Two trains leave stations 456 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour while the other travels at 105miles per hour. How long will it take for the two trains to meet?

Answer:

D. No solution

Step-by-step explanation:

Given

[tex]y = 3x + 7[/tex]

[tex]y = 3x + 2[/tex]

Required

The number of solutions

We have:

[tex]y = 3x + 7[/tex] and [tex]y = 3x + 2[/tex]

Equate both i.e.

[tex]y = y[/tex]

So, we have:

[tex]3x + 7 = 3x + 2[/tex]

Subtract 3x from both sides

[tex]3x -3x + 7 = 3x -3x + 2[/tex]

[tex]7 = 2[/tex]

The above is false

i.e. [tex]7 \ne 2[/tex]

Hence, the system has no solution

Answer:

tom ate 1/4 pizza, so that left him with 3/4 pizza.

Now that 3/4 is divided into 1/12 , so now he got 3/4  : 1/12

= 9 slices of 1/12 pizzas , or 9/12 of the original pizzas

Now it remained 1/6 or 2/12 of the original pizzas.

which mean, the amount of friends that got pizza are : 9 - 2 = 7 friends

hope this helps

Step-by-step explanation:

Answer:

[tex]remaining = 1 - ( \frac{1}{4} + \frac{1}{4} ) \\ = \frac{1}{2} \\ fraction \: given \: to \: father = \frac{1}{3} \times \frac{1}{2} \\ = \frac{1}{6} \\ pizza \: left \: for \: brother = \frac{1}{2} - \frac{1}{6} \\ = \frac{1}{3} [/tex]

Answer:

0.4114 = 41.14% probability that he answers at most three of them are correct

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.

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.

20 questions:

This means that [tex]n = 20[/tex]

Assume that each question has five possible choices, and only one of them is correct.

This means that [tex]p = \frac{1}{5} = 0.2[/tex]

What is the probability that he answers at most three of them are correct?

This is:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

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

[tex]P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115[/tex]

[tex]P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576[/tex]

[tex]P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369[/tex]

[tex]P(X = 3) = C_{20,3}.(0.2)^{3}.(0.8)^{17} = 0.2054[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0115 + 0.0576 + 0.1369 + 0.2054 = 0.4114[/tex]

0.4114 = 41.14% probability that he answers at most three of them are correct

Use the chain rule:

[tex]\frac{\mathrm dy}{\mathrm dx}=3(-3x^5+1)^2\frac{\mathrm d[-3x^5+1]}{\mathrm dx}=3(-3x^5+1)^2(-15x^4)=\boxed{-45x^4(1-3x^5)^2}[/tex]

Let A be the first sequence, and denote by [tex]a_n[/tex] the n-th term in A.

Consider the forward differences of A :

16 - 7 = 9

30 - 16 = 14

49 - 30 = 19

73 - 49 = 24

Call this sequence of first differences B, so that for n ≥ 1,

[tex]b_n=a_{n+1}-a_n[/tex]

where [tex]b_n[/tex] is the n-th term of B.

Now consider the forward differences of B, which is another sequence we'll call C :

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

Then if [tex]c_n[/tex] is the n-th term of C, we have for all n ≥ 1,

[tex]c_n=b_{n+1}-b_n=5[/tex]

which gives

[tex]b_{n+1} = b_n+5[/tex]

This tells us B is an arithmetic sequence - the first term is 9 and the difference between consecutive terms is 5, so we have for n ≥ 1,

[tex]b_n = 9 + 5(n-1) = 5n + 4[/tex]

Plug this into the recurrence for A :

[tex]a_{n+1} = a_n + b_n = a_n + 5n + 4[/tex]

We don't need to solve for [tex]a_n[/tex], fortunately; we just want the next term, which would be

[tex]a_6 = a_5 + 5^2 + 4 = 73 + 25 + 4 = \boxed{102}[/tex]

Answer:

huh?

Step-by-step explanation:

whats the questionnnnnnn

Answer:

a circle is 2d and a cone is 3d and a cone has a circle on the bottom

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Since f(x) = x, then where there is x, we will substitute g(x). So since f(x) = x, then f[g(x)] = 2x + 7, since there is only on x.

