A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.5 minutes and the standard deviation was 0.70 minutes. What is the probability that calls last between 3.5 and 4.0 minutes? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

Answer:

Amount of material for chain link = 30 feet

Amount of material for rope = 50 feet

Step-by-step explanation:

Let the amount of chain link = X

The amount of rope be represented by Y

He bought a total of 80 feet of materials

Hence we have:

X + Y = 80 ....... Equation 1

Y = 80 - X

The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135

X × $2 + Y × $1.50 = $135

2X + 1.5Y = 135 ......Equation 2

Substitute 80 - X for Y in Equation 2

2X + 1.5(80 - X) = 135

2X + 120 - 1.5X = 135

Collect like terms

2X - 1.5X = 135 - 120

0.5X = 15

X = 15/0.5

X = 30 feet

Substitute 30 feet for X in Equation 1

X + Y = 80 ....... Equation 1

30 + Y = 80

Y = 80 - 30

Y = 50 feet

Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet

Answer:

(-11,-7)

Step-by-step explanation:

 U           V

(-8,5) + (-3,-12)

(-8 - 3) , (5 - 12)

-11 , -7

(-11,7)

Answer:

(-11,-7)

Step-by-step explanation:

u =  (-8, 5)

v =  (-3, -12)

u+v = ( -8+-3, 5+-12)

      = (-11,-7)

Answer:

523.33 cm³

Step-by-step explanation:

Volume of sphere is given by the formula :

V = (4/3)×pi×r³

= (4/3)×3.14×125

= 523.33 cm³

Answer:

27

Step-by-step explanation:

3^3 = 3 x 3 x 3 = 27

Answer:

8.

Step-by-step explanation:

[tex]\sqrt{57} =\sqrt{3 * 19}[/tex]

Since this cannot be further simplified, we will calculate the square root of 57 with our calculators.

We find that the square root of 57 is 7.549834435, and since the tenths place is a 5, we will round up to the next whole number. So, the point on the number line that best represents the square root of 57 is 8.

Hope this helps!

Answer: Yes the sum of any two numbers is greater than the larger of the two numbers.

Step-by-step explanation:

Yes the sum of any two numbers is greater than the larger of the two numbers.

Let us assume that the two numbers are a and b and ab is the number.

a + b > a

b > a – a

b > 0

This therefore implies that b > 0.

This may however not be true when the value of b is zero(0) or a negative number.

Answer:

1. a²-a-12

2. 2x-6

3. 2a²+862a-28644

4. x³-x²-26x+30

Step-by-step explanation:

1. (a + 3)(a - 4) = a²-4a+3a-12 = a²-a-12

2. (x - 3)2 = 2x-6

3. (2a – 62)(a + 462) =2a²+924a-62a-28644 = 2a²+862a-28644

4.(x - 5)(x²+ 4x - 6) = x³+4x²-6x-5x²-20x+30 = x³-x²-26x+30

Answer:

Answer is 3

Step-by-step explanation:

[tex] \frac{ \sqrt{144} }{ \sqrt[5]{243} } - 5 + 16 \div \sqrt[3]{64} \\ = \frac{12}{3} - 5 + (16 \div 4) \\ \\ = 4 - 5 + 4 \\ = 3[/tex]

Answer:

3

Step-by-step explanation:

step by step explaination is in picture

The complete version of the question is attached below :

The length of Cityscape Bike Path is [tex]3 \frac{1}{9} miles[/tex]

Given that :

Cityscape Bike Path is [tex]2 \frac{2}{3}[/tex]

times longer than Bay View Bike Path

Length of Bay View Bike Path = [tex] \frac{7}{6} miles[/tex]

Hence, to compute the length of Cityscape Bike Path :

Cityscape Bike Path = [tex]2 \frac{2}{3} \times [/tex] Length of Bay View Bike Path

Therefore, length of Cityscape Bike Path =

[tex]2 \frac{2}{3} \times \frac{7}{6} [/tex]

Length of Cityscape Bike Path =

[tex] \frac{8}{3} \times \frac{7}{6} = \frac{56}{18} = 3 \frac{1}{9} miles[/tex]

Hence, the length of Cityscape Bike Path is [tex]3 \frac{1}{9} miles[/tex]

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Answer:

D

Step-by-step explanation:

Sector of Area=(theta/360)*pi*r^2

Sector of area=(135/360)*pi*19^2=(1083)/8 pi

BECAUSE ACCORDING TO THE PERIMETER (TRIANGLE ) FORMULA = B * H / 2.

