What is the slope of the line showed?

Answer:

The passenger train is moving at 45 miles per hour

Step-by-step explanation:

Let the amount of time it took the two trains to travel the distance = t.

Since the two trains traveled the distance at the same time,

Rate of the passenger train =[tex]\frac{180}{t}[/tex]

Rate of the freight train = [tex]\frac{120}{t}[/tex]

Where t is in hours.

From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as

[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]

from the above equation, we can now get our value for t  as

[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]

We have our time of travel for the two trains as 4 hours.

The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour

Step-by-step explanation:

check the tile whose side length is divisible by both 150 and180 in such a way that you don't get decimal points

150÷4=37.5 so that is impossible

150÷8=18.75 so that is also impossible

150÷6=25 180÷6=30

so the six sided tile is applicable

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

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The fraction that each person gets is 1/2.

It should be noted that 2 1/2 cases of soda to split between 5 families.

In their case, the fraction that each person will get will be:

= Total / Number of people

= 2 1/2 ÷ 5

= 2.5/5

= 0.5 or 1/2.

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2 1/2 cases of soda to split between 5 families. What fraction will each person get?

Answer:

fourth option

Step-by-step explanation:

∠ FTC = ∠ MTL ( vertical angles )

Since FC and ML are parallel, then

∠ FCT = ∠ TML (corresponding angles )

Thus

Δ TCF ~ Δ TML by the AA postulate

Answer:

[tex]\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}[/tex]

Step-by-step explanation:

The two triangles are similar.

We can prove by angle-angle similarity, in [tex]\mathrm{AA}[/tex] similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.

[tex]\angle U[/tex] and [tex]\angle M[/tex] are a pair of congruent corresponding angles.

[tex]\angle V[/tex] and [tex]\angle L[/tex] are a pair of congruent corresponding angles.

Therefore,

[tex]\Delta TUV \sim \Delta TML[/tex]

Answer:

Its commutative property..

Step-by-step explanation:

Commutative property says A×B=B×A

Explanation is attached below.

Answer:

length: 9cm

width: 9cm

Step-by-step explanation:

9×9=81

Answer:$40.00

Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00

Answer:

  C. G(x) = x - 9

Step-by-step explanation:

You know that the transformation ...

  g(x) = f(x -h) +k

causes parent function f(x) to be shifted right h units and up k units.

You're looking for a function that is shifted right, so you want something that looks like ...

  g(x) = f(x -constant) = x - constant

Choice C has that form:

  C. G(x) = x - 9

_____

A. the function is shifted up 2 units

B. the function is vertically expanded by a factor of 4 (no shift)

C. shifted right

D. the function is reflected over the y-axis (no shift)

Answer: C [G(x) = x-9]

Step-by-step explanation:

I got it right

Answer:

600

Step-by-step explanation:

first, 40% of 15000 is 6000,

10% of 6000, which is the number of students studying mathematics as well as science, 600

Answer:

•600 students studied both the subject.

Answer:

22.57 x 28

Step-by-step explanation:

10.86 + 4x = 101.14

-10.86           -10.86

            4x = 90.28

             /4       /4

              x = 22.57

5.43 + 22.57 = 28

22.57

Answer:

[tex]\boxed{6.875 \text{\: grams}}[/tex]

Step-by-step explanation:

Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by [tex]2^{x}[/tex], where x  is equal to the amount of half-lives.

In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.

[tex]\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}[/tex]

Ernie will owe an interest of $268

Answer:

bonds: $65,000

cd's: $30,000

stocks: $20,000

Step-by-step explanation:

b + c + s = 115000

0.045b + 0.0325c + 0.082s = 5540

b = c + 35000

b = 65,000

c = 30,000

s = 20,000

Answer:

(d-4)(c-9)

Step-by-step explanation:

cd-9d-4c+36

d(c-9)-4(c-9)

pull out the (c-9),

(d-4)(c-9)

Answer:

x=9; one ticket is $9

Step-by-step explanation:

4x+12=48

4x=48-12

4x=36

x=36/4

x=9

Answer:

Here,

a= 12

b = 6

Then,

a+b

= 12 + 6

= 18

.°. 18 is the solution

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{18}}}}[/tex]

Step-by-step explanation:

If the values of variables of algebraic expressions are given, the value of the term or expression can easily obtained by replacing the variables with numbers.

