8 mi. 133 yd. 2 ft. – 5 mi. 107 yd. 2 ft.

faltersainse [42]

Answer:

$x+2y-z=5 ...(1)\\ -x-y+2z=-13...(2) \\ 2x+y-2z=14...(3) \\ \\ add \: (2) + (3) \\\boxed{x= 1} \\ 2 \times (1) + (2) \\ x + 3y = - 3 \\ 1 + 3y = - 3 \\ 3y = - 4 \\ \boxed{y = - \frac{4}{3} }\\ solve \: for \: z \\ x + 2y - z = 5 \\ 1-\frac{4}{3}(2)-z=5\\3-8-3z=15\\3z=-20\\\boxed{z = - \frac{20}{3} }$

3 0

3 years ago

A car can travel 400 miles on a full tank of petrol. A more efficient car can travel 30% further. How many miles further can it

xxTIMURxx [149]

Answer:160 miles

Explanation:

You can work out this type of question by using the 'unitary' method, which means finding out how much for ONE.

If you set out the steps with short sentences it will be clearer.

On 15 gallons, a car can travel 400 miles÷15↓

On 1 gallon, a car can travel 400÷15=262

miles

Once you know the distance travelled on 1 gallon of fuel, you can work out the distance travelled for any number of gallons.

On 6 gallons the car can travel

6

×

26

2

3

miles.

(6 times further than on 1 gallon)

6

×

80

3

=

160

miles

4 0

3 years ago

One year Roger had the lowest ERAâ€‹ (earned-run average, mean number of runs yielded per nine inningsâ€‹ pitched) of any male p

baherus [9]

Answer:

(a) The z-score of Roger is -1.56 and the z-score of Amber is -1.13.

(b) Roger had a better year relative to his peers.

Step-by-step explanation:

If X follows N (µ, σ₂), then $z=\frac{x-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z follows N (0, 1).

Let X = ERA of male pitchers and Y = ERA of ERA of female pitchers.

It is provided that the mean and standard deviation of X are:

$\mu_{X}=4.371\\\sigma_{X}=0.787$

Also, the mean and standard deviation of Y are:

$\mu_{Y}=4.363\\\sigma_{Y}=0.869$

ER of Roger is 3.14 and ERA of Amber is 3.38.

(1)

Compute the z-score of Roger as follows:

$z=\frac{x-\mu_{X}}{\sigma_{X}}=\frac{3.14-4.371}{0.787}=-1.56$

Thus, the z-score of Roger is -1.56.

Compute the z-score of Amber as follows:

$z=\frac{x-\mu_{Y}}{\sigma_{Y}}=\frac{3.38-4.363}{0.869}=-1.13$

Thus, the z-score of Amber is -1.13.

(2)

Compute the probability of ERA's that are greater than Roger's ERA as follows:

$P(X>3.14)=P(\frac{X-\mu}{\sigma}>\frac{3.14-4.371}{0.787})\\=P(Z>-1.56)\\=P(Z$

This implies that 94% of the other male pitchers had an ERA higher than 3.14.

Compute the probability of ERA's that are greater than Amber's ERA as follows:

$P(Y>3.38)=P(\frac{Y-\mu_{Y}}{\sigma_{Y}}>\frac{3.38-4.363}{0.869})\\=P(Z>-1.13)\\=P(Z$

This implies that 87% of the other female pitchers had an ERA higher than 3.38.

As it is provided that the lower the ERA the better the pitcher, then it can be concluded that Roger had a better year relative to his peers.

4 0

4 years ago

the table shows the number of yards a football player runs in each quater of a game find the mean number of yards the player run

zalisa [80]

We know the number of yards run per quarter:

Quarter 1: -2 yards
Quarter 2: 14 yards
Quarter 3: -18 yards
Quarter 4: -6 yards

$\text{Mean number of yards run} = \frac{\text{Sum of yards run across quarters}}{\text{Total number of quarters}}$

Sum of yards run across quarters = (-2) + 14 + (-18) + (-6) = -12

Total number of quarters = 4

⇒ $\text{Mean number of yards run} = \frac{\text{Sum of yards run across quarters}}{\text{Total number of quarters}}$

⇒ $\text{Mean number of yards run} = \frac{-12}{4}$ = -3

Hence, he ran -3 yards per quarter

7 0

4 years ago

lilli has $3.65 comprised of quarters and dimes floating on the bottom of her bag she has five more dimes than twice her quarter

marta [7]

Answer:

= 3.65.

Step-by-step explanation:

You know that Tom has 23 coins in total. That means the number of dimes and the number of quarters equals 23.

D + Q = 23

You also know that the total value of the coins is $3.65. A dime is worth $0.10 and a quarter is worth $0.25, so:

0.10*D + 0.25*Q = 3.65

That says that 10 cents per dime times the number of dimes, plus 25 cents per quarter times the number of quarters is three dollars and sixty-five cents.

So you have a system of linear equations:

D + Q = 23

0.10D + 0.25Q = 3.65

I'm going to multiply the bottom row by 100 to clear the decimals.

D + Q = 23

10D + 25Q = 365

Now I can multiply the top row by -10 to eliminate the D terms

-10D - 10Q = -230

10D + 25Q = 365

________________

0D + 15Q = 135

15Q = 135

Q = 9

Tom has 9 quarters.

If D + Q = 23, and Q = 9, then:

D + 9 = 23

D = 14

Tom has 14 dimes.

Always good to double check:

9 quarters is worth $2.25. 14 dimes is worth $1.40. These should sum to $3.65.

2.25 + 1.40

8 0

3 years ago