What is the side length of a square with a perimeter of 96 meters

Factor the algebraic expression.<br> 72 +63

Ira Lisetskai [31]

Answer:135

Step-by-step explanation:72 + 63 =135

5 0

3 years ago

The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM : MN : NO is equal to 3 : 1

jasenka [17]

Answer:

NO = 20

Step-by-step explanation:

If the pieces are in the ratio of 3:1:5 and the whole thing is 36, then set up an equation:

3x + 1x + 5x = 36

and solve, see image.

5 0

2 years ago

Based on an indication that mean daily car rental rates may be higher for Boston than for Dallas, a survey of eight car rental c

Elina [12.6K]

Answer:

$t=\frac{(47 -44)-(0)}{3\sqrt{\frac{1}{8}+\frac{1}{9}}}=2.058$

The degrees of freedom are:

$df=8+9-2=15$

And the p value would be:

$p_v =P(t_{15}>2.058) =0.0287$

Since we have a p value lower than the significance level given of 0.05 we can reject the null hypothesis and we can conclude that the true mean for car rental rates in Boston are signiﬁcantly higher than those in Dallas

Step-by-step explanation:

Data given

$n_1 =8$ represent the sample size for group Boston

$n_2 =9$ represent the sample size for group Dallas

$\bar X_1 =47$ represent the sample mean for the group Boston

$\bar X_2 =44$ represent the sample mean for the group Dallas

$s_1=3$ represent the sample standard deviation for group Boston

$s_2=3$ represent the sample standard deviation for group Dallas

We can assume that we have independent samples from two normal distributions with equal variances and that is:

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

Let the subindex 1 for Boston and 2 for Dallas we want to check the following hypothesis:

Null hypothesis: $\mu_1 \leq \mu_2$

Alternative hypothesis: $\mu_1 > \mu_2$

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t student distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

Replacing we got:

$\S^2_p =\frac{(8-1)(3)^2 +(9 -1)(3)^2}{8 +9 -2}=9$

And the deviation would be just the square root of the variance:

$S_p=3$

The statitsic would be:

$t=\frac{(47 -44)-(0)}{3\sqrt{\frac{1}{8}+\frac{1}{9}}}=2.058$

The degrees of freedom are:

$df=8+9-2=15$

And the p value would be:

$p_v =P(t_{15}>2.058) =0.0287$

Since we have a p value lower than the significance level given of 0.05 we can reject the null hypothesis and we can conclude that the true mean for car rental rates in Boston are signiﬁcantly higher than those in Dallas

5 0

3 years ago

a ladder is leaning against the side of a building the building in the ground form a right angle how high on the building will t

GrogVix [38]

8 ft up the building is where the top of the ladder touches (use Pythagorean Theorem)
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3 0

3 years ago

Use polar coordinates to find the volume of the given solid. bounded by the paraboloid z = 5 + 2x2 + 2y2 and the plane z = 11 in

podryga [215]

Using cylindrical coordinates,

$\displaystyle\int_{x=0}^{x=\sqrt3}\int_{y=0}^{y=\sqrt{3-x^2}}\int_{z=5+2x^2+2y^2}^{z=11}\mathrm dz\,\mathrm dy\,\mathrm dx$
$\displaystyle=\int_{\theta=0}^{\theta=\pi/2}\int_{r=0}^{r=\sqrt3}\int_{z=5+2r^2}^{z=11}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\frac\pi2\int_{r=0}^{r=\sqrt3}r(11-(5+2r^2))\,\mathrm dr$
$=\displaystyle\pi\int_{r=0}^{r=\sqrt3}(3r-r^3)\,\mathrm dr$
$=\dfrac{9\pi}4$

3 0

3 years ago