Princess Poly and Prince Digit are trying to find out who is taking all of Poly's potato crisps from the pantry. While they're investigating, they come across the royal handyman, Wizard N. Gineer, who is checking whether the air conditioner (AC) is working properly in the castle. The King is complaining that the castle is too hot. Poly and Digit ask Mr. N. Gineer if he has seen anyone lurking around the pantry, and he tells them he will offer some advice if they help him perform some calculations related to the AC issues. Poly and Digit agree to help the handyman in order to gather potential evidence. "The King thinks the AC was particularly inefficient yesterday," Wizard N. Gineer tells them, "but I think the AC is working properly. I determined that the function f(x)=24−5cosπ12t represents the outside temperature in degrees Celsius, where t represents the number of hours past midnight yesterday. I want to calculate the hours during which the air conditioner was cooling the castle and show the results to the King." Help ensure that Poly and Digit receive some helpful advice from the royal handyman by using the handyman's function to answer the following questions.

Add 5 to both sides.

x−5+5≥9+5

Answer: x≥14

Answer:

The perimeter of [tex]\triangle DMN[/tex] will be 62.1939...

Step-by-step explanation:

In [tex]\triangle DMN[/tex], the length of side [tex]DM = 10\sqrt{3}[/tex] and the measures of [tex]\angle M[/tex] and [tex]\angle N[/tex] are 75° and 45° respectively.

As the sum of all angles in a triangle is always 180°, so the measure of [tex]\angle D[/tex] will be:  180°- (75°+45°) = 180°- 120° = 60°

Now using Sine rule, we will get......

[tex]\frac{MN}{Sin(D)}=\frac{DN}{Sin(M)}=\frac{DM}{Sin(N)}\\ \\ \frac{MN}{Sin(60)}=\frac{DN}{Sin(75)}=\frac{10\sqrt{3}}{Sin(45)}\\ \\ MN= \frac{10\sqrt{3}}{Sin(45)}*Sin(60)=21.2132...\\ \\ DN=\frac{10\sqrt{3}}{Sin(45)}*Sin(75)=23.6602...[/tex]

So, the perimeter of [tex]\triangle DMN[/tex] will be: [tex]DM+MN+DN = 10\sqrt{3}+21.2132...+23.6602... =62.1939...[/tex]

The area of a rectangle is the width times the length:

[tex] A = w\cdot l \iff 228 = w\cdot 12 \iff w = \dfrac{228}{12} = 19 [/tex]

The perimeter is twice the sum of the dimensions:

[tex] 2p = 2(12+19) = 2\cdot 31 = 62 [/tex]

The perimeter of the rectangle with dimensions 19 ft*12 ft comes to be 62 square feet.

Suppose the breadth of the rectangle is x.

The perimeter of a rectangle is the sum of all its sides i.e. the sum of two lengths and two breadths.

If length and breadth are a and b respectively then perimeter =2(l+b).

According to the question

Length =12 ft

Area=228 square ft

So, length * breadth = 228

[tex]12x =228[/tex]

[tex]x=\frac{228}{12}[/tex]

x=19

So, breadth of the rectangle =19 ft

So, perimeter = 2(12+19) = 62 square feet.

Hence, the perimeter of the rectangle with dimensions 19 ft*12 ft comes to be 62 square feet.

To get more about rectangles visit:

https://brainly.com/question/25292087

[tex]8x > -32\qquad|\text{divide both sides by 8}\\\\x > -4\\-----------------------------------\\\\6x\leq-48\qquad|\text{divide both sides by 6}\\\\x\leq-8\\\\Answer:\ c)\ x > -4\ or\ x\leq-8[/tex]

Answer:

[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]

C is correct

Step-by-step explanation:

In the given graph function break at point x=2.

Left side about point x=2 is parabolic and right side straight line.

So, it would be piece wise function.

For parabola:

vertex: (0,4) and passing point (2,8)

[tex]y=a(x-h)^2+k[/tex]

[tex]y=ax^2+4[/tex]

[tex]a=1[/tex]

[tex]y=x^2+4[/tex]    For x<2

For straight line:

Twp points (4,0) and (2,2)

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-2=\dfrac{0-2}{4-2}(x-2)[/tex]

[tex]y-2=-1(x-2)[/tex]

[tex]y=-x+4[/tex]     For x≥2

Hence, The piece wise function will be

[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]

Answer:

12.5

Step-by-step explanation:

Using mathematical operations we know that 170 straws were used in all.

So, the total straws used:

Then, calculate as follows:

Therefore, using mathematical operations we know that 170 straws were used in all.

Know more about mathematical operations here:

https://brainly.com/question/28937023

#SPJ2

All we have to do is divide 120 by 15

120 ÷ 15 = 8

Therefore, it will take 8 hours to drive 120 miles at a speed of 15 mph

Hope this helps

-AaronWiseIsBae

15miles = 60minutes

divide 15 by 120 which equals 8

8 times 60 equals 480

your answer should be 8 hours

precise and accurate are two different things in measurements:

most precise means the most detailed. here Alice has 2 decimals so her measurements are the most precise.

but her measurements are very different so they are not accurate.

most accurate measurements are Ivan's as they are very close to each other.