Now, we substitute the value of x, 2(11) + 7 = 22 + 7 = 29

Solution :

Let x = number of coach class tickets sold per day on $ 10 reduced price

y = number of the business class tickets sold per day on $ 50 reduced per price.

Number of the coach class tickets sold = 20 per day at a price of $ 250

Number of the business class tickets sold = 10 per day at a price of $ 750

Decrease in the price of coach class tickets by $ 10 increases the number of tickets sold by 4 per day

Decrease in the price of business class tickets by $ 50 increases the number of tickets sold by 2 per day.

Therefore, the coach price, p(x) = 250 - 10x

Business class price, p(y) = 750 - 50y

Coach tickets, q(x) = 2 + 4x

Business class tickets, q(y) = 6 + 2y  

Revenue R(x, y) = p(x) q(x) + q(y) q(y)

R(x, y) = (250-10x)(20+4x)+(750-50y)(6+2y)

R(x) = (250-10x)(0.4)+(20+4x)(-10)+0 = 0

1000-40x-200-40x=0

80x = 800

x = 10

R(y) = 0 + (750 - 50y)(0.2) + (6+2y)(-50) = 0

1500 - 100y+(-300-100y) = 0

200 y = 1200

y = 6

P(x) = 250 - 10(10) = $ 150

P(y) = 780-50(6) = $450

q(x) = 20 + 4(10) = 60

q(y) = 6 + 2(6) = 18

Maximum revenue = 150 x 60 + 450 x 18

                              = 9000 + 8100

                              = $ 17100

Answer:

1. 490.6 mm²

2. 14.1 ft²

Step-by-step explanation:

1. 3.14×(12.5)²= 3.14 × 156.25 =490.6mm²

2. ½×3.14×3²= 3.14×4.5= 14.1 ft²

Answer:

11

Step-by-step explanation:

Por mera logica

Answer:

11

Step-by-step explanation:

3 X 4 =  12

12-1 = 11

Order of operations says you multiply first.

The problem tells you that x = 4

multiply 3 and 4= 12

next take the answer and subtract 1 to get 11

Answer:

7/2 is the slope and 5 is the y-intercept

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

7x-2y=-10

subtract 7x on both sides

-2y=-7x-10

divide by -2 on both sides

y=(7/2)x+5

7/2 is the slope and 5 is the y-intercept.

Answer:

s= 15

Step-by-step explanation:

The entire angle equals 180 degrees.

We already know the value of part of the angle, 37 degrees.

So, subtract 37 from 180. You get 143.

Create an equation: 143=9s+8

Subtract 8 from 143. You get 135.

135=9s

135/9=15

So, s=15

Answer:

put all 3 together. so...

8 + 6 + 3 = 17

-35 + (-5) + (-1) = -41

17x - 41 = 180 (how many degrees a triangle has)

+ 41. + 41

17x = 221

÷17. ÷17

x = 13

Answer:

A cube size is 150mm

Step-by-step explanation:

I think it will be

Answer:

Step-by-step explanation:

Start

<F = <Q                     Given

<GPF = <RPQ           Vertically opposite angles

<FGP = <QRP            A triangle has 180 degrees. 2 equal angles means the third pair must be equal

Triangle GPF ~ Triangle RPQ   AAA

end

I don't see any way to make these triangles similar except by stating the statement and why it is so. There really are no yes / no choices. If you get another answer, choose it.

20

JL/LE = 90/27                 Given

KL /LD = 90/27               Given

<JLK = <DLK                   Vertically opposite

Are the ratios equal       Yes  Then is the angle included Yes

Then the triangles are similar.

Are the ratios not equal  No then the triangles cannot be similar

Is the angle not included  Then similarity cannot be proved.

ΔJLK ≈ ΔDLK                  Equal Ratios and included angle === similarity

9514 1404 393

Explanation:

19) ∠F ≅ ∠Q; ∠FPG ≅ ∠QPR  ⇒  ∆FPG ~ ∆QPR (AA)

__

20) LE/LK = 3/10; ∠ELD ≅ ∠KLJ; LD/LJ = 3/10*  ⇒  ∆ELD ~ ∆KLJ (SAS)

* the ratios are the same, hence the sides are proportional

_____

The above format A; B; C ⇒ (similarity statement) (postulate) is intended to be sufficient for you to fill in a flowchart diagram similar to the one attached.

