Amodel is made of a car. The car is 9 feet long and the model
is 6 inches long. What is the ratio of the length of the actual car
to the length of the model?

Answer:

[tex]\frac{24}{25}[/tex]

Step-by-step explanation:

Given

cosA = [tex]\frac{3}{5}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]

Then the opposite side using Pythagorean triple is 4, thus

sinA = [tex]\frac{4}{5}[/tex]

Using the trigonometric identity

sin2A = 2 sinAcosA, then

sin2A = 2 × [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex]

         = [tex]\frac{2(4)(3)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]

Answer:

[tex]\sin(2A)=\frac{24}{25}[/tex]

Step-by-step explanation:

Double angle identity for sine is

[tex]\sin(2A)=2\sin(A)\cos(A)[/tex].

We know [tex]\cos(A)[/tex]. We now need to find [tex]\sin(A)[/tex] to find our answer.

Recall the following [tex]Pythagorean Identity[/tex]:

[tex]\sin^2(A)+\cos^2(A)=1[/tex].

Replace [tex]\cos(A)[/tex] with [tex]\frac{3}{5}[/tex]:

[tex]\sin^2(A)+(\frac{3}{5})^2=1[/tex]

[tex]\sin^2(A)+\frac{9}{25}=1[/tex]

Subtract [tex]\frac{9}{25}[/tex] on both sides:

[tex]\sin^2(A)=1-\frac{9}{25}[/tex]

[tex]\sin^2(A)=\frac{25}{25}-\frac{9}{25}[/tex]

[tex]\sin^2(A)=\frac{25-9}{25}[/tex]

[tex]\sin^2(A)=\frac{16}{25}[/tex]

Now to finally get the value of [tex]\sin(A)[/tex] take the square of both sides:

[tex]\sin(A)=\pm \sqrt{\frac{16}{25}}[/tex]

Since [tex]A[/tex] is in the interval [tex](0,90)[/tex], then [tex]\sin(A)>0[/tex].

[tex]\sin(A)=\sqrt{\frac{16}{25}}[/tex]

[tex]\sin(A)=\frac{\sqrt{16}}{\sqrt{25}}[/tex]

[tex]\sin(A)=\frac{4}{5}[/tex]

So let's finally find the numerical value of [tex]\sin(2A)[/tex].

[tex]\sin(2A)=2\sin(A)\cos(A)[/tex]

[tex]\sin(2A)=2\cdot \frac{4}{5} \cdot \frac{3}{5}[/tex]

[tex]\sin(2A)=\frac{2(4)(3)}{5(5)}[/tex]

[tex]\sin(2A)=\frac{24}{25}[/tex]

Side note:

If [tex]A[/tex] is between 0 and 90 degrees, then we are in the first quadrant.

If we are in the first quadrant, both [tex]x=\cos(A)[/tex] and [tex]y=\sin(A)[/tex] are positive.

Answer: 29.25

Step-by-step explanation:

3(9.75)

Answer:

7 erasers

Step-by-step explanation:

Since we know that she bought the same exact amount of pencils and erasers, we can assume that they are the same price. So, to find how many things she can purchase, divide 252 by 18, which will give you 14.

Then, since she bought the same number of pencils and erasers, divide 14 by 2, which is 7. So, Krista bought 7 pencils and 7 erasers.

You can check your work by multiplying 7 by 18 and adding that to 7 multiplied by 18. You'll get 252, which is the amount Krista started with.

Hope this helps! :)

Answer:

14 erasers.

Step-by-step explanation:

Just simple division!

252/18=14

Answer:

We will buy it at $9.95 plus  5% tax because it is slightly cheaper than other price

Step-by-step explanation:

$9.95 x 18 = 179.10 + 5% sales tax(8.95) = 188.055

$9.75 x 18 = 175.50 + 15 = 190.50

hence sales tax can be get back by submitting monthly return file. so the first method is cheaper than second one,

The first shop offers a better price for 18 rolls of film. You will pay [tex]$179.10[/tex]for 18 rolls of film at the first shop.

