How many triangles.

Solve this simultaneous equation x+2y=11 x-2y=1

lana [24]

Answer:

Equation 1,

$x + 2y = 11$

Equation 2,

$x - 2y = 11$

Take equation number 2.

$x - 2y = 11 \\ x = 11 + 2y$

Substitute 'x' in Equation number 1.

$x + 2y = 11 \\ 11 + 2y + 2y = 11 \\ 11 + 4y = 11 \\ 4y = 11 - 11 \\ 4y = 0 \\ y = \frac{0}{4} \\ y = 0$

y = 0.

So x,

$x = 11 - 2y \\ x = 11 - 2(0) \\ x = 11 - 0 \\ x = 11$

x = 11.

7 0

3 years ago

Read 2 more answers

Solve the equation 7x-12=6x-1 x=_

seropon [69]

Answer:

x = 11

Step-by-step explanation:

Combine the like terms in the given 7x-12=6x-1:

7x - 6x = -1 + 12, or

x = 11

3 0

3 years ago

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

Thomas has purchased a $129,000 home with a 30-year mortgage at 5.25%.

vagabundo [1.1K]

Answer: 177 months

Step-by-step explanation:

7 0

3 years ago

Which ordered pair represents the y-intercept of the graph of the equation y = - 4 x - 7 ?

Degger [83]

Answer:

(0, -7)

Step-by-step explanation:

Since -4x is the slope, then -7 is the y-intercept.

For finding y intercept we substitute x=0

y = -7

The ordered pair would be

(0,-7)

hope this helps and is right. p.s. i really need brainliest :)

4 0

3 years ago