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igomit [66]
2 years ago
10

The Parker family drove a total of 180 miles on the road trip. This distance is 1.5 times the distance they drove on the first d

ay. How many miles did the Parker family drive on the first day?
​
Mathematics
1 answer:
Veronika [31]2 years ago
4 0

Parker family drove 120 miles on the first day

Step-by-step explanation:

Given:

Total miles driven on the road trip= 180 miles

solution:

Lets assume the distance drove on the first day is x

The total distance covered on the road trip is 180 miles.  so,

(x) *1.5 = 180

x=\frac{180}{1.5}

Hence, x = 120.

The distance travelled on the first day is 120 miles.

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If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this
otez555 [7]

Answer:

10

Step-by-step explanation:

If there is a direct relation between two variables x and y then it can be represented as

y = kx ,

where y is dependent variable

x is  independent variable

k is constant of variation

_____________________________

First condition

y = 400

x = r

using y = kx then relationship will be

400 = kr

finding k here

k = 400/r

Second condition

y = r

x = 4

using y = kx then relationship will be

r = 4k

finding k

k = r/4

since  in both condition equation is same

thus, value of k will also be same

thus,

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

\sqrt{r^{2} }  = \sqrt{1600} \\r = 40

Thus, 40 is the value of r

k = r/4 = 40/4 = 10

Thus, constant of variation is 10 which is correct choice.

To cross validate

k = 400/r = 400/40 = 10

7 0
1 year ago
Read 2 more answers
Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean an
vovangra [49]

Let's assume initial population is in 1999

so, production of passenger cars in Japan is 3.94 million in 1999

so, P=3.94 million

and the  production of passenger cars in Japan is 6.74 million in 2009

so, A=6.74 million in t=2009-1999=10 years

now, we can use formula

A=P(1+r)^t

here , r is interest rate

so, we can plug values

6.74=3.94(1+r)^{10}

now, we can solve for

\left(1+r\right)^{10}=\frac{337}{197}

r=0.05516

so,

the geometric mean annual percent increase is 5.516%............Answer

7 0
1 year ago
L = loudness, in decibels (dB); I = sound intensity, in watts/m2; I0 = 10−12 watts/m2
irina [24]
The sound intensity of the Pile Driver is 39.5
 or nearly 40 times the sound intensity of the jackhammer.


Given with Loudness in dB for pile driver = 112 dB
We have to convert it in terms of sound intensity.
First,
112dB/10 = 11.2 

Then we'll use this as exponent of 10
(10)^(11.2) = 1.5849 * 10 ^ 11

Then use the equation of Watts per square meter to find the intensity:
I / (10^-12 W/m^2) =1.5849 * 10 ^ 11
I = sound intensity = 0.158

Then compare:

Sound intensity of Pile Driver/ Sound intensity of Jackhammer
(0.158) / (0.004)
= 39.5
or nearly 40 times the jackhammer.
3 0
2 years ago
Read 2 more answers
A bicycle wheel with diameter 16 inches rides over a screw in the street. The screw is on level ground before it punctures the b
Julli [10]

Answer:

The correct option is;

16 inches

Step-by-step explanation:

The parameters of the motion given are;

The diameter, D of the bicycle = 16 inches;

The distance the bike moves (forward) after the screw punctures the tire = 56·π inches

We note that the circumference of the bicycle = π·D = π × 16 = 16·π inches

Therefore;

56·π inches/(16·π inches) = 3.5

Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.

The height, h of the screw in the final half turn is given by the relation;

h = A×cos(Bx - C) + D

A = Amplitude of the motion = Diameter/2 = 16/2 = 8

P = The period of the motion 2·π/B

B·x = The angle described by the motion = Half of one revolution = π = 180°

C = Phase shift = π

D = The midline = Diameter/2 = 8 inches

Therefore;

h = 8×cos(π - π) + 8 = 16 inches

After the bike moves forward another 56·π inches the height of the screw = 16 inches.

3 0
2 years ago
Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and th
il63 [147K]

Answer:

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U

Step-by-step explanation:

The expression below means RS/VU = ST/UT

See the attachment for better explanation.

6 0
2 years ago
Read 2 more answers
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