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2 years ago

Which expression gives the value of QR?

Mathematics

1 answer:

Montano1993 [528]2 years ago

8 0

Answer:

Step-by-step explanation:

using the Sine Rule in Δ QRS

$\frac{QR}{sinS}$ = $\frac{RS}{sinQ}$ ( substitute values )

$\frac{QR}{sin52}$ = $\frac{67}{sin80}$ ( cross- multiply )

QR × sin80° = 67 × sin52° ( divide both sides by sin80° )

QR = $\frac{67sin52}{sin80}$

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Paul needs to buy paint to cover all outside surfaces of his shed, depicted below. How much area, in square yards, does he need

Alekssandra [29.7K]

Answer:

Area = 145.7 Square yards

Step-by-step explanation:

Since there is no picture attached to depict the house and its dimension, I am taking values of a similar problem.

Dimensions of Shed

2 walls with dimensions of 15 ½ ft. by 12 ft.

2 walls with dimensions of 25 ¼ ft. by 12 ft.

Ceiling with dimensions of 15 ½ ft. by 25 ¼ ft.

2 windows that are each 2 ft. by 4½ ft. as well as an 8-ft. by 5-ft. door

Solution

We need to find the total wall area and ceiling area which when combined will give us the total area shed's outer surface that needs to be painted.

For total area of the wall, we need to first find the sum of area for each wall and subtract area of windows and door

Wall Area = Area of 1st two walls+Area of other two walls-Area of 2 windows-Area of door=[15.5(12)(2)] + (25.25) (12) (2) - (2)(2) (4.5) -(8)(5)

Wall Area = 371 + 606 - 17 - 40

Wall Area = 920 square ft = 102.2 square yards

Ceiling Area is just the area of the ceiling

Ceiling Area = (15.5) (25.25 )

Ceiling Area = 391.375 square ft= 43.486 square yard

Total Area = Wall Area+Ceiling Area =102.2+43.486=145.7 Square yards

Which is the area paul needs to cover with paint.

Note: Converted Square foot to square yard as the problem requires that.

8 0

3 years ago

some psychologists believe that a genius should be defined as anyone having an IQ over 140. If IQ scores are normally distribute

denis23 [38]

Answer:

61,239,550

Step-by-step explanation:

We let the random variable X denote the IQ scores. This would imply that X is normal with a mean of 100 and standard deviation of 17. We proceed to determine the probability that an individual chosen at random from the population would be a genius, that is;

Pr( X>140)

The next step is to evaluate the z-score associated with the IQ score of 140 by standardizing the random variable X;

$Pr(X>140)=Pr(Z>\frac{140-100}{17})=Pr(Z>2.3529)$

The area to the right of 2.3529 will be the required probability. This area from the standard normal tables is 0.009314

From a population of 6,575,000,000 the number of geniuses would be;

6,575,000,000*0.009314 = 61,239,550

6 0

4 years ago

Read 2 more answers

How many gallons of gas are left after driving 200 miles

BaLLatris [955]

The equation y = -0.04x + 12 gives the number of gallons of gas in your car where x is the number of miles drivene

easy

y=gas left
x=miles

sub 200 for x
y=-0.04(200)+12
y=-8+12
y=4

4 gallons left

8 0

3 years ago

Help me please I will give brainliest

ExtremeBDS [4]

The correct answer would be B because it is is written in correct simplified format

8 0

3 years ago

A person borrows $10,000 and repays the loan at the rate of $2,400 per year. The lender charges interest of 10% per year. Assumi

omeli [17]

Answer:

a) $M(t)=24000-14000e^{t/10}$

b) It takes 5.390 years to pay off the loan.

Step-by-step explanation:

(a) The differential equation for the variation in the amount of the loan M is

$\frac{dM}{dt}=0.1M-2400$

We can express this equation as:

$\frac{dM}{dt}=0.1M-2400\\\\10\int \frac{dM}{M-24000} =\int dt\\\\10ln(M-24000)=t\\\\M-24000=Ce^{t/10}\\\\M=Ce^{t/10}+24000\\\\M(0)=Ce^{0/10}+24000=10000\\\\C+24000=10000\\\\C=-14000\\\\M(t)=24000-14000e^{t/10}$

(b) We can calculate this as M(t)=0

$M(t)=24000-14000e^{t/10}=0\\\\e^{t/10}=24000/14000=1.714\\\\t=10ln(1.714)=10* 0.5390=5.390$

It takes 5.390 years to pay off the loan.

8 0

3 years ago