Answer:
=204.13 inches.
Step-by-step explanation:
Using the side x, we can use sine to find the hypotenuse of the triangle with the angle marked 30°.
Sin 30 =x/hypotenuse.
sin 30 = 27/hyp
hyp= 27/sin 30
=54 inches
We can also find the adjacent as follows.
Cos 30 = adjacent/ 54
Adjacent= 54 cos 30
=46.77 inches
Using the angles marked 45 we can find the hypotenuse of the isosceles triangle.
sin 45= x/hypotenuse
sin 45 =27/hypotenuse
hypotenuse = 27/sin 45
=38.18 inches
The hypotenuse of both the triangles making the isosceles triangle are 38.18 inches long.
Perimeter = 54+ 46.77+27+ 38.18+38.18
=204.13 inches.
For both of the contests, the variable is the number of competitors which we can set as x.
Consequently, the equation should be 5.50x+34.60=4.25x+64.60
5.50x=4.25x+30
1.25x=30
x=24
The fee of the contests is the same when there are 24 competitors
Answer:
a. $270
b. $3,278.18
Step-by-step explanation:
Given that
The principal amount is $3,000
Annual rate of interest is 3%
And, the time period is 3 years
We need to find out the simple interest & compound interest
The following formulas should be used
a. For simple interest
= Principal × rate of interest × time period
= $3,000 × 3% × 3 years
= $270
b. For compound interest
= Principal × (1 + rate of interest)^time period
= $3,000 × (1 + 0.03)3
= $3,000 × 1.03^3
= $3,278.18
From the very beginning, each door had a 1/3 probability chance to be holding the grand prize. And the fact that she saw the consolation prize behind one of them does not change this probability.
From the beginning, all doors had equal chances.
Based on this, the answer to your question would be:
She could either accept or not accept the host's offer <span>because the probabilities of the three doors were equal from the beginning.</span>
Answer:
The solutions of the equation |2 x-3|=17
are x=10
and x=-7
Step-by-step explanation:
Given equations is |2 x-3|=17.
It is required to find out the values of x satisfying the given equation.
To find it out, use the fact that the solution of this type of equation is 2x-3=17.
Or 2x-3=-17 and simplify the equations using simple mathematical operations.
Step 1 of 2
Solve the equation 2x-3=17,
Add 3 on both sides of the equation 2x-3=17,
2x-3+3=17+3
2x=20
Divide by 2 on both sides of the equation 2x=20,
Step 2 of 2
Solve the equation 2x-3=-17,
Add 3 on both sides of the equation 2x-3=-17,
Divide by 2 on both sides of the equation 2x=-14,
