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The number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name. If the numbe

Anestetic [448]

Answer:

19 letters

Step-by-step explanation:

Suppose Number of Amy's full name letters = X

Number of Stephanie's full name letters = Y

Now, according to given condition that ''number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name'',

Equation 1 becomes

Y = 2X-16

Now, according to second condition, product of their names' letter is 418. So,

Equation 2 becomes

XY = 418

Deducing value of X from equation 1,

X = (Y+16)/2

Putting this value in equation 2 we get,

{(Y+16)/2}*Y = 418,

By simplifying this equation we get a quadritic equation

(Y^2)+16Y-836=0

By breaking middle term (You can use quadratic formula here as well)

(Y^2)+38Y-22Y-836=0

Y(Y+38)-22(Y+38)=0

(Y-22)(Y+38)=0

At this stage we have two values for Y,

Y=22, or Y=-38

Now considering only positive value since the number of letters in a name can not be in negative number,

Y=22,

So X=(Y+16)/2

X=19

7 0

3 years ago

As part of your training schedule you plan to jog once a week around the reservoir shown below on the map.

jarptica [38.1K]

The actual length of 1 lap is 250m.

6 0

3 years ago

Solve -4 < 3x+2<5.

denis-greek [22]

The answer choice which represents the solution to the inequality as given in the task content is; x>-2 or x≤ 1.

<h3>What is the solution of the give complex inequality?</h3>

On this note, it follows that the inequalities can be solved individually as follows;

-4 < 3x +2

-6 < 3x

x > -2

Also, 3x +2 ≤ 5

3x ≤ 3

x ≤ 1.

Ultimately, the correct answer choice is; Choice C; x>-2 or x≤ 1.

Read more on complex inequality;

brainly.com/question/24761100

#SPJ1

5 0

1 year ago

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ 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 score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

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:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (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:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

$df=n-1=10-1=9$

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

$p_v =P(t_9>10.349)=1.34x10^{-6}$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

5 0

3 years ago

A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

sesenic [268]

Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$