What is the perimeter of the figure below?

Paha777 [63]

<span>0.48333333333 or if u round it off it would be 0.48</span>

4 0

3 years ago

A hospital bill is estimated to be $462. It ends up actually costing the patient $525. What is the percent of error in the bill?

scoundrel [369]

Answer:

18.86 percent

Step-by-step explanation:

462/525 = (about) 81.14 percent

100-81.14 =18.86

3 0

3 years ago

A motorboat can travel 35mph in still water. If the boat can travel 7 miles downstream at the same time it takes to travel 3 mil

LenaWriter [7]

Answer: the rate of the river's current is 14 mph.

Step-by-step explanation:

Let x represent the rate of the river's current.

The speed of the motor boat in still water is 35 mph.

Since the boat travelled more miles downstream than upstream at the same time, it means that while going downstream, it moved in the direction of the current and while going upstream, it moved against the direction of the current. The total speed downstream would be

(35 + x) mph and the total speed upstream would be (35 - x) mph.

Time = distance/speed

If the boat can travel 7 miles downstream, the time spent travelling downstream is

7/(35 + x)

At the same time it takes to travel 3 miles upstream, the time spent travelling upstream is

3/(35 - x)

Since the time is the same, then

7/(35 + x) = 3/(35 - x)

Cross multiplying, it becomes

7(35 - x) = 3(35 + x)

245 - 7x = 105 + 3x

3x + 7x = 245 - 105

10x = 140

x = 140/10

x = 14

6 0

3 years ago

Two machines are used for filling plastic bottles to a net volume of 16.0 ounces. A member of the quality engineering staff susp

aleksandrvk [35]

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the two machines are filling the bottles with a net volume of 16.0 ounces or if at least one of them is different.

The parameter of interest is μ₁ - μ₂, if both machines are filling the same net volume this difference will be zero, if not it will be different.

You have one sample of ten bottles filled by each machine and the net volume of the bottles are measured, determining two variables of interest:

Sample 1 - Machine 1

X₁: Net volume of a plastic bottle filled by the machine 1.

n₁= 10

X[bar]₁= 16.02

S₁= 0.03

Sample 2 - Machine 2

X₂: Net volume of a plastic bottle filled by the machine 2

n₂= 10

X[bar]₂= 16.01

S₂= 0.03

With p-values 0.4209 (for X₁) and 0.6174 (for X₂) for the normality test and using α: 0.05, we can say that both variables of interest have a normal distribution:

X₁~N(μ₁;δ₁²)

X₂~N(μ₂;δ₂²)

Both population variances are unknown you have to conduct a homogeneity of variances test to see if they are equal (if they are you can conduct a pooled t-test) or different (if the variances are different you have to use the Welche's t-test)

H₀: δ₁²/δ₂²=1

H₁: δ₁²/δ₂²≠1

α: 0.05

$F= \frac{S^2_1}{S^2_2} * \frac{Sigma^2_1}{Sigma^2_2} ~~F_{n_1-1;n_2-1}$

Using a statistic software I've calculated the test

$F_{H_0}= 1.41$

p-value 0.6168

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis then you can conclude that both population variances for the net volume filled in the plastic bottles by machines 1 and 2 are equal.

To study the difference between the population means you can use

$t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}$

The hypotheses of interest are:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α: 0.05

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(N_2-1)S^2_2}{n_1+n_2-2}} = \sqrt{\frac{9*9.2*10^{-4}+9*6.5*10^{-4}}{10+10-2} } = 0.028= 0.03$

$t_{H_0}= \frac{(16.02-16.01)-0}{0.03*\sqrt{\frac{1}{10} +\frac{1}{10} } } = 0.149= 0.15$

The p-value for this test is: 0.882433

The p-value is greater than the significance level, the decision is to not reject the null hypothesis.

Using a significance level of 5%, there is no significant evidence to reject the null hypothesis. You can conclude that the population average of the net volume of the plastic bottles filled by machine one and by machine 2 are equal.

I hope this helps!