Let's calculate the total cost for each shop:

For the first shop:

- The price per roll is [tex]$9.95[/tex].

- There is a 5% sales tax.

- The total cost without tax for 18 rolls is [tex]18 rolls * $9.95/roll = $179.10[/tex].

- The sales tax on this amount is 5% of [tex]$179.10[/tex], which is [tex]0.05 = $8.955.[/tex]

- The total cost including tax is [tex]$179.10[/tex][tex]+ $8.955[/tex] [tex]=$188.055.[/tex]

 For the second shop:

- The price per roll is [tex]$9.75.[/tex]

- There is no sales tax.

- The shipping cost is a flat rate of [tex]$15.00.[/tex]

- The total cost for 18 rolls, excluding shipping, is 18 rolls *[tex]$9.75/roll[/tex] [tex]= $175.50.[/tex]

- Adding the shipping cost, the total cost is [tex]$175.50[/tex][tex]+ $15.00 = $190.50[/tex].

 Comparing the two total costs:

- First shop: [tex]$188.055[/tex] (approximately [tex]$179.10[/tex] without rounding the tax)

- Second shop: [tex]$190.50[/tex]

 The first shop offers a better price for 18 rolls of film. You will pay approximately [tex]$179.10[/tex] for 18 rolls of film at the first shop, which is less than the [tex]$190.50[/tex] you would pay at the second shop.

Answer:

Step-by-step explanation:

parallelogram, because the figure has exactly one pair of parallel sides

-> 40 hours per week, 52 weeks a year

shop and save grocers

monthly wages: $3,800

hourly wages: $3800 / 160 = $23.75 per hour

yearly wages: $23.75 per hour x 40 hours per week x 52 weeks a year

= $49,400

unbelievable toys

yearly wages: $43,000

convenience store

$16.50 per hour x 40 hours per week x 52 weeks a year

= $34,320

49,400 - 34,320 = 15,080

..? that's not even an answer choice what-

Answer:

36

Step-by-step explanation:

when you multiply 2x9 you get 18 and since 2 is half of 4 that means you have to do that twice so do 2x9 again and add both of them up to get a product of 36

The solution to the expression 4 × 9 using 2's facts is;

36

For example; 2 × 5 means double of 5 which is 10.

We are given; 4 × 9

Now, we know that 4 is a double of 2 and so we have;

2 × 2 × 9

Since we want to express the result as a double, let us multiply one of the 2 by 9 and retain the other 2.

2 × 9 means double of 2 and it is 18

Then we now have 2 × 18 which implies double of 18 which is 36.

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3 3/4 is the answer

10 3/4 --- 43/4

6 4/4--- 7 or  28/4

43/4- 28/4=  15/4

15/4 simplified is 3 3/4

Answer:

43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4

Step-by-step explanation:

10 3/4 - 6 4/4 . The expression means we should find the difference between 10 3/4 and 6 4/4. The best approach to find the difference of this kind of fractions with whole number is by turning each to an improper fraction.

10 3/4 . This whole number fraction can be turn to an improper fraction as follows

10 × 4 + 3 = 43 then 43/4

6 4/4.   4 × 6 + 4 = 28/4.

Now , let's find the difference

The denominator is same, which is 4

43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4

Answer:

c. Cos 52 = 17/c

Step-by-step explanation:

sin(x) = cos(90-x)

Based on the given figure if sin52=17/c if trigonometric ratio then the correct option is C)cos38=17/c

The trigonometric functions are the ratio of the sides of a right angled triangle. Sin, cos, tan, cosec, sec,cot are the trigonometric functions.

We have been given sin 52=17/c

We know that sin x= cos(90-x)

sin52=cos(90-52)=cos 38

So the value will be cos38=17/c

Hence the correct answer is cos38=17/c.

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Answer: 99.

Step-by-step explanation: To answer this, you must reverse the operation to find the number being multiplied. The operation done: multiplication. Multiplication in reverse: division. 495 divided by 5 is 99.

Answer:

The other number is 99.

