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4 years ago

So, is this is the right way to do this question?

Mathematics

2 answers:

Wittaler [7]4 years ago

7 0

Step-by-step explanation:

A parallelogram is a two-dimensional geometric structure that always has four sides, of which opposite sides are the same length, and parallel.

On the contrary, a parallelogram is a slanting rectangle with two sets of parallel opposite sides. The basic difference between rhombus and parallelogram lies in their properties, i.e. all the sides of a rhombus have the same length, whereas parallelogram is a rectilinear figure whose opposite sides are parallel. For me this a bit complicating.

Hope this helps

musickatia [10]4 years ago

4 0

Answer:

Step-by-step explanation:

a parallelogram is a four sided plane rectilinear figure with opposite sides parallel.

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A new dental bondlng agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive(called "Smartbon

Gemiola [76]

Answer:

(a) H₀: μ ≥ 5.70 vs. Hₐ:μ < 5.70

(b) The rejection region is (t₀.₀₁,₉ ≤ -2.821).

(d) The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

Step-by-step explanation:

A hypothesis test should be conducted to determine that the if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(a)

The hypothesis is:

H₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. μ ≥ 5.70.

Hₐ: The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, i.e. μ < 5.70.

(b)

The alternate hypothesis indicates that the hypothesis test is left-tailed.

The rejection region for the left tailed test will be towards the lower tail of the t-distribution curve.

The significance level of the test is: α = 0.01.

The critical value is:

$t_{\alpha ,(n-1)}=t_{0.01,(10-1)}=t_{0.01,9}$

Use the t-table for the critical value.

$t_{\alpha ,(n-1)}=t_{0.01,9}=-2.821$

Since rejection region is in the lower tail the critical value will be negative.

Thus, the rejection region is (t₀.₀₁,₉ ≤ -2.821).

(c)

The test statistic value is:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}$

Given:

$\bar x=5.07\\s=0.46\\n=10\\\mu=5.70$

Compute the value of the t-statistic as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{5.07-5.70}{0.46/\sqrt{10}} =-4.33$

The value of the test statistic is -4.33.

(d)

The value of the test is less than the critical value.

$t=-4.33$

This implies that the test statistic lies in the rejection region.

Hence the null hypothesis will be rejected at 1% significance level.

Conclusion:

As the null hypothesis is rejected it can be concluded that the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(e)

The conditions required for the t-test for single mean to be valid is:

The data should be continuous.
The parent population should be normally distributed.
The sample should be randomly selected.

5 0

3 years ago

Find how long it takes for $500 to double if it is invested at 6% interest compounded monthly

EastWind [94]

Answer:

11.581 years

Step-by-step explanation:

Formula:

$AV=PV(1+\frac{i}{n})^{nt}\\1000=500(1+\frac{.06}{12})^{12t}\\2=1.005^{12t}\\log_{1.005}2=12t\\138.9757=12t\\t=11.5813$

6 0

3 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

3 years ago

A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 140 lb and each bo

Stells [14]

Answer:

21 boxes of books

Step-by-step explanation:

guy= 140 lbs

each box= 40lbs elevator can only weigh up to 1010

i took 1010- 140 and got 870lbs left for the books

then i took 870 divided by 40 (to see how many boxes of books can be put on the elevator) and got 21.75

so 21 boxes could go on the elevator at a time

5 0

3 years ago

Please help me ASAP! I will friend you (probably)! The first correct answer will get brainiest! Terry and Tao are canoeing on a

ivann1987 [24]

erry starts rowing at 2 pm from the west end of the lake, and Tao starts rowing from the east end of the lake at 2:05 pm.
------
Terry DATA:
rate = 60 meter/min ; time = x min ; distance = r*t = 60x meters
-----
Tao DATA:
rate = 40 meter/min ; time = x-5 min ; distance = r*t = 40(x-5) meters
--------------------------
If they always row directly towards each other at what time will the two meet?

------
Equation:
dist + dist = 2000 meters
60x + 40(x-5) = 2000
20x = 1800
x = 90 minutes
---

8 0

3 years ago