explanation:

All the given arcs cover the entire circle circumference, so their measures add up to a full 360.

(2x - 16) + (x + 40) + x + 60 = 360

4x + 84 = 360

4x = 276

x = 69

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From an industrial area 70 companies were selected at random and 45 of them were panning for expansion next year. Find 95% confi

Lana71 [14]

Answer:

Confidence limit = [52.8%, 75.2%]

Step-by-step explanation:

$P=\frac{45}{70}= 0.64$

$(1-P)=1-0.64=0.36$

$n= 70$

$P$ ± $z$ $\sqrt{\frac{P(1-P)}{n} }$

where the value $z$ will be taken from the z-table for 95% confidence interval

1-0.95= 0.05/2= 0.025

0.95+0.025= 0.0975

From the z-table the value of $z$ corresponding to 0.0975 is 1.96

$0.64$ ± $1.96$ $\sqrt{\frac{0.64*0.36}{70} }$

$0.64$ ± $1.96$ $(0.057)$

$0.64$ ± $0.112$

$64%$ % ± $11.2$ %

so the confidence interval is

$64+11.2=75.2$ %

$64-11.2=52.8$ %

$[52.8, 75.2]$

8 0

1 year ago

Given f(x) = log2x, which of the functions below represents g(x) resulting from reflecting the graph of f(x) in the x-axis and s

enot [183]

Answer:

$g(x) = log(2x+2)$

Step-by-step explanation:

<em>The question has missing options ; However, the question is still solvable</em>

Given

$f(x) = log2x$

Direction = 2 units left

Required

Shift the function by 2 units in the x axis

The general format of shifting a function along the x axis (by the left) is as follows

$g(x) = log(ax+c)$

Where c represents the direction;

$c = 2$

Since $f(x) = log2x$ , then

$g(x) = log(2x+2)$

8 0

1 year ago

Read 2 more answers

Cameron, Arthur, and Jamie are playing soccer. Their locations are recorded by a motion tracking system. The grid shows distanc

Luden [163]

Answer:

1. Arthur is about 54 meters away from Cameron.

2. Jamie is about 56 meters away from Cameron.

3. Arthur is closer to Cameron.

Step-by-step explanation:

We have been given the locations of Cameron (70,10), Arthur (20,30) and Jamie (45,60) on the the grid in meters.

1. To find the distances of Arthur and Jamie from Cameron we will use distance formula.

$\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$\text{Distance between Cameron and Arthur}=\sqrt{(70-20)^{2}+(10-30)^{2}}$

$\text{Distance between Cameron and Arthur}=\sqrt{(50)^{2}+(-20)^{2}}$

$\text{Distance between Cameron and Arthur}=\sqrt{2500+400}$

$\text{Distance between Cameron and Arthur}=\sqrt{2900}$

$\text{Distance between Cameron and Arthur}=53.8516480713450403\approx 54$

Therefore, the distance Arthur is about 54 meters away from Cameron.

2. Let us find the distance between Cameron and Jamie.

$\text{Distance between Cameron and Jamie}=\sqrt{(70-45)^{2}+(10-60)^{2}}$

$\text{Distance between Cameron and Jamie}=\sqrt{(25)^{2}+(-50)^{2}}$

$\text{Distance between Cameron and Jamie}=\sqrt{625+2500}$

$\text{Distance between Cameron and Jamie}=\sqrt{3125}$

$\text{Distance between Cameron and Jamie}=55.9016994374947424\approx 56$

Therefore, Jamie is about 56 meters away from Cameron.

3. We can see that 56 is greater than 54, therefore, Arthur is closer to Cameron.

4 0

2 years ago

Read 2 more answers

A rock is thrown in the air from the edge of a seaside cliff. Its height in feet is represented by f(x) = –16(x^2 – 8x – 9), whe

algol13

Since x is the number of seconds it took the rock to hit the water, x is the value that we are looking for. When the rock hits the water, it's height is 0, therefore, f(x) = 0. So, we can set the expression on the right equal to 0, and solve for 0. Let's do just that:
$0 = -16(x^2-8x-9)$

We can divide by -16, nothing will happen because 0 divided by anything is 0:
$0 = x^2-8x-9$

To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":
$0 = ax^2 + bx + c$

So, for this specific question, let's find two numbers that add to -8 and multiply to 9. These are clearly 9 and -1. We can write it in this way now:
$0 = (x-9)(x+1)$

Both answers would be valid, but there can't be negative time, so your answer is "It takes 9 seconds for the rock to reach the water."

4 0

2 years ago

Read 2 more answers

To aid in sea navigation, Little Gull Island Lighthouse shines a light from a height of 91 feet above sea level with an unknown

algol13

Answer:

$\approx 6^\circ$

Step-by-step explanation:

Given that:

Little Gull Island Lighthouse shines a light from a height of 91 feet above the sea level.

The angle of depression is unknown.

Distance of the point at sea surface from the base of lighthouse is 865 ft.

This situation can be modeled or can be represented as the figure attached in the answer area.

The situation can be represented by a right angled $\triangle ABC$ in which we are given the base and the height of the triangle.

And we have to find the value of $\angle BAD \ or \ \angle C$ (Because they are the internal vertically opposite angles).

Using tangent ratio:

$tan\theta = \dfrac{Perpendicular}{Base}$

$tanC = \dfrac{AC}{BC}\\\Rightarrow tanC = \dfrac{91}{865}\\\Rightarrow tanC = 0.105\\\Rightarrow \angle C \approx 6^\circ$

Therefore, the angle of depression is: $\approx 6^\circ$

7 0

1 year ago