admin

2 months ago

Guest #10047

2 months ago

i think it would be 30 ways

Question

At 59 F, crickets chirp at a rate of 76 times per minute, and at 65 F they chirp 100 times per minute. Write an equation in slope-intercept form that represents the situatio.

Solution 1

Y = 4x-160 is your simplified answer to this question.

Question

A math book sells for $106.50. (a) find the amount of sales tax, to the nearest cent, if the sales tax rate is 8.5%. (b) find the total purchase price

Solution 1

if the sales tax rate is 8.5% ."

→ 8.5% of 106.50 = (8.5/100) * 106.50 = 0.085 * 106.50 ;

= 9.0525 ;

→ round to the nearest cent:

→ $ 106.50

+ 9.05

Question

A rectangle has a perimeter of 34 cm and an area of 52 cm2. its length is 5 more than twice its width. write and solve a system of equations to find the dimensions of the rectangle

Solution 1

Width=4cm

length=13cm

length=13cm

Question

A rectangular prism has a volume of 150 cm3. if the height measures 3 cm and the width measures 2 cm, what must the length be to achieve the given volume?

Solution 1

A Legnth of 25 must be achieved

3 x 2 x 25 = 150

3 x 2 x 25 = 150

Question

A square can be changed into a rectangle by increasing the length of the square by 5 units and increasing the width by 3 units. which expression represents the area of the rectangle in square units?

Solution 1

To represent the area of this rectangle, you will write expressions that represents the new length and the new width. x Will represent the original side length.

l = x + 5

w = x - 3

A= lw

(x + 5)(x - 3)

This becomes x^2 + 2x - 15.

l = x + 5

w = x - 3

A= lw

(x + 5)(x - 3)

This becomes x^2 + 2x - 15.

Question

A circle has a radius of 7.2 feet and a central angle aob that measures 112°. what is the area of sector aob? use 3.14 for pi and round your answer to the nearest tenth.

Solution 1

The area of the sector will be given by:

A=θ/360πr²

but

θ=112°, r=7.2 ft, π=3.14

hence

A=112/360×3.14×7.2²

A=50.64192 ft²

A~50.6 ft²

A=θ/360πr²

but

θ=112°, r=7.2 ft, π=3.14

hence

A=112/360×3.14×7.2²

A=50.64192 ft²

A~50.6 ft²

Question

A car rental company has two rental rates. rate 1 is $64 per day pluus $.16 per mile. rate 2 is $128 per day plus $.08 per mile. if you planto rent for one day, how many miles would you need to drive to pay less by taking rate 2

Solution 1

D is days

m is miles

0.16m + 64d (this is rate 1)

0.08m + 128d ( this is rate 2)

since you plan to rent for one day, input d as 1.

0.16m + 64(1)

0.08m + 128(1)

i hope i gave you enough hints

m is miles

0.16m + 64d (this is rate 1)

0.08m + 128d ( this is rate 2)

since you plan to rent for one day, input d as 1.

0.16m + 64(1)

0.08m + 128(1)

i hope i gave you enough hints

Question

A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

Solution 1

Trip upstream took 90v−390v−3 hours and trip downstream took 90v+390v+3 hours. Also given that the difference in times was 1212 hours --> 90v−3−90v+3=1290v−3−90v+3=12;

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

Question

Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)

Solution 1

The volume of the ball is given by:

V = (4/3) πr ^ 3

Deriving we have:

V '= (3) (4/3) (π) (r ^ 2) (r')

Clearing r 'we have:

r '= V' / ((3) (4/3) (π) (r ^ 2))

Substituting values:

r '= 4 / ((3) (4/3) (π) ((24) ^ 2))

r '= 0.000552621 c / min

Then, the surface area is:

A = 4πr2

Deriving we have:

A '= 8πrr'

Substituting values:

A '= 8π (24) (0.000552621)

A '= 0.33 cm ^ 2 / min

**Answer:**

**The surface area of the balloon is shrinking at:**

**A '= 0.33 cm ^ 2 / min**

V = (4/3) πr ^ 3

Deriving we have:

V '= (3) (4/3) (π) (r ^ 2) (r')

Clearing r 'we have:

r '= V' / ((3) (4/3) (π) (r ^ 2))

Substituting values:

r '= 4 / ((3) (4/3) (π) ((24) ^ 2))

r '= 0.000552621 c / min

Then, the surface area is:

A = 4πr2

Deriving we have:

A '= 8πrr'

Substituting values:

A '= 8π (24) (0.000552621)

A '= 0.33 cm ^ 2 / min

Question

How much would it be to get 67.1 to 73.3?

Solution 1

6.2.. 73.3 - 67.1 = 6.1...

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