If the following inequality is divided by −2, what is the resulting inequality? −2x≤−20

Answer:

2.54 miles/hr

2.04 miles/hr

Step-by-step explanation:

Given: Distance between the two towns = 1100 miles

Difference between speeds = [tex]\frac{1}{2}[/tex] miles/hr

Total time when they meet = 240 hours

To find:

Let distance traveled by first group = [tex]x[/tex] miles.

Now, the distance traveled by second group = (1100-[tex]x[/tex]) miles/hr

The relation between Speed, Time and Distance is given as:

[tex]\text{Speed =} \dfrac{\text{Distance}}{\text{Time}}[/tex]

Let speed of first group = [tex]S_1[/tex]

[tex]S_1 = \dfrac{x}{240}[/tex]

Let speed of second group = [tex]S_2[/tex]

[tex]S_2 = \dfrac{1100-x}{240}[/tex]

As per question, [tex]S_1[/tex] = [tex]S_2[/tex] + [tex]\frac{1}{2}[/tex]

[tex]\dfrac{x}{240} = \dfrac{1100-x}{240} + \dfrac{1}{2}\\\Rightarrow \dfrac{x}{240} - \dfrac{1100-x}{240} = \dfrac{1}{2}\\\Rightarrow \dfrac{x-1100+x}{240} = \dfrac{1}{2}\\\Rightarrow 2x - 1100 = 120\\\Rightarrow 2x = 1220\\\Rightarrow x = 610 ft[/tex]

Now,

[tex]S_1 = \dfrac{x}{240}[/tex]

Putting value of [tex]x[/tex]:

[tex]S_1 = \dfrac{610}{240}\\\Rightarrow S_1 = 2.54\ miles/hr[/tex]

Similarly, putting value of [tex]x[/tex] in [tex]S_2[/tex]:

[tex]S_2 = \dfrac{1100-610}{240}\\\Rightarrow S_2=\dfrac{490}{240}\\\Rightarrow S_2 = 2.04\ miles/hr[/tex]

Answer:

The expression created is: [tex]3x^2+3x+8x-7[/tex]

Simplified, we obtain : [tex]3x^2+11x-7[/tex]

Step-by-step explanation:

We are to create an expression that satisfies the following conditions

Let the two like terms be 3x and 8x

Let the integer term = -7

Let the other term [tex]=3x^2[/tex]

Our written expression is therefore:

[tex]3x^2+3x+8x-7[/tex]

We simplify the expression by solving the like terms for a single term

[tex]3x+8x=11x\\$Therefore\\3x^2+3x+8x-7=3x^2+11x-7[/tex]

Answer:

  [tex]d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}[/tex]

Step-by-step explanation:

The Law of Cosines gives an immediate result. No translation to Cartesian coordinates is necessary. That law makes use of the angle between the vectors, u2-u1

  [tex]d^2=r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)\\\\\boxed{d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}}[/tex]

Answer:

45

please see the attached picture for full solution

hope it helps

Good luck on your assignment

Answer:

76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Step-by-step explanation:

Given:  In​ 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.

To find: year when 76 % of babies born out of​ wedlock

Solution:

A sequence is said to be in arithmetic progression if the difference between the terms is same.

For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]

The given situation also forms an arithmetic progression with  [tex]a=28\,,\,d=0.6[/tex]

Also, put [tex]a_n=76[/tex]

So,

[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]

So, 76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Answer:

Step-by-step explanation:

The probability that the forester does not get the seedlings is 1/2 if the mean density of seedlings is 5 per square metre.

Density means the area within which a substance is collected or taken.

We have been given the mean density =5 square metre.

And we  have to calculate the probability that the forester will not get any seedlings.

So the probability that he will get the seedlings will be=5/10

which is 1/2

So the probability that he will not get the seedlings will be 1-1/2

that is 1/2.

Hence the probability that he will not get seedlings will be 1/2.

Learn more about probability at https://brainly.com/question/24756209

#SPJ2

Answer:

V=16x^5+8x^4+56x^3.

Step-by-step explanation:

The volume of the rectangular prism is V=16x^5+8x^4+56x^3.

