Please fill in the boxes with correct answers (see attachment for question)

Answer:

Let x be the number.

It is given that a 15 : 9 aspect ratio and a screen that is 42 inches.

Aspect ratio states that  the ratio of the display image’s width to its height.

Then;

Width of the television of(w) = 15x

and

height of the television(h) = 9x.

Since, television is in the form of Rectangle.

and it is also, given that the screen is 42 inches .

⇒Diagonal of the television(D) = 42 inches

Using formula of diagonal of the rectangle :

[tex]D^2 =w^2+h^2[/tex]

Substitute the given values to solve for x;

[tex]42^2 = (15x)^2+(9x)^2[/tex]

[tex]1764 = 225x^2 + 81x^2 = 306x^2[/tex]

or

[tex]x^2 = \frac{1764}{306} = 5.76[/tex]

[tex]x = \sqrt{5.76} = 2.4[/tex]

Then:

width of the television (15x) = 15(2.4) = 36 inches and

Height of the television (9x) = 9(2.4) = 21.6 inches.

Therefore, the actual dimensions of the television are;

width = 36 inches and height = 21.6 inches.

Answer:

(1,-4)

Step-by-step explanation:

Remember, the diameter of a circle crosses through the center from one side of the circle to the other. It is 2 times the radius. This means the center of the circle is the midpoint of the diameter. We find it using the midpoint formula:

[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})[/tex]

[tex](\frac{-4+6}{2} , \frac{-5+-3}{2})=(\frac{2}{2} , \frac{-8}{2})=(1,-4)[/tex]

Answer:

B

Step-by-step explanation:

under a dilatation about the origin of scale factor 3

since dilatation is about the origin multiply the coordinates of A, B and C by 3

A(8, 15) → A' (24, 45)

B(12, 13) → B'(36, 39)

C(8, 10) → C'(24, 30)

using the distance formula

with (x₁, y₁ ) = C'(24, 30) and (x₂, y₂ ) = B'(36, 39)

BC = [tex]\sqrt{(36-24)^2+(39-30)^2}[/tex]

     = [tex]\sqrt{144+81}[/tex] = [tex]\sqrt{225}[/tex] = 15 → B

Answer:

5%

Step-by-step explanation:

(4.2- 4.0)/4.0 * 100 = 5%

Answer:

The percent of increase in the cost of gasoline, from May to June, is 5%.

Step-by-step explanation:

We were given the following:

In May the price of gasoline was $4.00 and in June the price went up to $4.20.

We can determine the percent increase as follows:

percentage increase in gasoline(%) = ((final price-original price)/final price)*100

let y be the final percentage increase of gasoline.

[tex]y=((4.2-4)/4.2)*100=5[/tex]

So the increase of gasoline as 5%

We can check this by multiplying the original prices by 5% and adding the original price.

[tex]4*0.05+4=4.2[/tex]

Answer:

A. -50 feet

Step-by-step explanation:

To find the number closest to sea level, take the absolute value of each number and see which is closest to zero.

A. -50 feet   abs (-50) = 50

B. -68 feet  abs (-68) = 68

C. -77 feet   abs (-77) = 77

D. -86 feet  abs ( -86) = 86

E. -97 feet  abs (-97) = 97

The smallest number is 50.  -50 ft is closest to sea level

Answer:

Step-by-step explanation:

A. 50

Answer:

1650

Step-by-step explanation:

If there are 275 pages and each page can fits 6 coins then you multiply 6 by 275.

Answer:

6 on each page; 1,650 in total coins for all the pages

Step-by-step explanation:

1. The first step is to multiply 1/6*6 to find out how many coins can fit on one page.

2.The second step is to multiply 6 *275. That equals 1,650

Answer:

Here’s the graph

Step-by-step explanation:

Table D if you graph them and do the line test ( where you take a vertical line and see if it touches two points on a graph) you will see that everything else EXCPET D will be touched by the vertical line.

Answer:

option c

Step-by-step explanation:

Below are the 3 major determining factors to determine a good credit score:-

1) Payment history - The payment history comprises of 35 percent of the total credit score and is the most important factor in calculating credit scores. An easiest way for borrowers to improve their credit score is by making quick timely payments.

2) Credit utilization - It is the percentage of available credit which has been borrowed. It makes up 30 percent of the total credit scores.

