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3 years ago

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Liam is deciding which of two gyms to join. Each gym charges a monthly rate plus one-time membership fee. Liam correctly wrote a

nd solved a system of linear equations by substitution to compare the cost of the memberships. In her work, she substituted an expression for one variable and solved the other. This resulted in the equation 75=75. What can loan conclude?

1 answer:

Brums [2.3K]3 years ago

8 0

Liam can conclude that the cost of the memberships for both gyms are equal.

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20/60+15/60=35/60><br> What dose it equal

stepladder [879]

Answer:

$\dfrac{7}{12}$

Step-by-step explanation:

1. Find the Greatest Common Factor of the numerator and denominator.

The prime factors of 35 are <u>5</u>, 7, 35

The prime factors of 60 are 2, 3, 4, <u>5</u>, 6, 10, 12, 15, 20, 30, 60

The only common factor of 35 and 60 is 5.

2. Divide the numerator and denominator by the Greatest Common Factor.

$\dfrac{35}{60} = \mathbf{\dfrac{7}{12}}$

8 0

3 years ago

A clothing business finds there is a linear relationship between the number of shirts, Q ,it can sell and the price, P , it can

Vlad [161]

Answer:

P = -0.004Q + 149

Step-by-step explanation:

The general form of the linear equation is:

$P=aQ+b$

The slope of the equation (a) can be found by using the two given points (4,000; $133) and (27,000; $41)

$a = \frac{\$41-\$133}{27,000-4,000}\\a=-0.004$

Applying the point (4,000; $133) to the equation below yields in the linear equation for Price as a function of the number of shirts:

$P-P_0=a(Q-Q_0)\\P-133=-0.004(Q-4,000)\\P = -0.004Q+149$

The linear equation is:

P = -0.004Q + 149

8 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

NEED HELP ASAP!! WILL GIVE BRAINLIST IF CORRECT

cupoosta [38]

Answer:

1385.28 m²

Step-by-step explanation:

apothem = √16² - 8² = √256 - 64 = √192 = 13.86

Base area = 3 x 16 x 13.86 = 665.28

6 side area = 3 x 16 x 15 = 720

surface area = 665.28 + 720 =1385.28

4 0

3 years ago

What is the coefficient of x in expansion of (2x-4)^2 ?

Sunny_sXe [5.5K]

Answer:

2

Step-by-step explanation:

the one which is near to x

8 0

2 years ago