Answer:

✔ Ivan

 took the most accurate measurements.

✔ Alice

took the most precise measurements.

Step-by-step explanation:

got it right:)

Marc and Corlina will have the same amount of CD's after 8 months.

45 + 4(8) = 77

61 + 2(8) = 77

Answer:

12.36

Step-by-step explanation:

Answer:

Its: 12.36

Step-by-step explanation:

To solve this problem you must think in this way.

First we see that function y is greater than 3-x, conclusion is the following

shaded area must be above function. That condition is satisfied by the graph 3 and 4.

Then we write inequality in the slope form  y> -x+3.

We see that the coefficient of direction is -1 (negative) which mean that the graph is decreasing. That condition is satisfied by the graph No 4.

The correct answer is graph number 4 ( or D.)

Good luck!!!

Answer:

5x^2+x+1

Step-by-step explanation:

the expression for f(x) - g(x) is 5x² - 9x - 1.

To find f(x) - g(x), we simply subtract the expression for function g(x) from the expression for f(x):

f(x) - g(x) = (5x² - 4x) - (5x + 1)

Now, let's simplify the expression by combining like terms:

f(x) - g(x) = 5x² - 4x - 5x - 1

Next, combine the x terms:

f(x) - g(x) = 5x² - (4x + 5x) - 1

Now, combine the x terms inside the parentheses:

f(x) - g(x) = 5x² - 9x - 1

So, the expression for f(x) - g(x) is 5x² - 9x - 1.

Learn more about function here

https://brainly.com/question/32638049

#SPJ2

667 pounds is the answer. There are 2000 pounds in a ton.  1/3 of a ton is 666.666667 pounds.  I think this question is a conversion from tons to pounds?

Answer: 546

Step-by-step explanation:

   14     ⇒    10 + 4    

x  39     ⇒   30 + 9      

   36 |   ←    9 x 4

   90 |   ←    9 x 10

  120 |   ←  30 x 4

 300 |   ←  30 x 10

 546

Last month, Carrie had 14 coins.

First we have to see which is the right angle.  This triangle has its legs oriented parallel to the axes. (-3,-1) and (1,-1) form the horizontal leg, (1,-1) and (1,2) the vertical leg.  

So the right angle vertex is (1,-1) and the hypotenuse endpoints are (-3,-1) and (1,2)

The length is given by

[tex]d = \sqrt{ (1 - -3)^2 + (2 - -1)^2} = \sqrt{4^2+3^2}=\sqrt{25} = 5[/tex]

This is a 3/4/5 right triangle.

Answer: 5

Answer:

4/9 probability

Step-by-step explanation:

Imagine winning something, there's 3 possible prizes that you get to choose from and get to keep let's say 4 days? These all written on the paper that you must pull from a box.

Your three prizes are

             D1    D2   D3    D4

1. a car

2. a bike

3. skateboard.

Now if you can imagine a grid and you mark 1 dot in each day we'll end up with 12 slots total.

Let's say you don't want a skateboard you rather have a car or a bike. We need to figure out of the 12 possibility (assuming all are equal) What's the possibility of you pulling out anything BUT a skateboard?

You want at least 3 days in either or. So we must find P = (Days without skateboard)

We know it's all equal outcomes, you're going to get 1 day of that 1 item.. soo..

p (DWS) = _____

                 12 outcomes

Now you want how many days MORE THAN 3, can you use anything but the skateboard?

You have 3 & 4 days with a car...

You have 3 or 4 days with a bike.. Which gives us 4 of the days we do want!

Giving your final problem the looking like this .. P(DWS) = 4/9

In respects/C to KhanAcademy.

Answer:

4/9 probrabitaty

Step-by-step explanation:

I'm so sorry if these are wrong...

1. y=-7/5x-3

2. y=1x+6

3. y=5/4x-8

4. y=1/4x-2

5.y=-5x-2

6. y=-2/5x-3

7. y=5x+19

8. y=2x-6

9. y=-4/5x-5

10. y=-4/5x+4

Given function: P(x) = -10x + 80.

Where function represents the amount of granola, in ounces and x represents the number of ounces Paula puts in each bag.

Range of the function is the values of the function we would get.

That is the amount of granola in ounces for different x values.

For x=0 the number of ounces would be -10(0)+80 = 80.

And for x=8, it would be -10(8) + 80 = 0.

But even we could take decimal values too.

Like x=0.5 ounces, x=0.55 ounces etc.

And that 0.55 would give a decimal value.

Therefore, we can take any real number for x between 0 and 8.

But we need to find the range.

So, the range would be between 0 and 80 and it could be any real number.

