Use the Distributive Property to solve the equation.
3
(8a + 12) = 25.8
4
3.
+ C •12) = 0
4.
a=
(Simplify your answers.)

Answer: 75.4 =

 70  

+ 5  

+   0.4

Step-by-step explanation:

Hope this helps :)

Answer:

[tex]y = 5x + 1[/tex] and [tex]y = 5x + 2[/tex] are two equations of lines that are perpendicular to the line whose equation is x + 5y = 50.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

In this question:

The equation of the line is:

[tex]x + 5y = 50[/tex]

Placing in the standard format:

[tex]5y = -x + 50[/tex]

[tex]y = -\frac{x}{5} + 10[/tex]

The slope is [tex]-\frac{1}{5}[/tex]

Slope of the perpendicular lines:

[tex]-\frac{m}{5} = -1[/tex]

[tex]m = 5[/tex]

So

[tex]y = 5x + b[/tex]

Attributing two values to b:

[tex]y = 5x + 1[/tex] and [tex]y = 5x + 2[/tex] are two equations of lines that are perpendicular to the line whose equation is x + 5y = 50.

Answer:

w < 15

Step-by-step explanation:

2(w+4) > 3w - 7

2w + 8 > 3x - 7

3w-2w = w

w - 7 < 8

w < 15

Answer:

P(6) is 1/12, P(Shaded) is 8/12, P(Odd or Unshaded) is 10/12, and P(Even and Shaded) is 11/12

Step-by-step explanation:

Answer:

Y

Step-by-step explanation:

Answer: D is correct

Step-by-step explanation:

Answer:

C.   x > 0 and x ≤ 3

Step-by-step explanation:

0 < x ≤ 3

when  0 < x then x > 0

Example: 0 < 2 then 2> 0

Therefor

x > 0 and x ≤ 3

Completion of question:

The Demon Drop at Cedar point in Ohio takes riders to the top of the tower and drops them 60 feet. A function that approximates this ride is h=-16^t2 + 64t + 60 where h is the height in feet and t is the time in seconds. About how many seconds does it take for riders to drop to the ground?

Answer:

4.78 s

Step-by-step explanation:

Given the equation :

h = - 16^t2 + 64t + 60

Using the quadratic formula ; where

a = - 16 ; b = 64 ; c = 60

Dropping to the ground, h = 0

16^t2 + 64t - 60 = 0

-b ± (√b²- 4ac) / 2a

-64 ± (√64²- 4(-16)(60)) / 2(-16)

-64 ± (√7936) / - 32

(-64 ± 89.08) / - 32

(-64 + 89.08) / - 32 = - 0.783 OR

(-64 - 89.08) / - 32 = 4.78

Reject the negative

t = 0.783 seconds

Answer:

The answer is B

Step-by-step explanation:

Length:

32ft. / 16ft. = 2

2 x 2cm. = 4 cm.

Width:

48ft. / 16ft. = 3

3 x 2cm. = 6cm

Answer:

b

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Plug in 12 in place of b

10+b+b

10+12+12

34

Answer:

I think the answer is $56,600

Step-by-step explanation:

I'm pretty sure you're just going to add $63,000+$8,400+$2,900+$1,1000. Then when you get a total of $75,400 and then I think you are going to subtract $15,400 from $75,400, you should get $60,000 then subtract $3,400 and you get $56,600.

Answer:

he drives 254 miles in 6 hours

Step-by-step explanation:

Answer:

254 miles in 6 hours

Step-by-step explanation:

Answer:

10% or 1%

Step-by-step explanation:

i swear u better not remove this

Answer:

B. All real numbers

Step-by-step explanation:

I calculated it logically

Answer:

I believe it is all real numbers

Answer:

A: NO

B: YES

C: NO

D: NO

Step-by-step explanation:

Answer:

C) 5/36

Step-by-step explanation:

Now, suppose, dice 1 gives 2. Here also, dice 2 can be anything between 1 and 6. But, the sum of both the dices will be 8 only if dice 2 shows 6.

Similarly, now, if dice 1’s face is 3, sum will be 8 only if dice 2’s upper face shows 5.

If dice 1 shows 4, sum = 8 only if dice 2 is 4.

If dice 1 is 5, sum = 8 only if dice 2 is 3.

If dice 1 is 6, sum= 8 only if dice 2 is 2.

Therefore, sum will be 8 only 5 times. But, sample space consists of 36 values ( combination of values of dice 1 and dice 2).

Therefore, probability = 5/36.

Hope it helps.

Answer:

Now, suppose, dice 1 gives 2. Here also, dice 2 can be anything between 1 and 6. But, the sum of both the dices will be 8 only if dice 2 shows 6.

Similarly, now, if dice 1’s face is 3, sum will be 8 only if dice 2’s upper face shows 5.

If dice 1 shows 4, sum = 8 only if dice 2 is 4.

If dice 1 is 5, sum = 8 only if dice 2 is 3.

If dice 1 is 6, sum= 8 only if dice 2 is 2.

Therefore, sum will be 8 only 5 times. But, sample space consists of 36 values ( combination of values of dice 1 and dice 2).

Therefore, probability = 5/36.

Hope it helps.