Formula for rectangle prism: V=whl

Formula: L*W*H

Answer: V=16x^5+8x^4+56x^3

Hope this helps.

Answer:

(a)(B)Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .

(b)P(20‑ to 24‑year‑old who is married)=0.027

(c)P(20–24 year old)=0.26

(d)P(married)=0.398

Step-by-step explanation:

Given the probability model below:

[tex]\left\begin{array}{|c|c|c|c|c|}$Age in years& 20 - 24& 25 - 29& 30 - 34& 35 - 39\\$Never married& 0.227& 0.156& 0.089& 0.054\\ $Married &0.027& 0.086& 0.137& 0.148\\$Widowed/divorced/separated &0.006 &0.015& 0.022& 0.033\end{array}\right\\[/tex]

(a)

0.526+0.398+0.076=1

Therefore this is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .

(b) The probability that the person chosen is a 20‑24-year‑old who is married

P(20‑ to 24‑year‑old who is married)=0.027

(c)Probability that the person chosen is 20 – 24 years old

P(20–24 year old)=0.227+0.027+0.006=0.26

(d)Probability that the person chosen is married

Answer:

The ratio of the government's expenses to it's receipts for 2013 is 1.3333333 trillion

Step-by-step explanation:

According to the given data we have the following:

Receipt=$2.1 trillion

Expenses=$2.8 trillion

Hence, it represent a decifit of $2.8 trillion-$2.1 trillion=$0.7 trillion

Therefore, to calculate the the ratio of the government's expenses to it's receipts for 2013 we would have to use the following formula:

ratio of the government's expenses to it's receipts=$2.8 trillion/$2.1 trillion

ratio of the government's expenses to it's receipts=1.3333333 trillion

The ratio of the government's expenses to it's receipts for 2013 is 1.3333333 trillion

Answer:

ED = 8

Step-by-step explanation:

AC = 21 which means AE is 1/3 of the length of AC.

So, ED must also be 1/3 of the length of BC.

1/3 x 24 = 8

Answer:

A. [tex]G(x) = x^2+7[/tex]

Step-by-step explanation:

To shift the function F(x), seven units upwards, there needs to be a 7 being added. Based on this, only "A," is correct.

Answer:

Hope this is correct

Answer:

B =33.69

Step-by-step explanation:

Since this is a right triangle, we can us trig functions

tan B = opposite side/ adj side

tan B = 6/9

Take the inverse tan of each side

tan ^ -1 tan B = tan ^-1 (6/9)

B =33.69006753

To the nearest hundredth

B =33.69

Answer:

33.69°

Step-by-step explanation:

From Trigonometry identity;

Tan<B = 6/9 = 2/3 [opposite/adjacent]

B = Tan^{-1} 2/3

=33.69°

Answer:

[tex]h \leq 5[/tex]

Step-by-step explanation:

Time already spent on the train is at least 5 hours

Since the trip to Fairbanks take 10 hours, we have that, the sum of the number of hours left, h and the time already spent will be equal to 10.

[tex]t+h=10\\$Since the time for which the passenger has been on the train \geq 5\\5+h \leq 10\\h \leq 10-5\\$The inequality that describes in how many more hours, h the train will reach Fairbanks, therefore, is:\\h \leq 5[/tex]

Answer: angle A = 72 and angle C = 72

Step-by-step explanation:

Angle A and C are opposites so they have to equal each other so do the equation 3y+27=5y-3. y would come out to be 15 and so to find the angles you would replace y with 15.

Answer:

The answer is 154 ft.

Step-by-step explanation:

You would take the total height (305) and subtract is by the actual statue(151) to get your answer.

305-151=154

Answer:

154

Step-by-step explanation:

Answer:

As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is

W

M

W

M

W

M

in that order.

Now as we four women, three seats for women can be filled in

X

4

P

3

=

24

ways

and similarly as we four men, three seats for men can be filled in

X

4

P

3

=

24

ways

Hence, total

24

×

24

=

576

permutations.

