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scoundrel [369]
2 years ago
5

1) (x - 2)/(x - 3) + (3x - 11)/(x - 4) = (4x + 13)/(x + 1)​

Mathematics
1 answer:
mote1985 [20]2 years ago
7 0

Step-by-step explanation:

or,(x-2)(x-4)+(3x-11)(x-3)/(x-3)(x-4)=(4x+13)/(x+1)

or,x^2-4x-2x+8+3x^2-9x-11x+33/x^2-4x-3x+12=(4x+13)/(x+1)

or,4x^2-4x-2x-9x-11x+8+33/x^2-7x+12=(4x+13)/(x+1)

or,4x^2-26x+41/x^2-7x+12=(4x+13)/(x+1)

or, (x+1)(4x^2-26x+41)=(4x+13)(x^2-7x+12)

or,4x^3-26x^2+41x+4x^2-26x+41=4x^3-28x^2+48x+13x^2-91x+156

or,-26x^2+4x^2+28x^2-13x^2+41x-26x-48x+91x=156-41

or,-7x^2+58x=115

or,-7x^2+58x-115=0

or,-(7x^2-58x+115)=0

or,7x^2-58x+115=0

or,7x^2-(35+23)x+115=0

or,7x^2-35x-23x+115=0

or,7x (x-5)-23 (x-5)=0

or, (x-5)(7x-23)=0

Either, Or,

(x-5)=0 (7x-23)=0

or,x=0+5 or,7x=23

:x=5 :x=23/7

Hence,x=5 or 23/7

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5) In a certain supermarket, a sample of 60 customers who used a self-service checkout lane averaged 5.2 minutes of checkout tim
Ne4ueva [31]

Answer:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

S_p=2.940

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

df=60+72-2=130

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

Step-by-step explanation:

Data given

Our notation on this case :

n_1 =60 represent the sample size for people who used a self service

n_2 =72 represent the sample size for people who used a cashier

\bar X_1 =5.2 represent the sample mean for people who used a self service

\bar X_2 =6.1 represent the sample mean people who used a cashier

s_1=3.1 represent the sample standard deviation for people who used a self service

s_2=2.8 represent the sample standard deviation for people who used a cashier

Assumptions

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\sigma^2_1 =\sigma^2_2 =\sigma^2

The statistic is given by:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

And t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

System of hypothesis

Null hypothesis: \mu_1 \geq \mu_2

Alternative hypothesis: \mu_1 < \mu_2

This system is equivalent to:

Null hypothesis: \mu_1 - \mu_2 \geq 0

Alternative hypothesis: \mu_1 -\mu_2 < 0

We can find the pooled variance:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

And the deviation would be just the square root of the variance:

S_p=2.940

The statistic is given by:

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

The degrees of freedom are given by:

df=60+72-2=130

And now we can calculate the p value with:

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

5 0
3 years ago
Venla is 5 years older than her cousin Kora. How old is Kora when Venla is 18 years old?
krek1111 [17]

Answer:

kora is 13

Step-by-step explanation:

venla is 5 years older than kora

18-5=13

5 0
3 years ago
Read 2 more answers
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den301095 [7]
Can you explain your question?
8 0
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Denise Cho is a broadcast technician and earns $29.00 an hour with time and a
Vladimir79 [104]

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4 0
1 year ago
A local coffee shop serves 2 9 as many customers as a shop run by a national coffee chain. The shop run by the chain serves 502
dexar [7]

I believe that it is 531 customers

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