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3 years ago

A point T on a segment with endpoints D(1, 4) and F(7, 1) partitions the segment in a 2:1 ratio. Finds T.

Mathematics

2 answers:

Dafna1 [17]3 years ago

5 0

In geometry, points are used to divide segments into subsegments using partitions or ratios.

The position of T is: (5,2)

Given that:

$D = (1,4)$ ---- $(x_1,y_1)$

$F = (7,1)$ ---- $(x_2,y_2)$

$m : n = 2:1$

The position of T is calculated using the following line ratio formula

$T = \frac{1}{m+n}(mx_2 +nx_1,my_2 +ny_1)$

So, we have:

$T = \frac{1}{2+1}(2 * 7 +1 *1,2 * 1 +1 * 4)$

$T = \frac{1}{3}(15,6)$

Expand

$T = (\frac{1}{3}*15,\frac{1}{3}*6)$

$T = (5,2)$

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The fracture strength of tempered glass averages 14.1 (measured in thousands of pounds per square inch) and has standard deviati

ololo11 [35]

Answer:

0.15866 is the probability of the average fracture strength of selected 100 pieces of glasses that of exceed 14.3.

Step-by-step explanation:

Given that, the strength of a tempered(x) a glass has average 14.1 and has standard deviation 2.

$\mu_x=14.1$ , $\sigma_x=2$

n=number of selected pieces= 100.

The probability that the average fracture strength of 100 pieces of this glass exceed 14.3 is

$P(\overline X>14.3)=P(\frac{\overline X-\mu_x}{2/\sqrt n}>\frac{14.3-14.1}{2/\sqrt{100}})$

$=P(\overline X>1)$

$=1-P(\overline X\leq 1)$

= 1 - 0.84134

=0.15866.

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3 years ago

The area of circular garden is 530.66 feet2. What is the circumference of the garden? (Use 3.14 for .

iVinArrow [24]

$\bf \textit{area of a circle}\\\\
A=\pi r^2\quad 
\begin{cases}
r=radius\\
------\\
A=530.66
\end{cases}\implies 530.66=\pi r^2
\\\\\\
\cfrac{530.66}{\pi }=r^2\implies \sqrt{\cfrac{530.66}{\pi }}=r
\\\\\\
\textit{circumference of a circle}\\\\
C=2\pi r\qquad \implies C=2\pi \left( \sqrt{\cfrac{530.66}{\pi }} \right)$

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3 years ago

I just need some quick help with this. Distributive properties aren't my best section.

Anni [7]

In this case u can’t use the distributive property. U just multiple whats in the parenthesis (39•5)=195 and that’s ur answer.
Let’s say if the problem said 5(2+1) u can’t use the distributive property bc u have to do what’s in the parentheses first. 5(3)=15
But If u had a problem like 2(4x+6) then u can use the distributive property. This is bc u can’t add 4x+6 bc they aren’t like terms. So u multiple the 2 by 4x which is 8x and the 2 by 6 which is 12 then ur answer would be : 8x+12

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3 years ago

A survey of shoppers is planned to determine what percentage use credit cards. prior surveys suggest 63% of shoppers use credit

Alona [7]

We would need a sample size of 560.

We first calculate the z-score associated. with this level of confidence:
Convert 95% to a decimal: 95% = 95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score of 1.96.

The margin of error, ME, is given by:
$ME=z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

We want ME to be 4%; 4% = 4/100 = 0.04. Substituting this into our equation, as well as our proportion and z-score,
$0.04=1.96\sqrt{\frac{0.63(1-0.63)}{n}}
\\
\\\text{Dividing both sides by 1.96,}
\\
\\\frac{0.04}{1.96}=\sqrt{\frac{0.63(0.37)}{n}}
\\
\\\text{Squaring both sides,}
\\
\\(\frac{0.04}{1.96})^2=\frac{0.63(0.37)}{n}
\\
\\\text{Multiplying both sides by n,}
\\
\\n(\frac{0.04}{1.96})^2=0.63(0.37)
\\
\\n(\frac{0.04}{1.96})^2=0.2331
\\
\\\text{Isolating n,}
\\
\\n=\frac{0.2331}{(\frac{0.04}{1.96})^2}=559.67\approx560$

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3 years ago

If the rule of the function is "multiply by 2 then add 3" and the input value is -2, what is the output value?

miv72 [106K]

The equation would be 2x+3 so when you plug it in it's 2(-2)+3 which simplify to -4+3 which is -1

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3 years ago