Given, a = 12 and b = 6

[tex] \sf{a + b}[/tex]

plug the values

⇒[tex] \sf{12 + 6}[/tex]

Add the numbers

⇒[tex] \sf{18}[/tex]

Hope I helped!

Best regards!!

Answer:

1. $-50

2. $25

Step-by-step explanation:

1. If she had $150 in her bank account and bought a bike for $200, then that means she spent all of her money PLUS $50 extra then what she had.  That means $200-$150=$50.  Her $150 is spent and that $50 becomes negative because she paid $200 when she only had $150.

2.  If she deposits $75 in her account then it will be $75+(-50).  That translates to $75-$50 which is $25.  

+ and - = -

+ and + = +

- and - = +

Answer:

1. $-50

2. $25

Step-by-step explanation:

1.

We know that Clare originally had $150 in her account. She then buys a bike, which means she must have taken money out of her account for this purchase.

Since she spent $200, we need to subtract 200 from 150:

150 - 200 = -50

So, her account balance is $-50.

2.

Clare earns $75 later, which means she's receiving the money and can add it back into her account. Her current balance is -50, so we add 75 to -50:

-50 + 75 = $25

Thus, her account balance is now $25.

~ an aesthetics lover

Answer:

  C.  -1

  D.  1

Step-by-step explanation:

A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.

The appropriate choices are ...

  C.  -1

  D.  1

Answer:

c=-1

d=1

Step-by-step explanation:

Answer:

infinite solutions along the line y = 2x+1

Step-by-step explanation:

3y – 6x = 3

y = 2x + 1

Replace y in the first equation with the second equation

3 ( 2x+1) -6x =3

6x +3 -6x = 3

3=3

This is always true so there are infinite solutions along the line y = 2x+1

Step-by-step explanation:

Hi, there!!!

you mean to solve it, right.

then let's begin...

3y-6x=3..........epuation 1.

y = 2x+1..........equation 2.

now, substituting the value y of equation 2 in equation 1. so, we get,

3y-6x=3

or, 3(2x+1) -6x = 3

or, 6x+3-6x=3

by simplifying it we get, 3=3

so, this equation can have infinite solution.

you may have wrote wrong question ..

Answer: Option "a" is the only expression that represents a function.

Step-by-step explanation:

A function f(x) = y is a "operator" that takes an input element, x, and assigns it to only one output element, y.

So, if we have that for a given value of x.

f(x) = y and f(x) = h

where y and h are different values, then this is not a function, because is assigning the input value x to two different output values.

Let's see the different options:

a) {(1, 2), (4, −2), (8, 3), (9, −3)}

This points are of the form (x, y)

We can see that each value of x is assigned to only one value of y, so this can represent a function.

b)  y^2 = 16 − x^2

Ok, suppose that x = 0, then:

y^2 = 16 - 0 = 16

then we have that y*y = 16.

So y can take two different values:

y = 4 ---> 4*4 = 16

y = -4 ---> -4*-4 = 16.

So this is not a function.

c) 2x^2 + y^2 = 5

First, we want to isolate y in one side:

y^2 = 5 - 2*x^2

Here we have a similar case to the option b, and we can use a similar argument to prove that this is not a function, so we can discard this.

d) x = 7.

Ok, this is not a relation between two variables, so this is not a function, as if x is the input value, we have only one value of x that solves the equation.

Answer:

Step-by-step explanation:

5x - 15 = 5(-4x - 3)

Multiply the terms in the bracket

5x - 15 = - 20x - 15

Group like terms

Send the constants to the right side of the line and those with variables to the left side

That's

5x + 20x = - 15 + 15

Simplify

25x = 0

Divide both sides by 25

We have the final answer as

Hope this helps you

Answer:

x=0

Step-by-step explanation:

5x - 15 = 5(-4x - 3)

To find the solution to this equation, we have to get x by itself on one side of the equation.

First, distribute the 5 on the right side. Multiply each term by 5.

5x - 15= (5*-4x) + (5*-3)

5x-15 = -20x + (5*-3)

5x-15= -20x -15

Next, add 20x to both sides of the equation.

(5x+20x) -15 = (-20x+20x) -15

(5+20x) -15 = -15

25x -15=-15

Next, add 15 to both sides of the equation.