3) Long-standing lines of credit - the amount of time each account has been open.It makes up 15 percent of the total credit score. In order to improve the credit scores, people without a credit history must begin using credit, and those having credit must maintain long-standing accounts.

Answer:

a = 7cm

b = 3cm

Step-by-step explanation:

84 - 21 = 63cm²

XYRQ = 63cm²

63 / 9 = 7cm

a = 7cm

21 / 7 = 3cm

b = 3cm

Answer:

Its 0.9

Step-by-step explanation:

this is a good enpugh answer

Answer,

X = 3/4

Explanation,

Step 1: Simplify both sides of the equation.

3.25 + 0.5x + (1)(1)/3 + 5/6x = (5)(11)/12

3.25 + 0.5x + 1/3 + 5/6x = 55/12

(0.5x + 5/6x) + (3.25 + 1/3) = 55/12 (Combine Like Terms)

4/3x + 3.583333 = 55/12

4/3x + 3.583333 = 55/12

Step 2: Subtract 3.583333 from both sides.

4/3x + 3.583333 − 3.583333 = 55/12 − 3.583333

4/3x = 1

Step 3: Multiply both sides by 3/4.

(3/4) * (4/3x) = (3/4) * (1)

x = 3/4

Answer:

13/7

Step-by-step explanation:

Simply add the slices!

3+2+3+5=13 Slices

Now, we know that a full pie is 7 slices, and the answer they want is a fraction of a whole pie. Simply put the slices we have over how many are in a whole pie.

Answer: 13/7

This means we have almost 2 pies worth of random leftover slices :)

Answer:

4:5 ,15:16

Step-by-step explanation:

divide 12 and 15 by 3 to get 4 and 5

Y-4X=-17 or -4x + y =-17

to convert it into standard from you first need to get X on the left, you can do that by subtracting x from both sides,

Answer:

-4x + y = -17

Step-by-step explanation:

The standard form of a linear equation is

ax + by = c

Your equation is

        y = 4x – 17     Subtract 4x from each side

-4x + y = -17

Answer:

27.2

Step-by-step explanation:

32*.85=27.2

Answer:

$27.20

Step-by-step explanation:

15 percent of 32 is 4.8

32-4.8= 27.20 so $27.20

Answer:

option (a) y=|x-4| is correct.

Step-by-step explanation:

Solve the question by elimination method i.e. put values of x in the given equations and check if equality holds.

(b) if x=2, then y= |2| - 4 = -2 , which is wrong

(c) if x=2, then y = |2| + 4 = 6, which is wrong

(d) if x= 2, then y = |2 + 4| = 6, which is wrong

The equality holds for (a).

Answer:

(17.8 , 1.6)

[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=5000(1+0.09)^x\implies A=5000(1.09)^x[/tex]

Answer:

Step-by-step explanation:

If there are 4 coins and two faces on those coins then that means there are 4 faces flipping them both at the same time means it will have a 25% chance of them landing on the same side

Answer:

25%

Step-by-step explanation:

Okay so let's just say that you are tossing one coin and you want to know the chance of it landing as tails well its a 50 out of 100 chance of it being tails that is because there are two sides. But you have two so all together there are 4 sides. So let's say that each coin is 50 so now we need to find a even number for all sides, So let's just do 50 -25 = 25 so that lets us know that we can make each side 25%... So now you have a 25%  chance of landing both coins as a tail.

I'm so sorry if this does not make seance I have a very hard time explaining things...  

Answer:

-8d^2+10d-3

Hope i helped if i am wrong tell me please :)

Step-by-step explanation:

combine like terms

Answer:

The equation of line would be y = 2

Step-by-step explanation:

Since the x-axis is horizontal, we would look for another horizontal line to be parallel. All horizontal lines can be written as y = (a number). We can find that number as the y-coordinate in the ordered pair (2)

y = 2

Answer:

29 students

Step-by-step explanation:

First you subtract 6 from 122 so you aren’t counting the remaining 6. You get 116

Then you divide 116 by 4 to find how many students are in his class which is 29

Answer:

y=f(x)

y=5x

y=3x

are examples of function

Step-by-step explanation:

definition of a function

if there is one to one relation between a relation

then  it is defined as a function

for example

y=5x is a function

because when we put some value of x it gives back only one value of y as output.

y=±5x is  not a function because one value of x gives two values(positive and negative) values of y hence not a function.