Step-by-step explanation:

"Ian multiplies a number by 5. The product of the two numbers is 495".

Therefore que know that 5 · x (a number we don't know yet) = 495.

This is an equation.

[tex]5*x=495\\[/tex] - To solve it we need to clear the equation.

Thus,

[tex]x=\frac{495}{5}[/tex]

x = 99

[tex]\bf G(\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad H(\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}}\implies \cfrac{-9}{4+3}\implies -\cfrac{9}{7}[/tex]

The shaded area's Fraction= 21/100 and Decimal = 0.21.

Step-by-step explanation:

When an area is divided into multiple smaller regions ( smaller squares ) is called parts.

In case of Squares, it can be divided into either rows or columns, sometimes both.  

Form the given diagram, the square consists of 10 rows and 10 columns which makes 100 (10×10) parts in it.

One fraction is obtained by dividing it by the total number of parts.

In this square, 21 shaded fractions are given.

∴ The fraction of shaded Area = 21/100.

Decimal of shaded Area=0.21.

Answer:

Domain: (-∞,∞) or  -∞ <[tex]x[/tex]<∞

Range: [1,∞) or [tex]y\geq 1[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-2x+2[/tex]

To find range and domain of the function.

Solution:

The given function is a second degree function as the highest exponent of the variable is 2. Thus, it is a quadratic function.

For all quadratic functions the domain is a set of all real numbers. So, the domain can be given as: (-∞,∞) or  -∞ <[tex]x[/tex]<∞

In order to find the range of the quadratic function, we will first determine if the function has a minimum point or the maximum point.

For a quadratic equation : [tex]ax^2+bx+c[/tex]

1) If [tex]a>0[/tex] the function will have a minimum point.

2) If  [tex]a<0[/tex] the function will have a maximum point.

For the given function: [tex]f(x)=x^2-2x+2[/tex]

[tex]a=1[/tex] which is greater than 0, and hence it will have a minimum point.

To find the range we will find the coordinates of the minimum point or the vertex of the function.

The x-coordinate [tex]h[/tex] of the vertex of a quadratic function is given by :

[tex]h=\frac{-b}{2a}[/tex]

Thus, for the function:

[tex]h=\frac{-(-2)}{2(1)}[/tex]

[tex]h=\frac{2}{2}[/tex]  [Two negatives multiply to get a positive]

[tex]h=1[/tex]

To find y-coordinate of the vertex can be found out by evaluating [tex]f(h)[/tex].

[tex]k=f(h)[/tex]

Thus, for the function:

[tex]k=f(1)=(1)^2-2(1)+2[/tex]

[tex]k=f(1)=1-2+2[/tex]

[tex]k=f(1)=1[/tex]

Thus, the minimum point of the function is at (1,1).

thus, range of the function is:

[1,∞) or [tex]y\geq 1[/tex]

Explanation:

We started with x = 1 and ended up with y = -2. So the point (x,y) = (1,-2) is on the diagonal line. In other words, point P is located at (1,-2).

Answer:

I think is d I need help please

Answer:

A

Step-by-step explanation:

12f means 12 x f

+24 means you add 24

Because of pedmas, you do the multiply first so its (12xf)+24

(Also twelve four isn't a number, so B and C don't make sense)

Answer:

the answer would be A

Step-by-step explanation:

Answer:

He can cook 52 or less than 52 batches of lasagna.

Step-by-step explanation:

0.9L+0.3S≤60

Putting the value of s = 44

0.9L+0.3 (44) ≤ 60

0.9L+ 13.2 ≤ 60

0.9L ≤ 60 -13.2

L ≤ 46.8/0.9

L ≤ 52

Answer:

Eldar can cook 555 batches of lasagna at most.

Step-by-step explanation:

Well, let's see. The problem gave you an ordered pair. In other words, you have an 'x' and a 'y' coordinate. All you need to do is put them into the equation.

