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1 year ago

What is the product? 5k/6 . 3/2k^3

Mathematics

2 answers:

Romashka-Z-Leto [24]1 year ago

7 0

Pls go help me at

brainly.com/question/8858488

and your answer is 5l4k^2

Molodets [167]1 year ago

7 0

Answer: The required product is $\dfrac{5}{4k^2}.$

Step-by-step explanation: We are to calculate the following product:

$P=5\dfrac{k}{6}\times \dfrac{3}{2k^3}.$

We will be using the following property of exponents:

$\dfrac{a^x}{a^y}=a^{x-y}.$

We have

$P\\\\\\=5\dfrac{k}{6}\times\dfrac{3}{2k^3}\\\\\\=\dfrac{5}{6}\times\dfrac{3}{2}k^{1-3}\\\\\\=\dfrac{5}{4}k^{-2}=\dfrac{5}{4k^2}.$

Thus, the required product is $\dfrac{5}{4k^2}.$

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A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sam

tatuchka [14]

Answer: $(15.263,\ 17.537)$

Step-by-step explanation:

According to the given information, we have

Sample size : n= 50

$\overline{x}=16.40$

$s=4.00$

Since population standard deviation is unknown, so we use t-test.

Critical value for 95 percent confidence interval :

$t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010$

Confidence interval : $\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}$

$16.40\pm (2.010)\dfrac{4}{\sqrt{50}}\\\\=16.40\pm1.13702770415\\\\=16.40\pm1.1370\\\\=(16.40-1.1370,\ 16.40+1.1370)\\\\=(15.263,\ 17.537)$

Required 95% confidence interval : $(15.263,\ 17.537)$

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2 years ago

Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.

kolbaska11 [484]

Answer:

See explanation

Step-by-step explanation:

Triangles ΔABC and ΔBAD are congruent. So,

AB ≅ BA;
AC ≅ BD;
BC ≅ AD;
∠ABC ≅ ∠BAD;
∠BCA ≅ ∠ADB;
∠CAB ≅ ∠DBA.

Consider triangles AEC and BED. In these triangles,

AC ≅ BD;
∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
∠AEC ≅ ∠BED (as vertical angles).

So, ΔAEC ≅ ΔBED. Thus,

AE ≅ EB.

This means that segment CD bisects segment AD.

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2 years ago

What is the slope-intercept equation of the line below?

ZanzabumX [31]

The slope intercept form for this line would be in the form of y=mx+b. The slope is m and the y-intercept is b.

y = (slope)x + (y-intercept)

y = 2x - 3

So, the answer is C.

Hope I could help! Have a good one!

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2 years ago

A pair of sunglasses is on sale for $26. The original price of the sunglasses was $40. What percent of the original price is the

GarryVolchara [31]

If the glasses were origanum 40, and were on sale for 26,we minus them from eachother to find out how much money was saved. So 40-26= 14, if $14 was saved we put 14 over the original price and times it buy 100 14/40x100= 35% So 35% was saved. 100-35= 65. Therefore 65% of the original price was paid and 35% was saved.

7 0

2 years ago

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec

masha68 [24]

Using the washer method, the volume is given by the integral

$\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx$

where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.

So the volume is

$\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}$

4 0

2 years ago