6. David leaves the house to go to school He walks 200 m west and 125 m

Cheryl is moving to a new house. Her old house is 3 kilometers and 457meters from her new house. How many meters is her old hous

MrRissso [65]

Answer:

Her old house is 3000m+457m = 3457m from her new house.

Step-by-step explanation:

Conversion of units problems can always be modeled as a rule of three problem.

Rule of three problem:

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In the case of a conversion of units problem, the measures are:

- the value in one unit

- the value in another unit

As the value of the first unit increases, so will the value of the second unit. It means that in a conversion of units problem, we will always have a direct rule of three.

The problem states that Cheryl's new house is 3 kilometers and 457meters from her old house. The problem wants to know this distance purely in meters, so we have to convert 3km to meters. 1km = 1000m, so:

1km - 1000m

3km - xm

x = 1000*3

x = 3000m

Her old house is 3000m+457m = 3457m from her new house.

5 0

2 years ago

The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commuting

Stolb23 [73]

Answer:

1. 0.1635

2. 0.0026

Step-by-step explanation:

The computation of the probability in the following cases are as follows:

1.

Given that

Mean = 25 minutes

ANd, the standard deviation is 6.1 minutes

So here the z score would be

= (31 - 25) ÷(6.1)

= 0.98

Now the probability is

= P(Z>0.98)

= 0.1635

2. the z score would be

= (8 - 25) ÷(6.1)

= -2.79

Now the probability is

= P(Z<-2.79)

= 0.0026

7 0

2 years ago

2. A particular resource class must perform at a level consistent with the rest of the school to avoid being discontinued. On th

Natali5045456 [20]

Answer:

$t=\frac{71.86-78}{\frac{17.52}{\sqrt{14}}}=-1.311$

$p_v =P(t_{13}$

If we compare the p value and a significance level assumed for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.

Step-by-step explanation:

Data given and notation

$\bar X=71.86$ represent the sample mean

$s=17.52$ represent the standard deviation for the sample

$n=14$ sample size

$\mu_o =78$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is less than 78, the system of hypothesis would be:

Null hypothesis: $\mu \geq 78$

Alternative hypothesis: $\mu < 78$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{71.86-78}{\frac{17.52}{\sqrt{14}}}=-1.311$

Calculate the P-value

First we need to find the degrees of freedom given by:

$df=n-1=14-1=13$

Since is a one-side left tailed test the p value would be:

$p_v =P(t_{13}$

Conclusion

If we compare the p value and a significance level assumed for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.

3 0

3 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if

Ksju [112]

Answer:

234

Step-by-step explanation:

The consecutive terms of the sequence have a common difference d

d = 17 - 10 = 24 - 17 = 7

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = 7 , thus

$a_{33}$ = 10 + (32 × 7) = 10 + 224 = 234

7 0

3 years ago

The ratio of apples to pears in Zach's basket is 6 to 8. If he has a total of 21 pieces of fruit, how many of them are apples?

sergij07 [2.7K]

Answer:

7 kg= weight of apples

4 0

3 years ago