What number should be added to both sides of the equation to complete the square?
x2 - 6x = 5

Answer:

d. f(x) = 4(x + 3)

Answer:

a) 0.1587 = 15.87% probability that a battery will break down during the warranty period.

b) The expected profit of the auto store on a battery is of $15.239.

c) The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.

This means that [tex]\mu = 40, \sigma = 16[/tex]

a. What is the probability that a battery will break down during the warranty period?

Two year warranty, that is, 24 months. This probability is the pvalue of Z when X = 24. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{24 - 40}{16}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

0.1587 = 15.87% probability that a battery will break down during the warranty period.

b. What is the expected profit of the auto store on a battery?

1 - 0.1587 = 0.8413 probability of a profit of $20.

0.1587 probability of a loss of $10. So

[tex]E = 0.8413*20 - 0.1587*10 = 15.239[/tex]

The expected profit of the auto store on a battery is of $15.239.

c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?

Multiplying the average for a battery by 500. So

15.239*500 = $7,619.50

The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.

Answer:

M < or = -20

Step-by-step explanation:

Brainlist please

Answer:

Imma guess around 350 cubic inches

Step-by-step explanation:

I'm just going off of my hand compared to my basketball

Answer:

About 433.526 inches^3

Step-by-step explanation:

Goal: Calculate the volume of a Basketball as accurately as possible. Objective 1: Calculate the volume of a basketball.

Step One: Find the radius of the basket ball inflated at 8 PSI. To do this we used a string to measure the circumference of the basket ball arriving at a measurement of 29 inches. Next we inserted that number into the formula C = 2πR where C= circumference and R= Radius. We found that where C= 29inches, R= 4.615 inches.

Solve with Volume of a ball or sphere = 4/3*pi*radius

Answer:

D

Step-by-step explanation:

Answer:

C) It will not change

Hope this helps! :)

Answer:

Step-by-step explanation:

36x^3 - 81x

9x(4x^2 - 9)

9x(2x - 3)(2x + 3)

She is right

Answer:

≈4776

Step-by-step explanation:

r=78/2

r=39

A=3.14r^2

A=3.14(39)^2

A=3.14*1521

A≈4776

Hope this helps :)

Answer:

Step-by-step explanation:

The length of the strip is equal to perimeter of the kitchen.

Cost of the strip is:

Hi there!

[tex]\large\boxed{x = \frac{\pi}{3} \text{ and } \pi}[/tex]

We are given:

cos(7x)cos(4x) = -1 - sin(7x)sin(4x)

Begin by moving all terms with variables to one side:

cos(7x)cos(4x) + sin(7x)sin(4x) = -1

The corresponding trig identity is cos(A - B). Thus:

cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1

cos(3x) = -1

cos = -1 at  π, so:

3x = π

x = π/3

We can also find another solution. Let 3π = -1:

3x = 3π

x = π

Thus, solutions on [0, 2π) are π/3 and π.

9514 1404 393

Answer:

  y = 6

Step-by-step explanation:

Let's call the marked angles A, B, C, clockwise from upper left.

Along the vertical transversal, we observe that A+90° and C are alternate exterior angles, so are congruent. This lets us find a value for x.

  A+90 = C

  4x +90 = 11x -8

  98 = 7x

  14 = x

Then angle A is ...

  A = 4x° = 4(14)° = 56°

__

Along the horizontal transversal, we observe that A and B are alternate exterior angles, so are congruent. This lets us find a value for y.

  A = B

  56° = (9y +2)°

  54 = 9y

  6 = y

The value of y is 6.

Answer:

(-1,-2)

Step-by-step explanation:

For a point (a,b) rotated 90° counterclockwise about the origin, it's new coordinates are (-b,a).

So since C is originally (-2,1), it's new coordinates are (-1,-2)

Answer:

the markup percentage is 66.67%

Step-by-step explanation:

The computation of the percent of markup based on cost is shown below:

= (Selling price - paid price) ÷ (paid price)

= ($15 - $9) ÷ ($9)

= 66.67%

By taking the difference of the selling price & paid price and then divided it by paid price we can get the percentage of markup

Hence, the markup percentage is 66.67%

Answer:

A) Yes; AA Similarity

Step-by-step explanation:

Yes; AA Similarity

Answer:

y = -3x + 8

Step-by-step explanation:

plug in the slope of -3 and the point (3, -1) into the equation: y = ax + b  to find b. (the slope of -3 = a)

=> -1 = 3(-3) + b

=> b = 8

plug in b= 8 & the slope of -3 into the equation: y = ax + b

=> y = -3x + 8

36 to the nearest hundredth is just 36

To round 36 to the nearest hundredth consider the thousandths' value of 36, which is 0 and less than 5. Therefore, the hundredths' value of 36 remains 36

Answer:

Round 36 to the nearest tenth, Leaving only one number after the decimal point, Then you have come to the right post.

