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2 years ago

In a random sample of 200 cars of a particular model,

1 answer:

8 0

By using proportions, We expect 150 defects out of the 10,000 cars if the 3 defects out of the 200 cars sampled is representative of all 10,000 cars.

Option A is correct.

First, let's set up the proportions.

A proportion is an equation in which two ratios are set equal to each other.

We have 3/200 cars with defects and we want to know X for X/10000.

So 3/200 = X/10000

Now solve for X.

3/200 = X/10000

X = $\frac{3}{200} \times 10000$

X = 150

So the answer is: We expect 150 defects out of the 10,000 cars if the 3 defects out of the 200 cars sampled is representative of all 10,000 cars.

Option A is correct.

Find out more information about proportions here

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HELP IM ON THE LAST ONE ILL GIVE BRAINLIEST

xxMikexx [17]

Answer:

this is hard what grade is this for

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Help! Thanks!!!!!!!!!

san4es73 [151]

∠BAC = ∠NAC - ∠NAB = 144 - 68 = 76⁰

AB = 370 m

AC = 510 m

To find BC we can use cosine law.

a² = b² + c² -2bc*cos A

|BC|² = |AC|²+|AB|² - 2|AC|*|AB|*cos(∠BAC)

|BC|² = 510²+370² - 2*510*370*cos(∠76⁰) =

|BC| ≈ 553 m

To find ∠ACB, we are going to use law of sine.

sin(∠BAC)/|BC| = sin(∠ACB)/|AB|

sin(76⁰)/553 m = sin(∠ACB)/370 m

sin(∠ACB)=(370*sin(76⁰))/553 =0.6492

∠ACB = 40.48⁰≈ 40⁰

∠BAC = 76⁰

∠ACB = 40⁰

∠CBA = 180-(76+40) = 64⁰

Bearing C from B =360⁰- 64⁰-(180-68) = 184⁰

Shortest distance from A to BC is height (h) from A to BC.

We know that area of the triangle

A= (1/2)|AB|*|AC|* sin(∠BAC) =(1/2)*370*510*sin(76⁰).

Also, area the same triangle

A= (1/2)|BC|*h = (1/2)*553*h.

So, we can write

(1/2)*370*510*sin(76⁰) =(1/2)*553*h

370*510*sin(76⁰) =553*h

h= 370*510*sin(76⁰) / 553= 331 m

h=331 m

4 0

3 years ago

The function h(t) = −5t2 + 20t shown in the graph models the curvature of a satellite dish: graph of parabola starting at zero c

ipn [44]

Answer:

Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) Option B: f(x) = (2x + 1)(2x − 1)

Part 5) Option A: The company earned 85 billion dollars in 2008

Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

$h(t)=-5t^{2}+20t$

This is a vertical parabola open downward

The vertex is a maximum

The x-intercepts are the points (0,0) and (4,0)

The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

The domain is the interval ----> [0,4]

$0\leq t\leq 4$

The range is the interval ----> [0,20]

$0\leq h(t)\leq 20$

Part 2) we have

$V=10x^{2} -17x+13$

where

x is the time in minutes

V is the volume in gallons

we know that

When the trough is empty, the volume is equal to zero

For V=0

$10x^{2} -17x+3=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$10x^{2} -17x+3=0$

$a=10\\b=-17\\c=3$

substitute in the formula

$x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}$

$x=\frac{17(+/-)\sqrt{169}} {20}$

$x=\frac{17(+/-)13} {20}$

$x=\frac{17(+)13} {20}=\frac{3}{2}$

$x=\frac{17(-)13} {20}=\frac{1}{5}$

$10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})$

simplify

$10(x-\frac{3}{2})(x-\frac{1}{5})=(2x-3)(5x-1)$

Part 3) we have

$f(x)=-x^{2}+20x+100$

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(10)=-(10)^{2}+20(10)+100=200$

$f(b)=f(20)=-(20)^{2}+20(20)+100=100$

$a=10$

$b=20$

Substitute

$\frac{100-200}{20-10}$

$-\frac{100}{10}=-10$ ----> is a decreasing function

therefore

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) we have

$f(x)=4x^{2} -1$

<em>Find out the x-intercepts</em>

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

For f(x)=0

$4x^{2} -1=0$

Solve for x

$4x^{2}=1$

$x^{2}=\frac{1}{4}$

take square root both sides

$x=(+/-)\frac{1}{2}$

$f(x)=4x^{2} -1=4(x-\frac{1}{2})(x+\frac{1}{2})=(2x-1)(2x+1)$

Part 5) we have

$t^{2}+14t+85$

Remember that

The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero

In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

t is the number of years since the end of 2008

For t=0 -----> represent the end of 2008

$(0)^{2}+14(0)+85=85\ billion\ dollars$

therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

The vertex represent a minimum

In this problem the vertex is the point (4,-1)

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

we have

(h,k)=(4,-1)

substitute

$y=a(x-4)^2-1$

take the point (2,3) and substitute in the quadratic equation to solve for a

For x=2, y=3

$3=a(2-4)^2-1$

$3=4a-1$

$4a=4$

$a=1$

The quadratic equation is

$y=(x-4)^2-1$

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

For y=0

$(x-4)^2-1=0$

Solve for x

$(x-4)^2=1$

take square root both sides

$(x-4)=(+/-)1$

$x=4(+/-)1$

$x=4+1=5\\x=4-1=3$

therefore

The x-intercepts are the points (3,0) and (5,0)

7 0

3 years ago

Read 2 more answers

2 1/7 + 9 15/28 + -9 5/14

Free_Kalibri [48]

Answer:

65/28 or 2 9/28

Step-by-step explanation:

Hope this helps!

3 0

3 years ago

Please help me<br>this is confusing

Mandarinka [93]

Answer:

divide 5/9 from 10/21 first then divide it again by 6/7

Step-by-step explanation:

4 0

2 years ago