1. If two parallel lines are cut by a transversal, then alternate interior angles are congruent
2. If two parallel lines are cut by a transversal, then corresponding angles are congruent
3. If two parallel lines are cut by a transversal, then alternate exterior angles are congruent
4. If two parallel lines are cut by a transversal, then complementary angles are congruent

Answer:

(317-7)/6≈52

Step-by-step explanation:

There was approximately 52 kids in each bus

Total number of kids = 317

Total number of buses = 6

Number of kids sick = 7

Therefore, the number of kids on each bus will be:

= (317 - 7) / 6

= 310/6

= 51 2/3

= 52 kids approximately

In conclusion, there was approximately 52 kids in each bus.

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Answer:

Step-by-step explanation:

The numbers 4/5 and 9/10 are fractions. They multiply the variable 'b' in each case.

How to solve an equation like this

An example of an equation like this without fractions is ...

  6 + 3b = 8b

You solve this sort of equation by rearranging the equation so the terms having 'b' in them are all on one side of the equal sign. You want all of the terms not containing 'b' to be on the other side of the equal sign.

Here, the terms are mixed on the left, but the right has only a 'b' term. So, if we can remove the 'b' term from the left side, we will have reached the goal

In the example equation, we do that by adding -3b to both sides of the equation.

  6 +3b -3b = 8b -3b

Simplifying, we have ...

  6 = 5b

Now, we divide by the coefficient of 'b', which is 5. We divide both sides of the equation by that:

  6/5 = (5b)/5

  6/5 = b . . . . after simplifying

_____

How to solve this equation

The given equation is solved exactly the same way. We add the opposite of the 'b' term that we don't want (which is 4/5b):

  6 + 4/5b -4/5b = 9/10b -4/5b

Simplifying, this is ...

  6 = (9/10 -4/5)b = (9/10 -8/10)b

  6 = 1/10b

We can make the coefficient of 'b' be 1 by multiplying it by 10. We have to do that to both sides of the equation:

  (10)(6) = (10)(1/10)b

  60 = b . . . . . the solution

_____

Comment on equations in general

The one absolute rule in Algebra is that the equal sign must remain valid. You keep that commandment by observing the properties of equality. Essentially, you can do anything you like to one side of an equation, as long as you do exactly the same thing to the other side.

Here, when we say "subtract 4/5b", the way we keep this commandment is that we do it to both sides of the equation. The same is true for "multiply by 10". This is emphasized by the bold highlighting in the solution shown above.

Comment on arithmetic

In solving this equation, we did the arithmetic using the given fractions. Often, for an equation like this, you will be told the first step is to "eliminate fractions". You can do that here by multiplying the equation by 10:

  10(6 +4/5b) = 10(9/10b)

  60 +8b = 9b

Now, the unwanted term is 8b, so subtracting that (from both sides) gives ...

  60 = b

This is essentially a "2-step" equation, either way you do it.

It is helpful if you are comfortable doing arithmetic with fractions, mixed numbers, decimals, percentages, and numbers in scientific notation, as well as integers.

[tex](f + g)(x) = - 4 {x}^{2} - 6x - 1 - {x}^{2} - 5x + 3 \\ [/tex]

[tex](f + g)(x) = - 5 {x}^{2} - 11x + 2 \\ [/tex]

And we're done.

Thanks for watching buddy good luck.

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the answer is instruments that detect earthquakes

Answer:

The mean for the probability mass function is 0.64287.

Step-by-step explanation:

The complete question is:

In a batch of ​28 pedometers, 3 are believed to be defective. A​ quality-control engineer randomly selects 6 units to test. Let random variable X = the number of defective units that are among the units tested.

The probability mass function ​f (x) is:

f (x)​ = {(0, 0.47009​), ​(1, 0.42308​), ​(2,​ 0.10073), ​(3, 0.00611​)}

Solution:

The mean of a discrete random variable X with probability mass function f (x) is:

[tex]\mu=\sum\limits^{n}_{x=1}{x\times f(x)}[/tex]

Compute the mean for the probability mass function above as follows:

[tex]\mu=\sum\limits^{n}_{x=1}{x\times f(x)}[/tex]

  [tex]=(0\times 0.47009)+(1\times 0.42308)+(2\times 0.10073)+(3\times 0.00611)\\=0+0.42308+0.20146+0.01833\\=0.64287[/tex]

Thus, the mean for the probability mass function is 0.64287.

