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2 years ago

RST is an equilateral triangle; . If RT = 8, then TX =

Mathematics

2 answers:

tino4ka555 [31]2 years ago

7 0

Answer:

$TX=4\sqrt{3}\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

An equilateral triangle has the three equal sides

RT=TS=RS

In this problem we have

$RT=8\ units$

In the right triangle RTX

Applying the Pythagoras Theorem

$TX^{2}=RT^{2}-RX^{2}$

we have

$RT=8\ units, RX=RS/2=4\ units$

substitute

$TX^{2}=8^{2}-4^{2}$

$TX^{2}=48$

$TX=\sqrt{48}\ units$

$TX=4\sqrt{3}\ units$

yulyashka [42]2 years ago

6 0

The answer on Odysseyware is 4root3

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The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3. Suppose 36 golfers play

kondaur [170]

Answer:

the probability that the exceeded 65 = 0.3707

The average score of the 36 golfers exceeded 65

= 36 X 0.3707 = 13.3452

Step-by-step explanation:

Step 1:-

The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3.

mean (μ) = 64

standard deviation (σ) =3

by using normal distribution

given (μ) = 64 and (σ) =3

i) when x =65

$z = \frac{x-mean}{S.D} = \frac{65-64}{3} = 0.33 >0$

P( X≥ 65) = P(z≥0.33)

= 0.5 - A(z₁)

= 0.5 - 0.1293 (see normal table)

= 0.3707

The average score of the 36 golfers exceeded 65

= 36 X 0.3707 = 13.3452

6 0

2 years ago

Andreyy89

Answer:

Here, BRX and NJY are two triangles in which,

BR = 30 cm, RX = 40 cm, BX = 60 cm, NJ = 15 cm, JY = 20 cm and NY = 30 cm,

Also, m∠B = m∠N, m∠R = m∠J and m∠X = m∠Y,

By the property of congruence,

$\angle B \cong \angle N$ , $\angle R \cong \angle J$ and $\angle X \cong \angle Y$

Thus, By AAA similarity postulate,

$\triangle BRX\sim \triangle NJY$

Hence, proved.

5 0

2 years ago

1.An object falls from rest on a high tower and takes 5.0 s to hit the ground. Calculate the object’s position from the top of t

Arte-miy333 [17]

We will be using this equation for this problem
d = ut + ½.at²
Given:
initial velocity, u = 0 (falling from rest) 
acceleration, a = +9.80 m/s²(taking down as the convenient positive direction) 
Time = 1.0s, 2.0s, 3.0s, 4.0s, 5.0s 

Using .. d = ½.at² each time (each calculation is the distance from the top) 
For 1.0s .. d = ½ x 9.80 x (1²) = 4.90 m 
For 2.0s .. d = ½ x 9.80 x (2²) = 19.60 m 
3.0s .. d = 44.10m (you show the working for the rest) 
4.0s .. d = 78.40 m 
5.0s .. d = 122.50m 

Plot distance (displacement from the top) on the y-axis against time on the x-axis (label axes and give units for each).The line of best fit will be a smoothly upward curving line getting progressively steeper. Do not join graph points with straight lines.

8 0

2 years ago

Read 2 more answers

Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. How much more money will he have after one year

11111nata11111 [884]

Assuming that the 1.5% annual interest is split into monthly basis with the same amount, then the monthly interest should be: 1.5%/12= 0.125%.
If you put $1000 for annual interest, the saving account would become: $1000*(100%+1.5%)= $1015

If you put $1000 for monthly interest, the saving account would become: ($1000*(100%+0.125%)= $1000*1.0151035559= $1015.10

Then, the money difference should be: $1015.10-$1015= $0.10

8 0

2 years ago

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure.

Alona [7]

Answer:

Step-by-step explanation:

Hello!

The monitoring system warn the driver when the tire pressure of the vehicle is 28% below target pressure.

Be X: target tire pressure of a certain car (pounds per square inch)

X= 28 psi

If the monitoring system will warn the driver when the pressure is 28% below the target pressure: X-0.28X

First step, you have to calculate the 28% of 28psi

28*0.28= 7.84

Second step, is to subtract the calculated 28% to the target pressure:

28 - 7.84= 20.16

The TPMS will trigger a warning at 20.16 psi.

If X~N(μ;σ²)

μ= 28psi (since the average is on target, then the target pressure for the car will be the average value of the distribution)

σ= 3psi

P(X≤20.16)

The standard normal distribution is tabulated. Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.

So to calculate each of the asked probabilities, you have to first, "transform" the value of the variable to a value of the standard normal distribution Z, then you use the standard normal tables to reach the corresponding probability.

Z= (X-μ)/σ= (20.16-28)/3= -2.61

Now you have to look for the corresponding value of probability using the Z-table. Since the value is negative you have to the use the left entry of the Z-table, in the first column you'll find the integer and first decimal of the value -2.6- and in the first row you'll find the second decimal value -.-1

The value of probability that corresponds to -2.61 is:

P(Z≤-2.61)= 0.005

You have to calculate the probability of inspecting a tire at random and it being inflated within recommended range, symbolically this is:

P(30≤X≤26)= P(X≤30)-P(X≤26)

Calculate both Z values:

Z= (30-28)/3= 0.67

Z= (26-28)/3= -0.67

P(Z≤0.67)-P(Z≤-0.67)= 0.749 - 0.251= 0.498

The probability of the tire being inflated within recommended inflation range is 0.498.

I hope this helps!

5 0

2 years ago