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expeople1 [14]
2 years ago
3

Brianna asked 45 students if they would vote for her to be student council president. She used her calculator to compare the num

ber of students who said yes with the total number of students. Her calculator showed the result as 0.6222.... Answer parts a and b. a. Write this number as a fraction.
Mathematics
1 answer:
goldfiish [28.3K]2 years ago
4 0

Complete question :

Brianna asked 45 students if they would vote for her to be student council president. She used her calculator to compare the number of students who said yes with the total number of students. Her calculator showed the result as 0.6222...

1. Write this number as a fraction (Steps)

2. How many students said they would vote for Brianna?

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Total number of students = 45

Proportion of those who said yes to the total number of students = 0.62222...

1.) writing 0.622222... as a decimal

0.62222 / 1

Multiply numerator and denominatior by 100000 to get rid of the decimal

62222/100000

= 31111 / 50000

Let number who said yes = y

Then,

y / 45 = 31111/50000

50000y = 1399995

y = 1399995 / 50000

y = 27.999

y = 28

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ZanzabumX [31]

Answer:

See the attached figure for better explanation :

Step-by-step explanation :

1. By the unique line postulate, you can draw only one line segment : <u>BC</u>

Since only one line can be drawn between two distinct points.

2. Using the definition of <u>reflection</u>, reflect BC over l.

To find line segment which reflects BC over l, we will use the definition of reflection.

3. By the definition of reflection, C is the image of itself and <u>A</u> is the image of B.

Definition of reflection says the figure about a line is transformed to form the mirror image. Now, CD is perpendicular bisector of AB so A and B are equidistant from D forming the mirror image of each other.

4. Since reflections preserve <u>length</u>, AC = BC

In Reflection the figure is transformed to form a mirror image, Hence the length will be preserved in case of reflection.

8 0
2 years ago
Read 2 more answers
A rectangular portrait measures 50cm by 70cm. It is surrounded by a rectangular frame of uniform width. If the area of the frame
snow_tiger [21]

Let us assume uniform width = x cm wide.

Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.

Therefore,  length of rectangle made by frame = 50 + x+x = (2x+50) cm.

And width of rectangle made by frame = 70+x+x = (2x+70) cm.

We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.

Total area of the rectangle made by frame would be =  (2x+50) * (2x+70)

We know,

Actual area of frame = Area of rectangle made by frame -  area of rectangular portrait.

We also given "the area of the frame is the same as the area of the portrait."

We can setup an equation now,

 3500 = (2x+50) * (2x+70) - 3500.

Subtracting 3500 from both sides, we get

3500-3500 = (2x+50) * (2x+70) - 3500-3500.

0 = (2x+50) * (2x+70) -7000.

FOIL (2x+50) * (2x+70), we get

0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.

0 = 4x^2 +140x +100x +3500 -7000.

4x^2 +240x -3500 = 0.

Dividing whole equation by 4, we get

x^2 +60x - 875 =0

Applying quadratic formula =\frac{-b\pm \sqrt{b^2-4ac}}{2a}, we get

=\frac{-60\pm \sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}

x=\frac{-60+\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}=5\left(\sqrt{71}-6\right)

x=\frac{-60-\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}:\quad -5\left(6+\sqrt{71}\right)

We cant take negative value.

So, x=5\left(\sqrt{71}-6\right)=12.13

We could take approximately 12 cm.



7 0
2 years ago
in the figure p is the incenter of isosceles rst what type of triangle is rpt? Thank you in advance .
snow_lady [41]

Answer:

\Delta \text{RPT is an isosceles triangle}

Step-by-step explanation:

As in the triangle RST,

RS=ST\ \ \ \Rightarrow m\angle SRT=m\angle STR

Because if in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another.

Incenter is obtained by the Intersection of a triangle's three angle bisectors and it is equidistant from the three sides of the triangle.

So, RP and TP are the angle bisectors of ∠R and ∠T respectively.

\Rightarrow \dfrac{m\angle SRT}{2}=\dfrac{m\angle STR}{2}

\Rightarrow m\angle PRT=m\angle PTR

\Rightarrow PR=PT

\Rightarrow \Delta \text{RPT is an isosceles triangle}

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dem82 [27]
We know the following relationship:

csc(\theta)=\frac{1}{sin(\theta)}

The domain of a function are the inputs of the function, that is, a function f is a relation that assigns to each element x in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function csc(\theta) we can write its domain as follows:

1. D<span>omain of validity for csc(\theta):
</span>
D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0 
 
When:

sin(\theta)=0?

when:

\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi

where k is an integer either positive or negative. That is:

sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...

To match this with the choices above, the answer is:

<span>"All real numbers except multiples of \pi"

</span>
2. which identity is not used in the proof of the identity 1+cot^{2}(\theta)=csc^{2}(\theta):

This identity can proved as follows:

sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)

The identity that is not used is as established in the statement above:

<span>"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

</span>\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)<span>


</span>
4 0
2 years ago
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frozen [14]

Answer:

$6,020,826.711

Step-by-step explanation:

The computation of the present value of that year salary is shown below:

As we know that

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where,

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The Time period is 6 years

And, the interest rate is 6.7%

Now placing these values

So, the present value is

= \frac{\$9,000,000}{e^{0.067 \times 6}}

= $6,020,826.711

6 0
2 years ago
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