25x -15 +15 = -15+15

25x= -15+15

25x=0

Finally, divide both sides of the equation by 25.

25x/25=0/25

x= 0/25

x= 0

The solution to this equation is x=0

x = number of 1-cent stamps

y = number of 8-cent stamps

z = number of 12-cent stamps

We have 31 stamps all together, so x+y+z = 31.

"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.

You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x

-------------

x+y+z = 31

x+x-8+z = 31 ... y replaced with x-8

x+x-8+0.5x = 31 ... plug in z = 0.5x

2.5x-8 = 31

2.5x = 31+8

2.5x = 39

x = 39/2.5

x = 15.6

Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).

The number of one-cent stamps is 14.

Total stamps = 31
We have three types of stamps: 1-cent stamps, 8-cent stamps, and 12-cent stamps.

The person has 4 more 1-cent stamps than 8-cent stamps.

The person has twice as many 1-cent stamps as 12-cent stamps.

We have to make equations with the given above statement.

Consider,

1-cent stamp = A

8-cent stamp = B

12-cent stamp = C

4 more 1-cent stamps than 8-cent stamps: A = 4 + B.

A = 4 + B

B = A - 4..........(1)

Twice as many 1-cent stamps as 12-cent stamps: A = 2C.

A = 2C

C = A/2...............(2)

Total number of stamps = 31

A + B + C = 31................(3)

Putting (1) and (2) in (3)

we get,

A + ( A - 4 ) + A / 2 = 31

A + A - 4 + A / 2 = 31

2A - 4 + A / 2 = 31

2A + A / 2 = 31 + 4

(4A + A) / 2 = 35

4A + A = 35 x 2

5A = 70

A = 70 / 5

A = 14

Thus the number of 1-cent stamps is 14.

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Answer:

the real answer is: 4493.75472

BUT for ESTIMATION STRATEGY it is: 4500

Step-by-step explanation:

Answer: an equation that has one term which is nameless and squared also no term which gets raised to higher power.

Step-by-step explanation:

Answer:

5 seconds

Step-by-step explanation:

Well we know that when the soccer ball is on the ground the height will be 0.

So we replace y with 0 and solve for x.

0=-12x²+60x

factor out and divide x, (this x is x=0, which is before he kicked it)

0=-12x+60

subtract 60 from both sides

-60=-12x

x=5

Answer:

23% increase

Step-by-step explanation:

13 - 10 = 3

3/13 = 0.2307 = 23%

Hope that helped!!! k

Step-by-step explanation:

Hey, there!

Given, equations are,

2x+y=10.............(i)

-3x+y= -5...........(ii)

From equation (i)

y=10- 2x...........(iii)

Putting the value of "y" from equation (iii) in equation (ii).

-3x+y= -5

-3x + (10-2x)= -5

-3x + 10-2x= -5

- 5x = -15

[tex]x = \frac{ - 15}{ - 5} [/tex]

Therefore, x= 3.

Now, putting the value of "x" in equation (iii).

y= 10- 2x

y= 10- 2×3

Therefore, y= 4.

Hope it helps...

Answer: 60°

Step-by-step explanation:

apply concept: the interior angle sum of triangle is 180°

x+x+x=180

     3x=180

       x=60

---------------

this is also an equilateral triangle which if you know it, you will know that each angles are all 60°

Answer: x=60°

Step-by-step explanation:

We know that the sum of the angles in a triangle is 180°. Since all of the angles are x°, we know that they are equal in degrees. Since there are 3x, we can use that to solve for x.

3x=180                              [divide both sides by 3]

x=60°

Answer:

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Step-by-step explanation:

Mean x`= 518 +548 +561 +523 + 536 + 499+  538 + 557+ 528 +563 /10

x`= 537.1

The Variance is  = 20.70

H0 μ≤ 520

Ha μ > 520

Significance level is set at ∝= 0.05

The critical region is t ( with df=9) for a right tailed test is 1.8331

The test statistic under H0 is

t=x`- x/ s/ √n

Which has t distribution with n-1 degrees of freedom which is equal to 9

t=x`- x/ s/ √n

t = 537.1- 520 / 20.7 / √10

t= 17.1 / 20.7/ 3.16227

t= 17.1/ 6.5459

t= 2.6122

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01