Step-by-step explanation:

Answer:

Option (A)

Step-by-step explanation:

Two inequalities have been given as,

y > 3x + 6 --------(1)

y < 3x - 7 ------(2)

Inequality (1) shows the solution area shaded in blue, means all the solutions for the inequality will lie in the blue area.

Similarly, solutions of inequality (2) will lie in red area.

No common area for the inequalities.

Therefore, system of inequalities will have no solution.

Option (A) will be the answer.

Answer:

4x²

Step-by-step explanation:

Your equation is 4x² - 6x² + 7x² - 20x² + 19x².

Since they all have the same variable, simply combine them all to find your answer.

4x² - 6x² + 7x² - 20x² + 19x²

-2x² + 7x² - 20x² + 19x²

5x² - 20x² + 19x²

-15x² + 19x²

4x²

Answer: 7,864,320

Step-by-step explanation:

Because the doubling time is 20 minutes, the bacteria would have gone through binary fission(cell division in bacteria) 18 times after 6hours(6*60/20)

Nt=N0 * 2^n

N0=starting population

n=number of times bacteria divide

So

30*2^18=7,864,320

The scale for the second values is 56/8 = 7

C = 3 x 7 = 21

C= 21

Answer:

Greater x =+ 7

Lesser x = -7

Step-by-step explanation:

G(x) = -10x2+ 490

Let the left side = 0

So we have

0= -10x2+ 490

Solving the above now by allowing the variable with the coefficient of x cross the equal sign.

10x²= 490

Dividing by 10

X²= 490/10

X² = 49

Taking the root of both sides

X= √49

X = + 7or -7

Bigger x =+ 7

Smaller x = -7

Answer:

x=4

Step-by-step explanation:

think of the equation like this: you have to do the inverse(opposite) operations so for adding you would subtract it. So for the adding 3 you would subtract it from both sides of the equation and get X=4

Answer:

The probability that a defective ball bearing was manufactured on a Friday = 0.375

Step-by-step explanation:

Let the event of making a mistake = M

The event of making a precision ball bearing production on Monday = Mo

The event of making a precision ball bearing production on Tuesday = T

The event of making a precision ball bearing production on Wednesday = W

The event of making a precision ball bearing production on Thursday = Th

The event of making a precision ball bearing production on Friday = F

the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04

4% on Wednesday, P(M|W) = 0.04

4% on Thursday, P(M|Th) = 0.04

8% on Monday, P(M|Mo) = 0.08

and 12% on Friday = P(M|F) = 0.12

The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.

P(Mo) = 0.20

P(T) = 0.20

P(W) = 0.20

P(Th) = 0.20

P(F) 0.20

The probability that a defective ball bearing was manufactured on a Friday = P(F|M)

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F)

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

We can obtain each of these probabilities by using the expression for conditional probability.

P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016

P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008

P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008

P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008

P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F) = 0.024

P(M) = 0.064

P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375

Hope this Helps!

Answer:

2.96 seconds

Step-by-step explanation:

Let H(x) = zero and solve for "x".

43 - 4.9x² = 0

4.9x²=43

x²=8.77

x=2.96

therefore, approximately when x=2.96seconds, the rock strike the ground.

Answer:

c.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

[tex] \frac{ \sqrt{75a} + \sqrt{12a} + \sqrt{27a} }{ \sqrt{3a} } \\ \frac{ \sqrt{(25 \times 3)a} + \sqrt{(4 \times 3)a} + \sqrt{(9 \times 3)a} }{ \sqrt{3a} } \\ \frac{ 5\sqrt{3a} + 2 \sqrt{3a} + 3\sqrt{3a} }{ \sqrt{3a} } \\ \frac{(5 + 2 + 3) \sqrt{3a} }{ \sqrt{3a} } = 10[/tex]

Answer: See below

Step-by-step explanation:

My old math notebook had simillar question,hope that help

√75a+√12a-√27a/√3a

=√a(3*25)+√a(3*4)+√a(3*9)/√3a

=√25*√3a+√4*√3a+√9*√3a/√3a

=(5+2+3)√3a/√3a

=5+2+3=10