Step-by-step explanation:

Answer:

Height = 167.47 cm

Step-by-step explanation:

volume of one sphere = 4/3πr³ = 4/3(3.14)(4³) = 267.9467 cm³

267.9467 cm³ x 100 spheres = 26794.67 cm³

volume of cube = L x W x H

26794.67 = 16 x 10 x H

H = 167.47 cm

Answer:

20 words with meaning

Step-by-step explanation:

Answer:

2/3 x + 20/21

Step-by-step explanation:

Answer:

261.7 mm³

Step-by-step explanation:

the volume= ⅓×3.14×5²×10

= ⅓× 785

= 261.7 mm³

Answer:

x=2

Step-by-step explanation:

Answer:

Bank One is offering a simple interest rate of 6.25% per annum.

Step-by-step explanation:

Given that Bank One offers a certificate of deposit that pays $ 5,000 in four years for exchange for $ 4,000 today, to determine what interest rate is Bank One offering the following calculation must be performed:

(5000 - 4000) / 4 = X

1000/4 = X

250 = X

4000 = 100

250 = X

250 x 100/4000 = X

25000/4000 = X

6.25 = X

Therefore, Bank One is offering a simple interest rate of 6.25% per annum.

Answer:

The demand reduces by $7.12 per month

Step-by-step explanation:

Given

[tex]p\to price[/tex]

[tex]x \to demand[/tex]

[tex]2x^2+5xp+50p^2=24800.[/tex]

[tex]p =10; \frac{dp}{dt} = 2[/tex]

Required

Determine the rate of change of demand

We have:

[tex]2x^2+5xp+50p^2=24800.[/tex]

Differentiate with respect to time

[tex]4x\frac{dx}{dt} + 5x\frac{dp}{dt} + 5p\frac{dx}{dt} + 100p\frac{dp}{dt} = 0[/tex]

Collect like terms

[tex]4x\frac{dx}{dt} + 5p\frac{dx}{dt} = -5x\frac{dp}{dt} - 100p\frac{dp}{dt}[/tex]

Factorize

[tex]\frac{dx}{dt}(4x + 5p) = -5(x + 20p)\frac{dp}{dt}[/tex]

Solve for dx/dt

[tex]\frac{dx}{dt} = -\frac{5(x + 20p)}{4x + 5p}\cdot \frac{dp}{dt}[/tex]

Given that: [tex]2x^2+5xp+50p^2=24800.[/tex] and [tex]p = 10[/tex]

Solve for x

[tex]2x^2 + 5x * 10 + 50 * 10^2 = 24800[/tex]

[tex]2x^2 + 50x + 5000 = 24800[/tex]

Equate to 0

[tex]2x^2 + 50x + 5000 - 24800 =0[/tex]

[tex]2x^2 + 50x -19800 =0[/tex]

Using a quadratic calculator, we have:

[tex]x \approx -113\ and\ x\approx88[/tex]

Demand must be greater than 0;

So: [tex]x=88[/tex]

So, we have: [tex]x=88[/tex]; [tex]p =10; \frac{dp}{dt} = 2[/tex]

The rate of change of demand is:

[tex]\frac{dx}{dt} = -\frac{5(88 + 20*10)}{4*88 + 5*10} * 2[/tex]

[tex]\frac{dx}{dt} = -\frac{5(288)}{402} * 2[/tex]

[tex]\frac{dx}{dt} = -\frac{2880}{402}[/tex]

[tex]\frac{dx}{dt} \approx -7.16[/tex]

This implies that the demand reduces by $7.12 per month

Answer:

y - 2/3 * 63 or y - 42

Step-by-step explanation:

two-thirds of the quantity 63: 2/3 * 63

two-thirds of the quantity 63 less than y: y - 2/3 * 63 = y - 42

Answer:

$73.60

$345

simple interest = amount deposited x time x interest rate

600 + (600 x 0.055 x 5) = $765

600 + (600 x 0.055 x 5) > $2000

$765  $2000

He would not have $2000 in 5 years

Step-by-step explanation:

Total cost of items purchased = $75 + (2 x $8.50) = 92

If there is a 20% discount, he would pay (100 - 20%) 80% of the total cost =

0.8 x $92 = $73.60

commission earned = percentage commission x amount of sales

10% x $3450

= 0.1 x 3450 = 345

Amount he would have in his account = amount deposited + simple interest

simple interest = amount deposited x time x interest rate

600 x 0.055 x 5 = $165

Amount in his account in 5 years = $165 + 600 = $765

He would have less than $2000 in his account. he would have $765

Answer:

Triangle has a greater perimeter.  

Step-by-step explanation:

Triangle perimeter = 21cm

Add the sides.

Square perimeter = 16cm

Add the sides (since it's a square the sides are the same.)

Answer:

Step-by-step explanation:

sorry i tried my best i think its like a 30

Answer:

0.2097 = 20.97% probability that your longest wait is less than 12 minutes

Step-by-step explanation:

To solve this question, we need to understand the uniform and the binomial distribution.

Uniform distribution:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the probability of finding a value lower than x is given by:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

Binomial probability 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.

Probability of a single bus having a waiting time of less than 12 times:

Uniformly distributed on the interval [0, 15] means that [tex]a = 0, b = 15[/tex]

[tex]P(X < 12) = \frac{12 - 0}{15 - 0} = 0.8[/tex]

What is the probability that your longest wait is less than 12 minutes?

This is the probability that all 7 buses have waiting time less than 12 minutes, which is [tex]P(X = 7)[/tex] when [tex]n = 7[/tex], with [tex]p = 0.8[/tex]. So

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

[tex]P(X = 7) = C_{7,7}.(0.8)^{7}.(0.2)^{0} = 0.2097[/tex]

0.2097 = 20.97% probability that your longest wait is less than 12 minutes

Answer:

3(4+3x)

Step-by-step explanation:

See Image below.