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faust18 [17]
3 years ago
11

What is the function with a rate of change of 3/2 whose graph passes through the point (4, 10.5)?

Mathematics
1 answer:
klio [65]3 years ago
3 0
<h2>Answer:</h2>

y= \frac{3}{2}*x+4.5

<h2>Step-by-step explanation:</h2>

We are given a slope and a point. That is why we will use point slope form.

The default equation is:

(y-a)=m*(x-b)

a is the y coordinate of our point and b is the x coordinate of our point

m is the slope.

We will plug in the values.

(y-10.5)=3/2*(x-4)

Now we just manipulate the equation

y= \frac{3}{2}*x+4.5

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According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e
slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that p = 0.09

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

So

P(X < 4) + P(X \geq 4) = 1

We want P(X \geq 4)

So

P(X \geq 4) = 1 - P(X < 4)

In which

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225

P(X = 1) = C_{12,1}.(0.09)^{1}.(0.91)^{11} = 0.3827

P(X = 2) = C_{12,2}.(0.09)^{2}.(0.91)^{10} = 0.2082

P(X = 3) = C_{12,3}.(0.09)^{3}.(0.91)^{9} = 0.0686

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3225 + 0.3827 + 0.2082 + 0.0686 = 0.982

Finally

P(X \geq 4) = 1 - P(X < 4) = 1 - 0.982 = 0.0180

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

6 0
3 years ago
Let ​f(x)=x2+3x−10​. Enter the x-intercepts of the quadratic function in the boxes. x = and x =
SIZIF [17.4K]

Answer:

X= 2.

X= -5.

Step-by-step explanation:

Hope it was helpful ;)

3 0
2 years ago
Solve this problem on paper using all four steps. A girl scout troop sold cookies. If the girls sold 5 more boxes the second wee
zhenek [66]
Assume the girls sold X boxes in the first week. They sold in the second week X+5 and 2X+10 in the third week.

The sum X + X + 5 + 2X + 10 = 431
4X = 416. Therefore X = 104
The answers are:
a0 = 104
a1 = 109
a2 = 218

Hope that helps you :)
6 0
3 years ago
5z3 - 224 - 9z2 + 2<br> What is the degree of the polynomial?<br> I
hoa [83]

Answer:

5{z}^{3}-222-9{z}^{2}5z

​3

​​ −222−9z

​2

Step-by-step explanation:

1 Collect like terms.

5{z}^{3}+(-224+2)-9{z}^{2}5z

​3

​​ +(−224+2)−9z

​2

​​  

2 Simplify.

5{z}^{3}-222-9{z}^{2}5z

​3

​​ −222−9z

​2

​​  

Done

7 0
3 years ago
Looking for the 2 correct answers please
Fynjy0 [20]

Answer:

  • ROQ
  • QOP

Step-by-step explanation:

The sine of an angle is equal to the cosine of its complement, and vice versa.

  sin ∠QOP = cos ∠ROQ

  cos ∠ROQ = sin ∠QOP

8 0
2 years ago
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