Step-by-step explanation:

This means that instead of --

-3x - 3y = 125 + 5y = -20

We would have:

-3(-5)-3(-5) = 125(-5) + 5(-5) = -20

From here, you just simplify it into:

30 = -650 = -20

Since the values are not the same, the ANSWER is NO. The ordered pair does not satisfy the following system of equations.

Final answer:

The ordered pair (-5, -5) does not satisfy either of the two given equations, thus it does not satisfy the system of equations.

Explanation:

To determine if the ordered pair (−5,−5) satisfies the given system of equations, we substitute x with −5 and y with −5 into each equation and check if the left-hand side equals the right-hand side.

For the first equation −3x−3y=12, substituting x and y gives us:

−3(−5) −3(−5) = 15 + 15 = 30 which does not equal 12. Therefore, the pair does not satisfy the first equation.

For the second equation 5x+5y=−20, substituting x and y gives us:

5(−5) + 5(−5) = −25 + −25 = −50 which does not equal −20. Therefore, the pair does not satisfy the second equation either.

Since the ordered pair does not satisfy both equations, we can conclude that (−5,−5) does not satisfy the system of equations.

Answer:

For 0 hours = $40

For 1 hours = $75

For 2 hours = $110

For 3 hours = $145

For 4 hours = $180

For 5 hours = $215

Step-by-step explanation:

Given equation is:- [tex]C=35n+40[/tex]

where, C=Cost in dollars, n=hours.

Now, Amy charge $40 for service call and $35 for per hour service.

So,

For 0 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 0)+40[/tex]

[tex]C=0+40[/tex]

[tex]C=40[/tex]

Therefore for 0 hours Amy charge $40.

For 1 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 1)+40[/tex]

[tex]C=35+40[/tex]

[tex]C=75[/tex]

Therefore for 1 hours Amy charge $75.

For 2 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 2)+40[/tex]

[tex]C=70+40[/tex]

[tex]C=110[/tex]

Therefore for 2 hours Amy charge $110.

For 3 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 3)+40[/tex]

[tex]C=105+40[/tex]

[tex]C=145[/tex]

Therefore for 3 hours Amy charge $145.

For 4 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 4)+40[/tex]

[tex]C=140+40[/tex]

[tex]C=180[/tex]

Therefore for 4 hours Amy charge $180.

For 5 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 5)+40[/tex]

[tex]C=175+40[/tex]

[tex]C=215[/tex]

Therefore for 5 hours Amy charge $215.

Answer:

The rate of change in number of subscriber for the six years is 3.62%

Step-by-step explanation:

Given as :

The initial subscriber of newspaper = p = 10225

The subscriber of newspaper after 6 years of publish = P = 8200

The time period = t = 6 years

Let The average yearly rate of change = r%

Now, According to question

The subscriber of newspaper after n years = initial subscriber × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, P = p × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, 8200 = 10225 × [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]

Or, [tex]\dfrac{8200}{10225}[/tex] =  [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]

Or, 0.80195 =  [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]

Taking power [tex]\dfrac{1}{6}[/tex] both side

So, [tex](0.80195 )^{\frac{1}{6}}[/tex] = [tex]((1 - \frac{r}{100} )^{6})^{\frac{1}{6}}[/tex]

Or, 0.9638 = 1 - [tex]\dfrac{r}{100}[/tex]

Or,  [tex]\dfrac{r}{100}[/tex] = 1 - 0.9638

Or,  [tex]\dfrac{r}{100}[/tex] = 0.0362

Or, r = 0.0362 × 100

i.e r = 3.62

So, The rate of change in subscriber = 3.62%

Hence, The rate of change in number of subscriber for the six years is 3.62% . Answer

Final answer:

After subtracting the manufacturing costs of the computer, monitor, and scanner from the selling price for one unit and multiplying by 408 customers, the approximate total profit is $247,050.00, which rounds to option C. $240,000.00.