Answer:

r = 8°

Step-by-step explanation:

6r - 3 = 45°  since we are trying to find r

6(8) - 3 = 45° substitute r for 8 and solve

48 - 3 = 45° r = 8

the answer is b

cccxcxcxcxcxzczczxc

The percentage of the rate of decrease in the medication will be 75%. Option A is correct.

The exponential function is characterized as a function that increases quickly and whose value is always positive. With the exponent y = aˣ, where a is the constant and a>1.

It is given that the function is,f(x) = 500(0.75)ˣ. The number x represents the number of hours since the patient took their medication.

f(x) = 500(0.75)ˣ

Compare the function with the standard function as

y=baˣ

Where b is the constant value, a is the percent of the rate of decrement and x is the time period,

The value of a for the given function will be 0.75. The value is in percentage form and can be written as,

=0.75 ₓ 100

=75%

Thus, the medication's rate of decline will be 75%. Option A is correct.

Learn more about the exponential function here:

brainly.com/question/11487261

#SPJ2

Answer:

3x + 30= 90

3x=60

x = 20

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

Answer:

the digit in the thousandths place is the 8

Step-by-step explanation:

Given:

The term is [tex]\sqrt{-80}[/tex].

To find:

The simplified form of the given term in terms of i.

Solution:

We have,

[tex]\sqrt{-80}[/tex]

It can be written as:

[tex]\sqrt{-80}=\sqrt{80\times (-1)}[/tex]

[tex]\sqrt{-80}=\sqrt{80}\times \sqrt{-1}[/tex]

[tex]\sqrt{-80}=\sqrt{16\times 5}\times i[/tex]         [tex][\because \sqrt{-1}=i][/tex]

On further simplification, we get

[tex]\sqrt{-80}=\sqrt{16}\times \sqrt{5}\times i[/tex]

[tex]\sqrt{-80}=4\times \sqrt{5}\times i[/tex]

[tex]\sqrt{-80}=4\sqrt{5}i[/tex]

Therefore, the required term is [tex]4\sqrt{5}i[/tex].

Answer:

AD = 6m

Step-by-step explanation:

Sin(30) = AD / 12

Sin(30) * 12 = AD

6 = AD

Hope this helps!

Find AD.

[tex] \sf a. \: 2\sqrt{3} \: m[/tex]

[tex] \sf b. \: 3 \sqrt{3} \: m[/tex]

[tex] \sf c. \: 6 \: m[/tex]

[tex] \sf d. \: 6 \sqrt{3} [/tex]

____________________

Here, Sin θ is 30°

Sin = [tex] \bf \frac{perpendicular}{hypotenuse} [/tex]

Here, θ is 30°

Substituting the values, We get,

∴ Sin ( 30 ) = [tex] \sf \frac{AD}{BC} [/tex]

Substituting the value of BC as 12, We get,

⇒ Sin ( 30 ) = [tex] \sf \frac{AD}{12} [/tex]

Transposing 12 to Left Hand Side, We get,

⇒ Sin ( 30 ) × 12 = AD

Calculating further, We get,

⇒ AD = 6 m

∴ AD = 6 m

The Length of AD is 6 m

Answer:

C. Denominator is a power of 10

Step-by-step explanation:

Answer:

[tex]Width = 4ft[/tex]

[tex]Height = 4ft[/tex]

[tex]Length = 8ft[/tex]

Step-by-step explanation:

Given

[tex]Volume = 128ft^3[/tex]

[tex]L = 2W[/tex]

[tex]Base\ Cost = \$9/ft^2[/tex]

[tex]Sides\ Cost = \$6/ft^2[/tex]

Required

The dimension that minimizes the cost

The volume is:

[tex]Volume = LWH[/tex]

This gives:

[tex]128 = LWH[/tex]

Substitute [tex]L = 2W[/tex]

[tex]128 = 2W * WH[/tex]

[tex]128 = 2W^2H[/tex]

Make H the subject

[tex]H = \frac{128}{2W^2}[/tex]

[tex]H = \frac{64}{W^2}[/tex]

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

[tex]A = LW + 2(WH + LH)[/tex]

The cost is:

[tex]Cost = 9 * LW + 6 * 2(WH + LH)[/tex]

[tex]Cost = 9 * LW + 12(WH + LH)[/tex]