Step-by-step explanation:

Round off to nearest 10. Rounding every place-value of number. Round off a number to the nearest tens round off to the nearest multiple of ten.

A large number may be rounded off to the nearest 10.

Hope It Helps!

Answer:

i think the answer is 105.96

Answer:

Step-by-step explanation:

Area of the Shaded region = area of the Trapezoid - Area of the triangle

Area of the Trapezoid

b1 = 14

b2 = 26

h = 15

Area = (b1 + b2 ) * h / 2

Area = (14 + 26) * 15/2

Area = 40 * 15/2

Area = 300 in^2

Area of the triangle

Area = 1/2 b * h

b = 26

h = 15 - 6

h = 9

Area = 1/2 * 26 * 9

Area = 117 in^2

Area of the shaded region

Area of the shaded region = 300 - 117

Area of shaded region = 183

Answer:

160pi

Step-by-step explanation:

the volume of a cylinder is found using the formula V=pi x r² x h. taking r=4 this means we have pi x 16 x10 =160pi

Answer:

∠GHJ and ∠FEC

Step-by-step explanation:

Alternate exterior angles are two angles that lie on the outer part of the parallel lines but on different sides.

∠GHJ and ∠FEC lie on the outer parts of the parallel lines, but different sides.

∠GHJ is on the lower left side.

∠FEC is on the upper right side.

Answer:

ok

Step-by-step explanation:

I think

Answer:

45.3 miles/h

Step-by-step explanation:

let 'x' be the speed of the car.

60 × 2/3 = 120/3 = 40  

30 × 1/5 = 151/5  

151/5 /40 = x / 60  

151 / 200 = x / 60

=> x = (151×60) / 200

=> x = 45.3

(hope this helps can i plz have brainlist :D hehe)

N is to the left of the zero which means it is a negative number.

P is the the right of zero which means it is a positive number.

A negative number is less than a positive number, so the answer would be:

The number with the least value is N

The number with the greatest value is P

Answer:

Option c is correct

Step-by-step explanation:

Hope it helps✌

Answer:

9.4

3rd option

The boats are 9.4 units apart.

Answer:

1) x- y = 8

x + y = 12

eliminate one variable by adding the equations

2x = 20

divided by 2 on both sides

x = 10

substitute the value of x in the equation 1

10 - y = 8

-y = 8- 10

y =2

[x , y]

[10 , 2]

2) 2x - y = 4

3x + y = 6

eliminate one variable by adding the equations

5x = 10

x = 2

substitute the value of x in the equation

2(2) - y = 4

4 - y = 4

y = 0

[x ; y]

[2; 0]

3) x + 2y = 10

x + 4y = 14

multiply equation 1 by - 1

-x -2y = -10

x + 4y = 14

eliminate one variable by adding the equations

2 y = 4

y = 2

substitute the value of y in the equation 1

x + 2(2) = 10

x + 4 = 10

x = 6

[x ; y]

[6 ; 2]

4 ) 3x + y = 9

y = 3x + 6

simplify the expression

3x + y = 9

- 3x + y = 6

eliminate one variable by adding the equations

2y = 15

y = 15/2

substitute the value of y in equation 1

3x + 15/ 2 = 9

3x = 3/2

x = 1/2

[x ; y]

[1/2 ; 15/ 2]

5) 4x + 5y = 15

6x - 5y = 18

eliminate one variable by adding the equations

10 x = 33

× = 33/10

substitute the value of x in equation I

4 (33/10) + 5y = 15

66/5 + 5y =15

5y = 9/5

y = 9/25

[x ; y]

[33/10 ; 9/25]

6) 5x = 7y

x + 7y = 21

in equation I move the variable to the left

5x - 7y = 0

x + 7 y = 21

eliminate one variable by adding the equations

6x = 21

x = 7/2

substitute the value of x in the equation

5(7/2) = 7y

35/2 = 7y

5/2 = y

[x ; y ]

[7/2 ; 5/2 ]

Answer:

45

Step-by-step explanation:

9x10/2=45

Answer:

(gof)(x) = x² + 2x + 1

Step-by-step explanation:

You can solve this by plugging  f into g and finding the result:

(gof)(x) = f(x)²

= (x + 1)²

= x² + 2x + 1

Answer:

x = 27.2

Step-by-step explanation:

Apply trigonometric function to solve for x.

Reference angle = 54°

Side length opposite to reference angle = 22

Hypotenuse = x

We would apply SOH:

Sin 54 = Opp/Hyp

Sin 54 = 22/x

x*sin 54 = 22

x = 22/sin 54

x = 27.1934955 ≈ 27.2 (nearest tenth)