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Setler79 [48]
3 years ago
7

A family has two cars. During one particular week, the first car consumed 15 gallons of gas. The two cars Drove a combined total

of 1475 miles and the sum of their fuel efficiency was 65 miles per gallon. What were the fuel efficiency of each of the cars that week?
Mathematics
1 answer:
julia-pushkina [17]3 years ago
6 0

Answer:

Car 1 : 40 miles per gallon

Car 2: 25 miles per gallon

Step-by-step explanation:

family has two cars. During one particular week, the first car consumed 15 gallons of gas. The second car consumed 25 gallons of gas. The two cars Drove a combined total of 1475 miles and the sum of their fuel efficiency was 65 miles per gallon. What were the fuel efficiency of each of the cars that week

Given that :

Fuel efficiency , car 1 = x

Fuel efficiency , car 2 = y

x + y = 65 - - (1)

15x + 35y = 1475 - - - (2)

x = 65 - y

15(65-y) + 35y

975 - 15y + 35y = 1475

20y = 14875 - 975

20y = 500

y = 25

Put y = 25 in (1)

x + y = 65

x + 25 = 65

x = 65 - 25

x = 40

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Step-by-step explanation:

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We have a function that is of degree 3, so it has 3 x-intercepts which means there are points (x₁, 0), (x₂, 0), (x₃, 0), so it is a many-to-one function

Correct option is D

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The correct answer above
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How do I solve the inequality for this: 10 &lt; 9 + x
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Solve the system by graphing. Y=2x-9 y=-2x-1
sattari [20]

Answer:

(2,-5)

Step-by-step explanation:

See attachment

One can also solve this by calculation:

y=2x-9

y=-2x-1

-

Rearrange either equation to find x.  I'll use the first:

y=2x-9

2x = y+9

x = (y+9)/2

Now use this value of x in the second equation:

y =  -2x-1

y =-2((y+9)/2)-1

y = (-2y-18)/2)-1

y = -y -9 - 1

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y = -5

Now use -5 for y in the rearranged equation:

y =  -2x-1

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But the question wants a graph solution, which is also fun when you use DESMOS.

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2 years ago
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So
tatyana61 [14]

Answer:

The probability that at least 13 flights arrive late is 2.5196 \times 10^{-6}.

Step-by-step explanation:

We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.

A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.

The above situation can be represented through binomial distribution;

P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........

where, n = number of trials (samples) taken = 18 Southwest flights

           r = number of success = at least 13 flights arrive late

          p = probability of success which in our question is probability that

                flights arrive late, i.e. p = 1 - 0.80 = 20%

Let X = <u><em>Number of flights that arrive late</em></u>.

So, X ~ Binom(n = 18, p = 0.20)

Now, the probability that at least 13 flights arrive late is given by = P(X \geq 13)

P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)

= \binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}

= \binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}

= 2.5196 \times 10^{-6}.

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