B = BASE.

H = HEIGHT.

THE HEIGHT IS A VARIABLE VLAUE NEEDED IN ORDER TO ONTINUE TO SOLVE AND EVENTUALLY LEADING TO THE ANSWER (TRIANGLE PERIMETER.

Answer:

x = 4.5

y = 3.25

Step-by-step explanation:

Use elimination

5x + 2y = 29

x + 4y = 13 (-5)

4y(-5) = 13(-5)

2y = 29

-20y = -65

y = 3.25

Sub it back into the equation

5x + 6.50 = 29

5x = 22.5

x = 4.5

Answer:

0.5+d=h

Step-by-step explanation:

If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).

0.5+d=h

The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.

Functions were originally the idealization of how a varying quantity depends on another quantity.

Now it is given that,

Height of sprout =  1 inch

Growth per day =  1/2 inch

Let h = height of the plant (inches), and let d = number of days (days)

∵ Growth per day =  1/2 inch

So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d

Thus,  height of the plant, h = 1 + Growth of plant in d days

⇒ h = 1 + 0.5d

Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.

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#SPJ2

Cost of 1 kg = $9

So, cost of 5 kg = $9 × 5 = $45

Answer:

The probability is 0.97682

Step-by-step explanation:

We start by finding the z-values of the runner times given.

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 13 seconds and SD = 0.3 seconds

So for 12.4 seconds, we have;

z = (12.4-13)/0.3 = -0.6/0.3 = -2

For 14 seconds, we have;

z = (14-13)/0.3= 1/0.3 = 3.33

So the probability we want to calculate is;

P(-2<z<3.33)

We can find this using the standard normal distribution table

Mathematically;

P(-2<z<3.33) = P(z<3.33) - P(z < -2)

Using the standard normal distribution table, the value of this is;

P(-2<z<3.33) = 0.97682

Answer:

c

Step-by-step explanation:

i did the quiz

Answer:

8(a + b)

Step-by-step explanation:

Sun of a and b = a + b

8 times of (a + b) = 8(a + b)

Step-by-step explanation:

The area of triangle given as 120 cm2

Area of Triangle = 1/2 x b x h = 120

therefore bxh = 240

240 can be factorized as 10 x 24

The perimeter of the triangle is given as 60

so the other side has to be 26 cm

As this is a right angle triangle it should satisfy pythagoras theorem

(10)2 + (24)2 = (26)2

100+576 =676

Hence the sides of the triangle are 10 cm, 24 cm and 26 cm

Answer:

Step-by-step explanation:

f(x) = 3x² + 1

g(x) = 1 - x

To find (f - g)(2) first find (f - g)(x)

To find (f - g)(x) subtract g(x) from f(x)

That's

(f - g)(x) = 3x² + 1 - ( 1 - x)

(f - g)(x) = 3x² + 1 - 1 + x

(f - g)(x) = 3x² + x

To find ( f - g)(2) substitute 2 into (f - g(x)

That's

( f - g)(2) = 3(2)² + 2

( f - g)(2) = 3(4) + 2

( f - g)(2) = 12 + 2

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

4x*(2x - y) - 3x(x - 2y) - 2x + 1  

Use distributive property

= 4x*2x - 4x*y -3x *x - (-3x) * 2y - 2x +1

= 8x² - 4xy - 3x² + 6xy - 2x + 1

= 8x² - 3x² - 4xy + 6xy - 2x + 1

Combine like terms

= 5x² + 2xy - 2x + 1

Substitute  x = -1  & y = 2

= 5(-1)² + 2*(-1)*2 - 2(-1) + 1

= 5*1 - 4 + 2 + 1

= 5 - 4 + 2 + 1

= 4

Answer:

The probability that 100 or fewer will have 3 ​girls is 0.00734.