This values represents the expected number of defective units for every 6 units tested.

Answer:

y=5

Step-by-step explanation: 8+2=10 so 10/2=5

Answer:

  1596 miles

Step-by-step explanation:

A suitable proportion can be ...

  [tex]\dfrac{\text{miles}}{\text{hours}}=\dfrac{M}{14\text{ h}}=\dfrac{342\text{ mi}}{3\text{ h}}\\\\M=\dfrac{14\cdot 342}{3}\text{ mi}=1596\text{ mi}[/tex]

We solved it by multiplying both sides by 14 hours. The units of hours cancel, leaving units of miles.

Michelle's car can travel 1596 miles in 14 hours.

Answer:

6

Step-by-step explanation:

y2-y1       y-3     =3     what -3 =3?    6 :)

x2-x1       4-2    = 2

slope is 3/2

Answer:

63

Step-by-step explanation:

Step 1: Define

f(x) = -x - 12

f(-5) is x = -5

f(-3) is x = -3

Step 2: Find f(-5)

f(-5) = -(-5) - 12

f(-5) = 5 - 12

f(-5) = -7

Step 3: Find f(-3)

f(-3) = -(-3) - 12

f(-3) = 3 - 12

f(-3) = -9

Step 4: Find f(-5) × f(-3)

-7 × -9

63

Answer:

9.4

Step-by-step explanation:

9/5 / 2/5=9.4

1 4/5 / 2/5 = 9.4

Answer: 9/2

Step-by-step explanation:

9/5 divided by 2/5  

you keep 9/5 you change the divide sing into a  times then you flip 2/5 to 5/2 then you times them and cross cancel.

Answer:

The answer is 4062.39

Step-by-step explanation:

A=$2,400(1+0.0681)1(8). Simplify using the order of operations: A=$2,400(1.068)8=$2,400(1.692661131)≈$4,062.39.

The amount of money after 8 years will be $4062.38.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.

Given that Karen invests $2,400 into an account with a 6.8% interest that is compounded annually. The amount after 8 years will be calculated as below:-

Amount = P [ 1 + ( r / n )]^(nt)

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Amount = 2400 [ 1 + ( 0.068 / 1 ) ] ⁸

Amount = 2400 [1.068 ) ] ⁸

Amount = 4062.38

Therefore, the amount of money after 8 years will be $4062.38.

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Answer:

2 mm

Step-by-step explanation:

let the radius of the semi-circle be r

Then,

length of curved portion = 1/2 x circumference = (1/2) (2)(π)r = πr

length of straight portion = diameter of circle = 2r

Hence, we can write an expression for the perimeter

Perimeter = length of curved portion + length of straight portion

Perimeter = πr + 2r

Perimeter = (π + 2)r

since we are given the perimeter = 5.14, assuming that π=3.14, our equation becomes:

5.14 = (3.14 + 2)r

5.14 = 5.14 r

r = 5.14 / 5.14 = 1

Hence, diameter = 2r = 2(1) = 2 mm

Answer:

ay

Step-by-step explanation: step by step

The answer is:

5.2 x 10^7 or 52,000,000

Answer:

(U+V) is the answer to the solution

Answer:

The probability that on any given day, there will be 9 individuals arriving at the food pantry is 0.1241

Step-by-step explanation:

Here, we are to use Poisson distribution probability formula

Please check attachment for detailed explanation

Answer:

237

Step-by-step explanation:

Answer:

$52.50

Step-by-step explanation:

C = 3.5t

C = 3.5 (15)

3.5 × 15 = 52.5

C = $52.50

Answer:

= -65x + 15

Step-by-step explanation:

You Welcome ❤

Answer:

=-65+18i think sorry I'm not much help but I hope it was right

Answer:

5

Step-by-step explanation:

mark braniac

Answer:

x = 5

Step-by-step explanation:

let's take the blank as x

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

3 × x/3 = 5

cross multiply

3x = 15

x = 5

Answer:

Multiply 5 by 4.22 because 5 cups of water is 4.22 liters

Answer:

2(2x+1)(x-3w)

Answer:

Let's see what to do buddy....

