A street in San Francisco rises 20 feet for every 100 feet horizontally. What is the measure of the angle of elevation,

Two skiers are 30 kilometers apart and head towards each other. They meet in 2 hours. If the second skier is 5 kilometers per ho

DENIUS [597]

Answer:

Speed of first skier = 5 km/h

Speed of second skier = 10 km/h

Step-by-step explanation:

Given:

Distance between skiers = 30 km

Time after which they meet = 2 hours

Second skier is 5 km/h faster than the first skier.

To find speed of each skier.

Solution:

Let the speed of first skier be in km/h = $x$

Distance covered in km 2 hours will be = $Speed\times time=x\times 2=2x\ km$

Speed of second skier in km/h can be given as = $x+5$

Distance traveled by second skier after 2 hours will be = $Speed\times time=(x+5)\times 2=(2x+10)\ km$ [Using distribution]

Since, the skiers were 30 km apart initially, so the total distance covered by both of them when they meet after 2 hours will be = 30 km

Thus, we have:

$2x+2x+10=30$

Solving for $x$

$4x+10=30$

Subtracting both sides by 10.

$4x+10-10=30-10$

$4x=20$

Dividing both sides by 4.

$\frac{4x}{4}=\frac{20}{4}$

$x=5$

Speed of first skier = 5 km/h

Speed of second skier = $5+5$ = 10 km/h

8 0

3 years ago

Help anyone can help me do the question 4,I will mark brainlest.

nasty-shy [4]

Answer:

Hello,

Step-by-step explanation:

$A=(1,2)\\B=(0,-1)\\\overrightarrow{AB}=((0,-1)-(1,2)=(-1,-3)\ ||\overrightarrow{AB}||^2=1+9=10\\\overrightarrow{BC}=((3,-2)-(0,-1)=(3,-1)\ ||\overrightarrow{BC}||^2=9+1=10\\\\Triangle\ is\ isosceles.\\\\\overrightarrow{AB}.\overrightarrow{BC}=(-1,-3)*\left[\begin{array}{c}3\\-1\end{array}\right] =-3+3=0\\\\Triangle \ is\ right.\\\\$

8 0

3 years ago

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A number b is at most 9

Travka [436]

b ≤ 9 (b is less than or equal to 9)

Hope this helps! ;)

8 0

3 years ago

To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil

Debora [2.8K]

Answer:

statistic value t= 5.43

p-value: < 0.00001.

Step-by-step explanation:

Hello!

To obtain information over the corrosion-resistance properties of a certain type of steel conduit a random sample of 45 specimens was taken and buried for two years.

The study variable is:

X: Max. penetration of a steel conduit.

The data of the sample

n= 45

sample mean X[bar]= 53.4

sample standard deviation S= 4.2

The conduits are manufactured to have a true average penetration of at most 50 mills, symbolically: μ ≤ 50

The hypothesis is:

H₀: μ ≤ 50

H₁: μ > 50

α: 0.05

To choose the corresponding statistic to use to study the population mean, the variable must have a normal distribution. There is no available information to check this, so I'll just assume that the variable has a normal distribution and, since the population variance is unknown and the sample is small, the statistic to use is a Student t.

Under the null hypothesis, the critical region and the p-value are one-tailed.

Critical value:

$t_{n-1; 1-\alpha } = t_{44; 0.95} = 1.68$

Rejection rule:

Reject the null hypothesis when t ≥ 1.68

t= $\frac{53.4 - 50}{\frac{4.2}{\sqrt{45} } }$

t= 5.43

The calculated value is greater than the critical value, thedecision is to rject the null hypothesis.

p-value:

P(t ≥ 5.43) = 1 - P(t < 5.43) = < 0.00001.

The p-value is less than α so the decision is to reject the null hypothesis.

Since the null hypothesis was rejected, then the population average of the penetration of the conduits specimens is greater than 50 mils. It is not recommendable to use these conduits.

I hope it helps!

4 0

3 years ago

The volume of a pyramid is 47 3. The height of the pyramid is 6 meters. What is the area of

AlladinOne [14]

473x6= 2,838

the answer should be 2,838?

8 0

3 years ago

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