Explanation:

To calculate the profit the company makes for each computer sold at $1,196.91 after giving away a monitor and a scanner, we need to subtract the cost of manufacturing the computer, monitor, and scanner from the selling price, and then multiply it by the number of customers. The costs for the computer, monitor, and scanner are $393.29, $151.44, and $46.39 respectively. Therefore, the total cost of manufacturing one set is:

Total cost = Cost of computer + Cost of monitor + Cost of scanner

Total cost = $393.29 + $151.44 + $46.39 = $591.12

The profit for one computer set would then be:

Profit per computer = Selling price - Total cost

Profit per computer = $1,196.91 - $591.12 = $605.79

To find the total profit for 408 customers, we multiply the profit per computer by the number of customers:

Total profit = Profit per computer × Number of customers

Total profit = $605.79 × 408 ≈ $247,060.32

When rounding to the nearest 50 dollars, we get:

Total profit ≈ $247,050.00

The closest answer to this would be option C. $240,000.00.

Kyle will have more time to play video games

Solution:

From given question,

Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.

5 hours of homework = 3 hours of video games

Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed.

1 hour of homework = 30 minutes of playtime

Suppose if victor spends 5 hours doing homework or reading, then he could play,

5 hours of victor homework = 30 minutes x 5 = 150 minutes of play

That is,

150 minutes = 120 + 30 = 2 hours 30 minutes

This 2 hours 30 minutes playtime of victor is less than kyle playtime (which is 3 hours )

So Kyle gets more play time

Answer:

Step-by-step explanation:

The cyclist's speed is 0.35 kilometers per minute. She will travel 0.7 kilometers in 2 minutes.

The question deals with converting speed from kilometers per hour to kilometers per minute, and also calculating distance given a certain time and speed.

First, we convert speed from kilometers per hour to kilometers per minute. There are 60 minutes in an hour, so we divide the speed of the cyclist (21 kilometers per hour) by 60: 21/60 = 0.35 kilometers per minute.

Next, we calculate the distance the cyclist will travel in 2 minutes. Distance equals rate times time, so we multiply the cyclist's speed by the time: 0.35 kilometers per minute * 2 minutes = 0.7 kilometers.

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Answer:

v= -0.61445783132

Step-by-step explanation:

Divide both sides by 8.3

-5.1 ÷ 8.3= -0.61445783132

8.3v ÷ 8.3= v

So, v=-0.61445783132

8.3v ÷ 8.3= v

Answer:

0.8

Step-by-step explanation:

We begin with the expression: [tex]0.5+(-\frac{3}{4} )+0.25-(-\frac{4}{5} )[/tex]

First, we need to convert the fractions into decimals to make this easier.

[tex]-\frac{3}{4}=-0.75[/tex] and [tex]-\frac{4}{5} =-0.8[/tex]

Once we have this, we can simplify it

[tex]0.5-0.75+0.25-(-0.8)\\\\0.5-0.75+0.25+0.8\\\\0.75-0.75+0.8\\\\0.8[/tex]

Answer: the answer would be c

Step-by-step explanation:

Answer:

y+2=2(x+1)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-(-2))/(2-(-1))

m=(4+2)/(2+1)

m=6/3

m=2

y-y1=m(x-x1)

y-(-2)=2(x-(-1))

y+2=2(x+1)

Answer:

$1080 annual

Step-by-step explanation:

200(# of thousands) x 5.4

1080

n = 15 when p=$213.75 and r=$9.50

Step-by-step explanation:

Given

p = overtime pay

n = number of hours

r = hourly pay rate

It is also given that the pay for working hours varied directly with Number of hours and hourly pay rate jointly

So

It can be denoted as:

p ∝ nr

It can also be written as:

[tex]p = knr[/tex]

where k is the constant of proportionality

Putting the given values of p,n and r in the equation

[tex]103.44 = k * 8 * 8.62\\103.44 = 68.96k\\k = \frac{103.44}{68.96}\\k = 1.5[/tex]

So the equation is now,

p = 1.5nr

Putting

p = 213.75

r = 9.50

[tex]213.75 = 1.5 * n * 9.50\\213.75 = 14.25n\\n = \frac{213.75}{14.25}\\n = 15[/tex]

Hence,

n = 15 when p=$213.75 and r=$9.50

Keywords: Proportion variation

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