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3 years ago

Find the greatest commonFoctor for these numbers 18, 42, 96

Mathematics

1 answer:

ycow [4]3 years ago

5 0

Answer:

The greatest common factor for 18,42 and 96 is 6.

Step-by-step explanation:

6 X 3 = 18

6 X 7 = 42

6 X 16 = 96

making 6 your largest common factor.

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Denise is a professional swimmer who trains, in part, by running. she would like to estimate the average number of miles she run

SSSSS [86.1K]

Given:
n = 20, sample size
xbar = 17.5, sample mean
s = 3.8, sample standard deiation
99% confidence interval

The degrees of freedom is
df = n-1 = 19

We do not know the population standard deviation, so we should determine t* that corresponds to df = 19.
From a one-tailed distribution, 99% CI means using a p-value of 0.005.
Obtain
t* = 2.8609.

The 99% confidence interval is
xbar +/- t*(s/√n)

t*(s/√n) = 2.8609*(3.8/√20) = 2.4309
The 99% confidence interval is
(17.5 - 2.4309, 17.5 + 2.4309) = (15.069, 19.931)

Answer: The 99% confidence interval is (15.07, 19.93)

4 0

3 years ago

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ (Approximated)

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ (Approximated)

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago

Order? 2x^2 - 4x + x^6+ 8 + 3x^10

polet [3.4K]

Answer:

3x^10 + x^6 + 2x^2 - 4x + 8

Step-by-step explanation:

In descending order by powers of x: 3x^10 + x^6 + 2x^2 - 4x + 8

3 0

3 years ago

Please help with this math problem for trig. A 6 m ladder is leaning against a wall. The base of the ladder is 1.5 m from the wa

VladimirAG [237]

Answer:

a = 5.81 m

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2

where b= 1.5 and c= 6

a^2 +1.5^2 = 6^2

a^2 +2.25 = 36

Subtract 2.25 from each side

a^2 +2.25-2.25 = 36-2.25

a^2 = 33.75

Take the square root of each side

sqrt(a^2) = sqrt(33.75)

a = 5.809475019

We only take the positive root because length must be positive

4 0

3 years ago

What's the circumference of a circle with radius of 18 in. Leave answer in terms of pie

Verdich [7]

We Know, Circumference of Circle = 2πr
Here, r = 18
Substitute it in to the expression,
C = 2π(18) = 36π

So, your final answer is 36π

Hope this helps!

7 0

3 years ago

Find the greatest commonFoctor for these numbers 18, 42, 96​

Find the greatest commonFoctor for these numbers 18, 42, 96