Step-by-step explanation:

_________________________________

Step (1)

[tex]f(x) = 3x - 2[/tex]

[tex]g(x) = {x}^{2} - 5 [/tex]

_________________________________

Step (2)

We need to find f(2) first ;

To do this we must put 2 instead of the x in f(x) function.

Let's do it :

[tex]f(2) = 3(2) - 2[/tex]

[tex]f(2) = 6 - 2[/tex]

[tex]f(2) = 4[/tex]

_________________________________

Step (3)

Now we are going to find g( f (2) ) ;

Look :

[tex]g( \: f(2) \: ) = g(4)[/tex]

So we want to find g(4) ;

which means we must put 4 instead of the x in g(x) function.

Let's do it :

[tex]g(4) = ({4})^{2} - 5 [/tex]

[tex]g(4) = 16 - 5[/tex]

[tex]g(4) = 11[/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

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Answer:

The ball will not reach a height of 41 meters.

The discriminate is 784

Step-by-step explanation:

You know that the height h of the ball, in meters, at time t seconds is modeled by the function h(t) = - 5*t² + 2*t + 39

To find out if the ball will reach a height of 41 meters, you must calculate the maximum of the function, that is, the highest or highest point on the graph.  That is, the maximum in a function f is the largest value that the function takes.

The vertex is a point that is part of the parabola, which has as its ordinate the maximum value (as in this case) or minimum value of the function. That is, the vertex is the maximum of the function (as in this case) or minimum.

In this case, the maximum of t is obtained by:

[tex]t=\frac{-b}{2*a}[/tex]

Being a=-5 and b=2 (comparing with a quadratic function of the form: f(x)=a*x² + b*x +c)

[tex]t=\frac{-2}{2*(-5)}[/tex]

t= 0.2

The maximum height value must be obtained by substituting the previously calculated value of t in the function:

h(0.2) = - 5*0.2² + 2*0.2 + 39

h(0.2)=39.2

So the maximum height the ball will reach is 39.2 meters. The ball will not reach a height of 41 meters.

The discriminate of a quadratic function is:

Δ=b²-4*a*c

In this case, being a=-5, b=2 and c=39, the discriminate is:

Δ=2²-4*(-5)*39

Δ= 4+780

Δ= 784

The discriminate is 784

The first derivative test is the process of analyzing functions using their first derivatives in order to find their extreme point.

No, ball can not reach at height of 41 meters.

Since, The height h of the ball, in meters, at time t seconds is modeled by the function  [tex]h(t)=-5t^2+2t+39[/tex]

To find maximum height where can ball reach. We use first and second derivative test.

[tex]h(t)=-5t^2+2t+39\\\\\frac{dh}{dt}=-10t+2[/tex]

Now, equate above derivative to zero.

 [tex]-10t+2=0\\\\t=1/5[/tex]

Now, find second derivative

[tex]\frac{d^{2}h }{dt^{2} } =-10[/tex]  , Which is less than zero.

Therefore, at t= 1/5 second , will give maximum height that can ball reach.

So,  h(1/5) = 39.2 meters.

That is, ball can reach at 39.2 meters.

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Answer:

Yes, they are paralle.

Step-by-step explanation:

Step-by-step explanation:

Hey there!

Here;

The equations are:

3x + 4y - 7 = 0.............(I)

6x + 8y -11 = 0.........(ii)

Let's simply work with this.

From equation (I)

[tex]slope(m) = \frac{ - coeff.of \: x}{coeff.of \: y} [/tex]

[tex]m1 = \frac{ - 3}{4} [/tex]

From equation (ii)

[tex]slope(m2) = \frac{ - coeff. \: of \: x}{coeff. \: of \: y} [/tex]

[tex]m2 = \frac{ - 6}{8} [/tex]

[tex]m2 = \frac{ - 3}{4} [/tex]

As per the condition of parallel lines;

M1 = M2

-3/4 = -3/4. (true)

Therefore, the lines are parallel to eachother.

Hope it helps...