Answer:

The right option is B) 12.60

Step-by-step explanation:

We have given,

Number of shares = 30

Cost of each share = $34

Total cost of shares = 30 × 34 = $1020

Since the company paid annual dividends of $0.42 per share.

i.e Total annual dividend company paid = 0.42 × 30

Total annual dividend company paid = $ 12.60

Hence the right option is B) 12.60

Answer:

Given: Scale factor, [tex]k = \frac{1}{4}[/tex] and centered at (5, -5).

Labelled the given figure as A, B and C.

The coordinates of the given triangle ABC are;

A = (-3, 7)

B = (-7, -5) and

C = (9, 3)

To find the image of the figure after a dilation with scale factor 1/4 centered at (5, -5).

The rule of dilation with scale factor 1/4 and centered at (5, -5) is given by;

[tex](x, y) \rightarrow (\frac{1}{4} (x -5) +5 , \frac{1}{4}(y+5) -5)[/tex]

or

[tex](x, y) \rightarrow (\frac{1}{4}x + \frac{15}{4}, \frac{1}{4}y -\frac{15}{4})[/tex]

The coordinates of the image of the figure after dilation are;

[tex]A(-3, 7) \rightarrow (\frac{1}{4}(-3) + \frac{15}{4}, \frac{1}{4}(7)-\frac{15}{4})=(\frac{-3}{4}+ \frac{15}{4}, \frac{7}{4}- \frac{15}{4}) = (\frac{-3+15}{4}, \frac{7-15}{4}) = (\frac{12}{4}, \frac{-8}{4}) = A'(3, -2)[/tex]

[tex]B(-7, -5) \rightarrow (\frac{1}{4}(-7) + \frac{15}{4}, \frac{1}{4}(-5)-\frac{15}{4})=(-\frac{7}{4}+ \frac{15}{4}, -\frac{5}{4}- \frac{15}{4}) = (\frac{-7+15}{4}, \frac{-5-15}{4}) = (\frac{8}{4}, \frac{-20}{4}) = B'(2, -5)[/tex]

[tex]C(9, 3) \rightarrow (\frac{1}{4}(9) + \frac{15}{4}, \frac{1}{4}(3)-\frac{15}{4})=(\frac{9}{4}+ \frac{15}{4}, \frac{3}{4}- \frac{15}{4}) = (\frac{9+15}{4}, \frac{3-15}{4}) = (\frac{24}{4}, \frac{-12}{4}) = C'(6, -3)[/tex]

As,You can see the graph as shown below in the attachment.

Answer:

1:8

Step-by-step explanation:

We know that every 9 computers there are 72 students, so if we divide 72 by 9 it will be 8. Therefore for 1 computer it has 8 students.

The law of large number states that , if number of trials increases in an experiment , in a fair trial where each outcome has same chance of occurring or having equal probabilities,when total number of trials  goes higher and higher the probabilities of each single outcome becomes approximately equal.→→In case of Experimental Probability

The Coin Possessed by Jake is a Magic coin.

Now Outcomes received by jake when he tosses the coin certain number of times.He flipped it 100 times, and found that it came up heads 64% of the time. He flipped it another 500 times, and it came up heads 57% of the time. He then flipped it 1000 times, and it came up heads 58% of the time. Then, he flipped it 1500 times, and it came up heads 62% of the time.

Based on the information provided , it appears that coin is not fair . It is  Unbiased.So , if we apply law of large numbers here after number of trials will go higher and higher , the chances of coming head will be more than tail i.e theoretical probability of the magic coin coming up heads is> 50%.

To test my hypothesis i have used the information provided by Jake, which shows that coin is not fair. The probability of head has more than tail i.e by 14%, 7%,8% and 12%.

The total number of seats in a row = 5

Lets suppose you are standing in front of the row, so you have 3 seats on one side of you then the passage of the plane and 2 seats on the other side. Out of 3 seats, 1 is window, 1 is middle and 1 is aisle. Similarly, out of the 2 seats on the other side, 1 is the window and 1 is aisle seat, Hence, a total of 5 seats.

As 2 friends have requested to be seated in the same row. So probability of them getting aisle seats becomes 2/5 for 1st friend (as there are 2 aisle seats out of 5 seats) and 1/4 (1 seat is already allocated to the friend so only 1 aisle seat is left out of 4 seats) for the second one.

So, joint probability becomes = [tex]\frac{2}{5}*\frac{1}{4}= \frac{1}{10}[/tex]

or probability becomes 0.1