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3 years ago

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Find the constant of proportionality and the unit rate for the data table. Then write an equaion to represent the relationship b

etween the time (t) and
the distance (d).

Please explain.

1 answer:

Akimi4 [234]3 years ago

6 0

$\dfrac{90}2=45$

$\dfrac{135}3=45$

$\dfrac{225}5=45$

$\dfrac{270}6=45$

The constant of proportionality is thus 45; the unit rate is 45 miles per hour.

The relationship between the time t (in hours) and the distance d (in miles) is thus $d=45\cdot t$

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Sue spent 1 hour 19 minutes less than Jared reading last week. Jared spent 45 minutes less than Pete. Pete spent 3 hours reading

polet [3.4K]

Sue spend 56 minutes in reading.

<h3>What is Unitary Method?</h3>

Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Sue spent 1 hour 19 minutes less than Jared

Lucas spent 45 minutes less than Pete.

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Since, pete spent 3 hours. So, Jared spent

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2 years ago

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3 years ago

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A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random

Yuliya22 [10]

Answer:

b) independent samples t-test

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =5$ represent the sample size for group 1

$n_2 =5$ represent the sample size for group 2

We can calculate the mean and deviation for eaach group with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_1 =5.92$ represent the sample mean for the group 1

$\bar X_2 =5.74$ represent the sample mean for the group 2

$s_1=1.88$ represent the sample standard deviation for group 1

$s_2=1.81$ represent the sample standard deviation for group 2

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

The degrees of freedom are given by:

$df=5+5-2=8$

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

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The value of b Lois gave to Clark to satisfy the given equation is -7.

The given parameters;

2x + 7 - x = 4x + 2b – 3x - 3b

To obtain the value of b, simplify the equation as follows;

2x + 7 - x = 4x + 2b – 3x - 3b

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(x - x) + 7 = -b

0 + 7 = -b

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Thus, the value of b Lois gave to Clark to satisfy the given equation is -7.

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