Therefore, correct option is :

C. all real numbers between and including 0 and 80.

it is A. for all plato users

need more info in order to kinda see how many women there were

[tex]24 > -3r\geq-9\ \ \ \ |\text{change the signs}\\\\-24 < 3r\leq9\ \ \ \ |\text{divide both sides by 3}\\\\\boxed{-8 < r\leq3}[/tex]

Inequalities are used to represent unequal expressions.

The solution to [tex]24>-3r \ge -9[/tex] is [tex]-8<r \le 3[/tex]

Given

[tex]24>-3r \ge -9[/tex]

Divide through by -3

[tex]\frac{24}{-3}>\frac{-3r}{-2} \ge \frac{-9}{-3}[/tex]

Negative division changes the inequality sign

So, we have:

[tex]-8<r \le 3[/tex]

Hence, the solution to [tex]24>-3r \ge -9[/tex] is [tex]-8<r \le 3[/tex]

See attachment for the graph of [tex]-8<r \le 3[/tex]

Read more about inequalities at:

https://brainly.com/question/15137133

Answer:

0.85 mile(rounded to nearest hundredth)

Step-by-step explanation:

We have to convert 1500 yards into miles.

To convert 1500 yards into miles, we first need to know the relation between yards and miles.

So we have,

[tex]1 \:\text{mile}=1760\:\text{yards}[/tex]

Now, to convert 1500 yards into miles, we need to know how many miles are there in 1 yard.

So, we have

               [tex]1\:\text{yard}=\frac{1}{1760} \:\text{miles}[/tex]

[tex]\implies1500 \:\text{yards}=\frac{1500}{1760} \:\text{mile}[/tex]

[tex]\implies1500 \:\text{yards}=\frac{150}{176} \:\text{mile}[/tex]

[tex]\implies1500 \:\text{yards}= \frac{75}{88}\:\text{mile}[/tex]

[tex]\implies1500 \:\text{yards}= 0.85\:\text{mile}[/tex]

Hence, 1500 yards is 0.85 mile, rounded to nearest hundredth.

The number 87.65487.65487, point, 654 can be placed on a place value chart as follows:

Tens Ones . Tenths Hundredths Thousandths

888 777 ..point 666 555 444  

Decimal place value

The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.

Example: 0.810.810, point, 81

The number 0.\blueD8\greenD10.810, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD is made up of \blueD88start color blueD, 8, end color blueD tenths and \greenD11start color greenD, 1, end color greenD hundredth.

We can also write this as:

0.\blueD8\greenD1=\blueD{0.8}+\greenD{0.01}0.81=0.8+0.010, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, 0, point, 8, end color blueD, plus, start color greenD, 0, point, 01, end color greenD

or

0.\blueD8\greenD1=\blueD{\dfrac8{10}}+\greenD{\dfrac1{100}}0.81=  

10

8

​  +  

100

1

​  0, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, start fraction, 8, divided by, 10, end fraction, end color blueD, plus, start color greenD, start fraction, 1, divided by, 100, end fraction, end color greenD

Or we can use a place value chart:

Ones . Tenths Hundredths

000 ..point \blueD88start color blueD, 8, end color blueD \greenD11start color greenD, 1, end color greenD

Want to learn more about decimal place value? Check out this video.

Want to review whole number place value? Check out this article.

Practice

Answer:

A. It is the total cost for entertainment and cleaning.

Step-by-step explanation:

If we look at the information it says:

Facility rental is dependent upon number of hours we are renting the facility for.

Linen, food, and decoration also depends upon the number of attendees. Also, the table decorations depend upon the number of attendee.

The things that are independent of the number of attendees are entertainment and cleaning fee. These are fixed charges.

So, the total cost for entertainment and cleaning are the constants in the expression. This is the amount that will remain constant regardless of the number of attendees.

ANSWER

In 16 years time.

EXPLANATION.

If the number of subscribers is 324 million, then it means

[tex]f(t)=324[/tex]

But we were given that,

[tex]f(t)=18.997t+16.711[/tex]

This implies that,

[tex]324=18.997t+16.711[/tex]

We now solve for t,

[tex]324-16.711=18.997t[/tex]

[tex]307.289=18.997t[/tex]

[tex]\frac{307.289}{18.997}=t[/tex]

[tex]16.17566=t[/tex]

That will be approximately in the 16th year.

In order to calculate the year where the number of US cell phone subscribers matches a certain number using the given linear model equation, you solve for the time variable. With the specified 324 million subscribers, the corresponding year would be approximately 2011.

To use the provided linear model F(t) = 18.997t + 17.711 to predict the year where the number of subscribers will be 324 million, we need to solve the equation for t with C(t) set to 324:

324 = 18.997t + 17.711

To do so, subtract 17.711 from both sides to isolate the term with t:

324 - 17.711 = 18.997t

Then, divide both sides by 18.997 to solve for t:

(324 - 17.711) / 18.997 = t

After calculating, you will get approximately t = 16.123. Remember, t is the number of years after 1995, so you would add 16 (rounded from 16.123) to 1995. Thus, the model predicts that the number of US cell phone subscribers will reach 324 million in 2011.

https://brainly.com/question/29122305

#SPJ3