Step-by-step explanation:

The complete question is:

In a family with ​3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with ​3 children, what is the approximate probability that 100 or fewer will have 3 ​girls? Approximate a binomial distribution with a normal distribution.

Solution:

Let X represent the number of families who has 3 girls.

The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.

But the sample selected is too large.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 [tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]

The mean and standard deviation are:

[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]

Compute the probability that 100 or fewer will have 3 ​girls as follows:

Apply Continuity correction:

[tex]P(X\leq 100)=P(X<100-0.50)[/tex]

                  [tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]

*Use a z-table.

Thus, the probability that 100 or fewer will have 3 ​girls is 0.00734.

Answer:

x/4+10=2

x/4=2-10

x/4=-8

x=-8 x 4

x=-32

Step-by-step explanation:

Answer:

33.14 ft^2

Step-by-step explanation:

First find the area of the circle

The diameter is 20 ft so the radius is 1/2 of the diameter of 20*1/2 = 10 ft

A = pi r^2 = pi ( 10)^2 = 100 pi

The central angle is 38

That is a fraction of the circle, which is 360 degrees

38/360 = 19/180

Multiply the fraction of the circle by the area

19/180 * 100 pi

19/9 * 5 pi

Using 3.14 for pi

33.144444

To the nearest hundredth

33.14 ft^2

The area of the slice of pie that was cut, rounded to the nearest hundredth   33.14 ft^2.

We have to first find the area of the circle.

The diameter is 20 ft so the radius is 1/2 of the diameter of

20*1/2 = 10 ft.

The area of a circle [tex]A = \pi r^2[/tex]

By using the formula we have,

A= pi ( 10)^2

A = 100 pi

The central angle is 38.

That is a fraction of the circle, which is 360 degrees

38/360 = 19/180

Multiply the fraction of the circle by the area

19/180 * 100 pi

19/9 * 5 pi

Using 3.14 for pi

33.144444

To the nearest hundredth, it is 33.14 ft^2.

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Answer:

$750,000

Step-by-step explanation:

$750,000 $680,000 $600,000 $880,000 $1,200,000 $760,000 $480,000

Write the prices in increasing order and choose the middle one.

$480,000 $600,000 $680,000 $750,000 $760,000 $880,000 $1,200,000

Answer: $750,000

Answer:

x = -9, 1

Step-by-step explanation:

x (x + 8 )= 9

x^2 + 8x = 9

x^2 + 8x - 9 = 0

(x + 9)(x - 1) = 0

x = -9, 1

Hope this helps!

Answer:

x = 3 and x = 0

Step-by-step explanation:

A way to solve is simplifying the given equation:

X^2 + 8x = 9

So

x = 3 and x = 0

3^2 + 8(0) = 9

9 + 0 = 9

9 = 9

Answer:

528 cm squared

Step-by-step explanation:

A parallelogram (slanted shape at the bottom) is essentially the same area as a rectangle.

Therefore, both shapes have the same measurements.

Multiply the length and height of the rectangle to get its area: 22cm×12cm =264cm squared

Since the area of the rectangle corresponds geometrically to the area of the parallelogram, just multiply the area of the rectangle (264cm squared), by 2.

So 264×2, = 528cm squared

Ta da...

Answer:20-33x

Step-by-step explanation:

Answer:

-1, 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer is (-1,4)

Answer:

Cost = RM 857143

Loss = RM 107143

Step-by-step explanation:

Given:

Cost price is found as:

Loss is:

Answer:

b = 3

Step-by-step explanation:

Substitute the y- coordinate 15 into the equation , that is

15 = 5x ( divide both sides by 5 )

3 = x

This is the x- coordinate of the point , so b = 3

Answer:

-1.666666...

Step-by-step explanation: