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Burka [1]
3 years ago
13

Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and x + 7y = 8

Mathematics
1 answer:
goblinko [34]3 years ago
5 0
\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y  = \frac{17}{14} } \atop {x+7y=8}} \right.

To solve this system by substitution, first isolate x in the second equation.

x+7y=8
x+7y-7y=8-7y
x=8-7y

Now, plug this expression (8-7y) for x in the top equation to solve for y.

\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}
3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}
72-63y+8y=17
72-55y=17
-55y=17-72
-55y=-55
y=1

Now that you have y, plug it into the second equation and solve for x.

x+7y=8
x+7(1)=8
x+7=8
x=1

Last step is to plug your x- and y-values in to both equations to check your work.

\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}

\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ;  \frac{1}{3} * \frac{8}{8} = \frac{8}{24}

\frac{9}{24} + \frac{8}{24} = \frac{17}{24}  <--True

1+7(1)=8
1+7=8   <--True

Answer:
x=1 \\ y=1
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Zebras migrate in a circle with a round trip of about 300 miles. They travel at 64 km/h. How many hours does it take zebra to do
Tresset [83]

Answer:

7.5 hours (7 hours and 30 minutes)

Step-by-step explanation:

ok Let's start with 64km/h.

1.6 km=1 mile,

64÷1.6=40miles

so 64km/h changes into 40miles/hour.

Zebras's round trip =300miles,

300/40=7.5

so answer is 7.5 hours.

8 0
3 years ago
A telemarketer is successful at getting people to donate money for her organization in 55% of all calls she makes. She must get
Tems11 [23]
An interesting twist to a binomial distribution problem.

Given:
p=55%=0.55 for probability of success in solicitation
x=4=number of successful solicitations
n=number of calls to be made
P(x,n,p)>=89.9%=0.899  (from context, it is >= and not =, which is almost impossible)

From context of question, all calls are assumed independent, with constant probability of success, so binomial distribution is applicable.

The number of successes, x, is then given by
P(x)=C(n,x)p^x(1-p)^{n-x}where
p=probability of success
n=number of trials
x=number of successesC(n,x)=\frac{n!}{x!(n-x)!}

Here we need n such that
P(x,n,p)>=0.899
given
x>=4, p=0.55, which means we need to find

Method 1: if a cumulative binomial distribution table is available, we can look up n=9,10,11 and find
P(x>=4,9,0.55)=0.834
P(x>=4,10,0.55)=0.898
P(x>=4,11,0.55)=0.939
So she must make (at least) 11 calls to make sure the probability of meeting her quota is 89.9% or more.

Method 2: using technology.
Similar to method 1, we can look up the probabilities directly, for n=9,10,11
P(x>=4,9,0.55)=0.834178
P(x>=4,10,0.55)=0.8980051
P(x>=4,11,0.55)=0.9390368

Method 3: using simple calculator
Here we need to calculate the probabilities for each value of n=10,11 and sum the probabilities of FAILURE S=P(0,n,0.55)+P(1,n,0.55)+P(2,n,0.55)+P(3,n,0.55)
so that the probability of success is 1-S.
For n=10,
P(0,10,0.55)=0.000341
P(1,10,0.55)=0.004162
P(2,10,0.55)=0.022890
P(3,10,0.55)=0.074603
So that
S=0.000341+0.004162+0.022890+0.074603
=0.101995
and Probability of getting 4 successes (or more) 
=1-S
=0.898005, missing target by 0.1%

So she will have to make 11 phone calls, bring up the probability to 93.9%.  The work is similar to that of n=10.
8 0
3 years ago
Which number line model represents the expression -2 + 4.5 ?
Lana71 [14]

Answer:

the second pic. A

Step-by-step explanation:

4 0
3 years ago
A dance school charges a registration fee in addition to a fee per lesson. The equation LaTeX: y=30x+25 y = 30 x + 25 represents
klasskru [66]
The equation is 30x + 25
 since the x is with the 30, that would be the cost per lesson, because you would multiply 30 by the number of lessons(x)

7 0
3 years ago
Which expressions are equivalent to –
olga_2 [115]

Answer:

The answer to your question is  10¹/⁴

Step-by-step explanation:

Expression

                            \frac{10}{10^{3/4}}

To solve this problem use the law of exponents.

-Use the division rule of exponents.

If the base if the same in the numerator and denominator, it stays the same and the exponents are subtracted.

                            10¹ ⁻ ³/⁴ = 10¹/⁴   This is the result

7 0
3 years ago
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