[tex]Cost = 9 * LW + 12H(W + L)[/tex]

Substitute: [tex]H = \frac{64}{W^2}[/tex] and [tex]L = 2W[/tex]

[tex]Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)[/tex]

[tex]Cost =18W^2 + \frac{768}{W^2}*3W[/tex]

[tex]Cost =18W^2 + \frac{2304}{W}[/tex]

To minimize the cost, we differentiate

[tex]C' =2*18W + -1 * 2304W^{-2}[/tex]

Then set to 0

[tex]2*18W + -1 * 2304W^{-2} =0[/tex]

[tex]36W - 2304W^{-2} =0[/tex]

Rewrite as:

[tex]36W = 2304W^{-2}[/tex]

Divide both sides by W

[tex]36 = 2304W^{-3}[/tex]

Rewrite as:

[tex]36 = \frac{2304}{W^3}[/tex]

Solve for [tex]W^3[/tex]

[tex]W^3 = \frac{2304}{36}[/tex]

[tex]W^3 = 64[/tex]

Take cube roots

[tex]W = 4[/tex]

Recall that:

[tex]L = 2W[/tex]

[tex]L = 2 * 4[/tex]

[tex]L = 8[/tex]

[tex]H = \frac{64}{W^2}[/tex]

[tex]H = \frac{64}{4^2}[/tex]

[tex]H = \frac{64}{16}[/tex]

[tex]H = 4[/tex]

Hence, the dimension that minimizes the cost is:

[tex]Width = 4ft[/tex]

[tex]Height = 4ft[/tex]

[tex]Length = 8ft[/tex]

Right circular cone

Solve for volume

r (Radius )

h( Height )

V=πr2h

Answer:

I am kind of sure it is B try it out!

Step-by-step explanation:

Answer:

The probability that the difference between the sample mean [tex]\bar{x}[/tex] and the true population mean [tex]\mu[/tex] is : [tex]P[|\bar{x}-\mu|\leq0.7]=0.9876[/tex]

Step-by-step explanation:

Given :

Population standard deviation [tex]\sigma=2.8[/tex].

Sample size [tex]n=100[/tex]

The sample mean standard deviation[tex]=\frac{\sigma}{\sqrt{n}}[/tex]

To find :

The probability that the difference between the sample mean [tex]\bar{x}[/tex] and the true population mean [tex]\mu[/tex]

[tex]\because\frac{\sigma}{\sqrt{n}}=\frac{2.8}{\sqrt{100}}=\frac{2.8}{10}=0.28[/tex]

Now, the probability that the difference between the sample mean [tex]\bar{x}[/tex] and the true population mean [tex]\mu[/tex] is :

  [tex]P[|\bar{x}-\mu|\leq0.7][/tex], [tex]n[/tex]is large [tex]\Rightarrow \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=z[/tex]

[tex]\Rightarrow P[\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{0.7}{\frac{\sigma}{\sqrt{n}}}]=P[z<\frac{0.7}{0.28}]=P[z<2.5][/tex]

[tex]\Rightarrow P[z<2.5]=P[-2.5<z<2.5][/tex]

[tex]\Rightarrow P[-2.5<z<2.5]=P[z<2.5]-P[z\leq-2.5]\\\Rightarrow P[z<2.5]-P[z\leq-2.5]=2P[z\leq2.5]-1\\\Rightarrow 2P[z\leq2.5]-1=0.9876[/tex]

Therefore, the probability [tex]P[|\bar{x}-\mu|\leq0.7]=0.9876[/tex]

Answer:

H0 : μ = 18000

H1 : μ < 18000 - - - > Claim

Test value = - 3.578

Critical value = ±2.58

There is significant evidence to accept the claim that mean debt at graduation is less than $18000

Step-by-step explanation:

H0 : μ = 18000

H1 : μ < 18000

From the data:

Sample size, n = 30

Sample mean, x = 16298.37

The test statistic :

(16298.37 - 18000) ÷ (2605/sqrt(30))

−1701.63 / 475.60575

= - 3.578

The critical value :

Using the standard normal table;

Critical value at α = 0.01

Critical value = ±2.58

Decison region :

|test statistic | > |Critical value | ; reject H0

|3.578| > |2.58| ; We reject H0 and conclude that Mean debt at graduation is less than $18000