Write a positive or negative integer that represent the situation?

Answer: The distance between them is 8.38 km

Step-by-step explanation:

Let's suppose both of them start at the point (0km, 0km), and that Jack walks along the positive x-axis, then Jill walks at an angle of 105° measured from the positive x-axis.

After 45 minutes, jack has walked 4.5km, then if his initial position was (0 km, 0 km)

Then his new position will be (4.5km, 0km)

Jill has walked 6km, but we need to write this in rectangular components.

We can think in this as a triangle rectangle, then the components will be:

x-component = 6 km*cos(105°) = -1.55 km

y-component = 6km*sin(105°) = 5.80 km

Then the new position of Jill is ( -1.55km, 5.80km)

Now, we know that the distance between two points (a, b) and (c, d) is:

Distance = √( (a - c)^2 + (b - d)^2)

Then the distance between Jill and Jack will be equal to the distance between ( -1.55km, 5.80km) and (4.5km, 0km)

This is:

Distance = √( (-1.55km - 4.5km)^2 + (5.80km - 0km)^2)

Distance = 8.38 km

This means that they are 8.38km apart.

Answer:

0.72 , 0.9 , 7/10 , 4/5

Step-by-step explanation:

This is how the order has to be and yeah

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial distribution:

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

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

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

To use the Poisson approximation for the binomial, we have that:

[tex]\mu = np[/tex]

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that [tex]p = \frac{1}{2500} = 0.0004[/tex]

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is [tex]P(X = 4)[/tex] when [tex]n = 7000[/tex]. So

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

[tex]P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558[/tex]

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

[tex]\mu = np = 7000*0.0004 = 2.8[/tex]. So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557[/tex]

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Answer:

Step-by-step explanation:

these expressions are equivalent

4(2x+4)= 8x+16 after multiplying 4 with 2x+4

Answer:

yes

Step-by-step explanation:

Yes. If I substitute a number for x, the result is the same.

Answer:

If a>b then the major axis of the ellipse is parallel to the x -axis (and, the minor axis is parallel to the y -axis)

if a<b then the major and minor axes of the ellipse with respect to the x and y -axes are reversed

Step-by-step explanation:

Answer: $525

Step-by-step explanation:

The formula for Simple interest is calculated as PRT where

P = Principal = $7500

R = Rate = 3.5%

T = Time = 2 years

Interest = PRT

= 7500 × 3.5% × 2

= 7500 × 0.035 × 2

= $525

SSS theorem

Step-by-step explanation:

KL = MN

KN = ML

KM = KM

Answer:

i think it's ASA

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the required number be x, then we have the following equation:

Answer:

112 feet

Step-by-step explanation:

Remember the formula for area. length x width. 56 x 2 = 112 feet

Answer:

-16,24  B

Step-by-step explanation:

To solve this simplify the equation until it's just the absolute value brackets

7=.5 |x-4|-3

Add 3 to both sides and divide by .5 to get

20=|x-4|

Then solve this equation where the leftmost side is a positive and then a negative

So 20=x-4  

x=24

24 is one of our answers

Then solve it when the left side is a negative

-20=x-4

x=-16 which is the other answer

Answer:

11 is 4:6

12 is 0

Step-by-step explanation:

Answer:

a 1/10 10%

Step-by-step explanation:

Answer:

Greatest Common Factor of 40+24 is 8

Rewriting the expression using the distributive property we get             8(5+3) =8(5)+8(3)

Step-by-step explanation:

We need to F=find the greatest common factor of the two numbers 40+24 and rewrite the expression using the distributive property

The greatest number that is divisible by both numbers is known as greatest common factor.

So, Greatest Common Factor of 40+24 is 8

Now, Taking 8 common we get: 8(5+3)

It is written as: a(b+c) = ab+ac

So, we have 8(5+3) =8(5)+8(3)

Rewriting the expression using the distributive property we get 8(5+3) =8(5)+8(3)

Answer:

answer is x = 2

.... .. . . . .....

:-))

hope it helps you

Answer:

45

Step-by-step explanation:

30% of 150 students is 45, therefore, 45 students voted for Bianca.

Answer:

625

Step-by-step explanation:

i dont know why people keeps on deleting my answers that are right, but yeah this IS CORRECT STOP DELETING MY ANSWERS THAT ARE RIGHT....please

Part (a)

------------------

Work Shown:

v = u + a*t

v = 7 + 10*8 ... plug in the given values

v = 7 + 80

v = 87

==================================================

Part (b)

------------------

Work Shown:

v = u + a*t

80 = 20 + 6*t .... plug in the given values

80-20 = 6t .... subtracting 20 from both sides

60 = 6t

6t = 60

t = 60/6 .... divide both sides by 6

t = 10

Answer:

first person is write

Step-by-step explanation:

Answer:

4yd, 1ft

Step-by-step explanation:

2yd + 2yd = 4yd

4yd + 1ft = 4yd, 1ft

Answer: It’s 0.75 is my best guess. Let me know if that wrong

Step-by-step explanation:

Answer: It’s 0.75 is my best guess. Let me know if that wronger:

Step-by-step explanation:

-6/8 in decimal form is -0.75

simple formula for that is y×2=x

Answer:

m∠A = 144°, m∠B = 36°

Step-by-step explanation:

Supplementary angles are angles that add up to 180 degrees.

Substitute 4(m∠B) for m∠A.

4(m∠B) + m∠B = 180

5(m∠B) = 180

m∠B = 36°

Substitute 36 for m∠B.

4(36) = m∠A

m∠A = 144°

Answer:

exhale :)

Step-by-step explanation:

Answer:

Exhale

Step-by-step explanation:

Wishing Well by Juice WRLD

Hope you have a good day :) and thx for the points

Answer:

eleven times nine is ninety nine

Answer:

B.

Step-by-step explanation:

Answer:

Bargain Busters shop sells the cheapest soup

Step-by-step explanation:

Bargain Busters sell 4 cans of soup for £3.76

Bargain Busters sell 1 cans of soup for

3.76÷4

=0.94

cost cutters sell 3 cans of soup for £2.85

cost cutters sell 1 cans of soup for 2.85÷3

=0.95

so

Bargain Busters<cost cutters

0.94<0.95

therefore

Bargain Busters shop sells the cheapest soup

Answer:

87%

Step-by-step explanation:

100-13 = 87

87 percent of 100 is 87

Answer:

Step-by-step explanation:

The greater the negative number the more small it is

-100<-2<-1/2

Percent can be turned into decimals by moving the decimal place two spaces to the left.