Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?

Answer:

Option (4) 12.2

Step-by-step explanation:

Hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation

y = 3.06 sin ( 0.017x - 1.40 ) + 12.23

We have to calculate the hours of daylight from the given equation for February 14, 2013.

From January 1, 2013 to February 14, 2013 number of days = 31 + 14 = 45 days.

Now we place x = 45 days in the equation

y = 3.06 sin (0.017 × 45 - 1.40) + 12.23

= 3.06 sin ( 0.765 - 1.40 ) + 12.23

= 3.06 sin ( - 0.635 ) + 12.23

= 3.06 ( - 0.0111) + 12.23

= -0.0339 + 12.23 = 12.196 = 12.20

Option (4) 12.2 is the correct answer.

The number of hours of daylight for the model for February 14 , 2013 is 12.2

Given data:

The function is represented as y=3.06sin(0.017x-1.40) + 12.23

To find the number of hours of daylight predicted by the model for February 14, 2013, substitute the corresponding value of x into the equation and evaluate it.

The total number of days , x = 31 days in January + 14 days in February

So, x = 45

Now, substitute x = 45 into the equation:

y = 3.06sin(0.017(45) - 1.40) + 12.23

Calculating the expression inside the sine function:

0.017(45) - 1.40 = -0.635

Substituting this value back into the equation:

y = 3.06sin(-0.635) + 12.23

The sine of -0.635 is approximately -0.593.

y = 3.06(-0.593) + 12.23

y ≈ 10.425

Rounding to the nearest tenth, the predicted number of hours of daylight for February 14, 2013, is 10.4.

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The probability that a student is male or a nursing major is expressed by the formula P(M OR N) = P(M) + P(N) - P(M AND N), which requires actual data to calculate.

To find the probability that a student is male or a nursing major, we can use the principle of addition in probabilities. Let's denote P(M) as the probability that a student is male, P(N) as the probability that a student is a nursing major, and P(M AND N) as the probability that a student is both male and a nursing major. The formula for the probability of either event occurring is given by P(M OR N) = P(M) + P(N) - P(M AND N). We need actual data to calculate these probabilities.

Since we don't have the actual probabilities, we can only provide the symbolic representation of the required probability as P(M OR N). However, if the events of being male and majoring in nursing are mutually exclusive (which in reality, they are not), the probability would simplify to just the sum of the two individual probabilities, P(M) + P(N).

Answer:

The answer for number one is $5.21. NOT $6.25

Step-by-step explanation:

The amount deducted from the paychecks are: 6.25 dollars

The annual premium of Dawson is D.$2462.40

To get Karas annual premium

$1000 of coverage.

$50,000  at 2.50 dollars cost

since she is paid semi monthly

2.50 / 2 = 1.25

annual premium = 1.25 / 100 * 50

= 6.25 dollars

2. Under 20 year coverage for a 40 - 44 year old mail we have $13.68 as the amount

180000 / 1000

= 180

180 x 13.68

= D.$2462.40

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Answer: C.) (20, 4, 5)

Step-by-step explanation:

The given system is

[tex]3x + 10y-12z = 40.....................(1)\\x-5y =0..........................(2)\\x- 4z=0............................(3)[/tex]

From (2), we have

[tex]x=5y\\\Rightarrow\ y=\frac{x}{5}[/tex]

From (3)

[tex]x=4z\\\Rightarrow\ z=\frac{x}{4}[/tex]

Substitute the values of y and z in equation (1), we get

[tex]3x+10(\frac{x}{5})-12(\frac{x}{4})=40\\\\\Rightarrow\ 3x+2x-3x=40\\\\\Rightarrow\ 20x=40\\\\\Rightarrow\ x=5[/tex]

Then [tex]y=\frac{20}{5}=4[/tex]

and  [tex]z=\frac{20}{4}=5[/tex]

Hence, the solution of the given system is (20,4,5)

Answer:

∠B=157°

Step-by-step explanation:

It is given that Quadrilateral ABCD ​is inscribed in the circle.

Also, we know that if the Quadrilateral ABCD ​ is inscribed in the circle, then the opposite angles of the quadrilateral are supplementary by the property of circles. Then,

∠B+∠D=180°

⇒[tex]x+6x+19=180[/tex]

⇒[tex]7x+19=180[/tex]

⇒[tex]7x=161[/tex]

⇒[tex]x=23^{{\circ}}[/tex]

Thus, the value of ∠B=6x+19=6(23)+19=138+19=157°.

Answer:

10 m

Step-by-step explanation:

I did the test

A photographer is planning to enlarge a photograph by a scale factor of 1:5 . The original photograph has an area of 154 square inches.

Solution:

The photograph is being enlarged by a factor 5.

So, each dimension of the photograph is enlarged by 5

So, area is enlarged by [tex] 5^{2} [/tex]

Or, Area is enlarged by a factor=5*5=25

So, the Area of enlarged photograph=[tex] 5^{2} [/tex] *Area of original photograph

Area of enlarged photograph=25*Area of original photograph

Area of enlarged photograph=25*154

On multiplying 25 by 154 we get 3850

Area of enlarged photograph=3850[tex] inches^{2} [/tex]

Answer:

Area of new photograph=3850[tex] in^{2} [/tex]

Answer:

The GCF of following literal terms is [tex]m^1n^4p^3[/tex].

Step-by-step explanation:

The given literal terms are

[tex]m^7n^4p^3[/tex]

[tex]m^1n^{12}p^5[/tex]

The factored form of the given terms are

[tex]m^7n^4p^3=m\times m\times m\times m\times m\times m\times m\times n\times n\times n\times n\times p\times p\times p[/tex]

[tex]mn^{12}p^5=m\times n\times n\times n\times n\times n\times n\times n\times n\times n\times n\times n\times n\times p\times p\times p\times p\times p[/tex]

The common factors are m,n,n,n,n,p,p,p. So, the G.greatest common factors is

[tex]GCF=m\times n\times n\times n\times n\times p\times p\times p[/tex]

[tex]GCF=m^1n^4p^3[/tex]

Therefore the GCF of following literal terms is [tex]m^1n^4p^3[/tex].

Answer:

0.9cm

Step-by-step explanation:

That was the answer on my assignment.

Answer:

A. r2 = 294 square feet ÷ 4π