What is the Greatest Common Factor GCF between two expressions?

Answer:

0.0499

Step-by-step explanation:

The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.

The p-value shows that the for 5% level of significance the null hypothesis can be rejected.

Shortest is Vindale to Wildgrove to Clarksville

18.9 + 13.2 = 32.1 km.

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Work Shown:

x = speed of train A

y = speed of train B

"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y

distance = rate*time

d = x*7

d = (4/5)y*7 = (28/5)y represents the distance train A travels

d = y*7 = 7y represents the distance train B travels

summing those distances will give us 693

(28/5)y + 7y = 693

5*(  (28/5)y + 7y ) = 5*693

28y + 35y = 3465

63y = 3465

y = 3465/63

y = 55

Train B's speed is 55 mph

4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph

Train A's speed is 44 mph

Answer:

[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

Step-by-step explanation:

We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.

[tex]s=\frac{a+b+c}{2}[/tex]

[tex]s : \mathrm{semi \: perimeter}[/tex]

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A : \mathrm{area}[/tex]

Answer:

Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.

Step-by-step explanation:

Answer:

52 green, 15 orange

Step-by-step explanation:

g + o = 67   g = green, o = orange, x = total

g = 3o + 7

use substitution: (3o + 7) + o = 67

solve for o:

4o + 7 = 67

4o = 60

o = 60/4 = 15

solve for g:

g + 15 = 67

g = 52

Answer:

7

Step-by-step explanation:

2b - 5b is -3b so it leaves the equation with -3b + 7 + 3b

-3b + 3b cancells out to 0 so it leaves the final answer to 7

Answer:

Step-by-step explanation:

From the information given:

For Adult Men

Mean [tex]\mu[/tex] = 69.5

Standard deviation [tex]\sigma[/tex] = 2.4

observed value X = 74

For Adult Women

Mean [tex]\mu[/tex] = 63.8

Standard deviation [tex]\sigma[/tex] = 2.6

observed value X = 70

Therefore ; the values for their z  scores can be obtained in order to determine who is more unusually tall within his or her respective sex

For Adult Men :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{74- 69.5}{2.4}[/tex]

[tex]z = \dfrac{4.5}{2.4}[/tex]

z = 1.875

For Adult Women :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{70- 63.8}{2.6}[/tex]

[tex]z = \dfrac{6.2}{2.6}[/tex]

z = 2.3846

Thus; we can conclude that , the women is more unusually tall within his or her respective sex

Answer:

C. 15 centimeters

Step-by-step explanation:

The Triangle Midsegment Theorem

segment LM = 1/2 of AC

LM = 1/2 * 30

LM = 15 cm

Answer:

(5,6), (-2,8)

Step-by-step explanation:

I have a good math expertise. Don't question my skills as they are correct. woof woof waffling behavior. Thnak you hr welcne

Answer:

a. x = 36°, y = 36°, z = 34°

Step-by-step explanation:

X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°

The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°

Answer

187.5 ml/hr

Step-by-step explanation:

1500ml/8hrs=187.5ml/hr

Answer:

5x 10 ^-5

Step-by-step explanation:

UHM that would be

NaN × [tex]10^{0}[/tex]

I hope this helps!

so my reasoning...  Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.  

Greetings from Brasil...

We know that the entire length of a circle its:

C = 2πR

C = 2π8

C= 16π      circumference length

now rule of 3:

 length              º

  16π   ---------  360

     X   ---------  135

360X = 135 · 16π

X = 2160π/360

Answer:

1/5 if a kilometer

Step-by-step explanation:

Since it was 1/60 of a kilometer which is 0.0166 of the kilometer.

So In 12 minutes he would cover 0.2 of the kilometer which is 1/5

The distance Olivia swims in 2 minutes is 1/30 km.

Given,

It takes Olivia one minute to swim 1/60 of a kilometer.

We need to find out how far can she swim in 12 minutes.

Suppose if we have,

3 items cost = $9

Cost of one item = $9 / 3 = $3

If in 5 minutes one can walk for 1km

In 10 minutes one can walk:

= (10/5 x 1) km

= 2 km

Find the distance Olivia swims in one minute.

= 1/60 km

Find the distance Olivia swims in 2 minutes.

We have,

1 minute = 1/60 km

Multiply both sides by 2.

2 x 1 minute = 2 x 1/60 km  

2 minutes = 1/30 km

Thus the distance Olivia swims in 2 minutes is 1/30 km.

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The formula C = π2r

Is used for the circumference.

We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:

C/d = π

And remember that the diameter is twice the radius, so we can write:

d = 2r

Then we can rewrite the equation for the circumference as:

C = π2r

Then we conclude that the correct option is B.

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Answer:

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220

The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.

Adult's ticket = [y]

Children's ticket = [x]

Student's ticket = [z]

and

y = 3x

Now -

x + y + z = 500

x + 3x + z = 500

4x + z = 500       ....[1]

and

12x + 18y + 15z = 8040

12x + 18(3x) + 15z = 8040

12x + 54x + 15z = 8040

66x + 15z = 8040     ....[2]

On solving [1] and [2], we get -

x = 90 and z = 140

and

y = 3x = 3 x 90 = 270

y = 270

Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

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Answer:

ln(2000) = 7.601

Step-by-step explanation:

For this we need to know the rules of logarithms, specifically the product rule and the power rule.  The product rule is simply ln(a*b) = ln(a) + ln(b).  The power rule is simply ln(a^b) = b ln(a).

With these rules, let's begin to simplify the expression:

4 ln(2) + 3 ln(5)

= ln(2^4) + ln(5^3)

= ln(16) + ln(125)

= ln(16 * 125)

= ln(2000)

= 7.601

Hope this helps.  Cheers.

A logarithm is a power to which a number must be raised in order to get some other number.

The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.

A logarithm is a power to which a number must be raised in order to get some other number.

Example:

log 10 = 1

log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3

log 0 = undefined

log 1 = 0

We have,

Some formulas for log:

log[tex]x^{n}[/tex] = n log x

log mn = log m + log n

Given,

4 log 2 + 3 log 5

= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]

= log 16 + log 125

= log (16 x 125)

= log 2000

= 3.30102

Thus the value of the expression 4 log 2 + 3 log 5 as a single number is

3.30102.

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Answer:

62

Step-by-step explanation:

180-116 makes us find out that angle C is 64, thus to find out the inner angles you gotta do 64+ (2x+4)+(3x-13)=180

You follow this operation, find out x and perform 3(25)-13, which ends up giving you 62

Answer:

62°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is not sharing a common side

2x + 4 + 3x - 13 = 116° add like terms

5x - 9 = 116°

5x = 125° divide both sides by 5

x = 25 and angle A is 3x - 13 so 3×25 - 13 = 62°

Answer:

work is shown and pictured

Answer:

The correct answer to this question is C: (72,24).

Step-by-step explanation:

We are given that:

The cost of 1 cap is $5 each

The cost of 1 t-shirt is $10 each

Let x be the number of caps sold

Let y be the number of t-shirt sold

In the context we are given that the drama club needs to raise at least $500 to go on the trip.

So based on this information we can create a inequality as:

the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500

Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.

Next we need to figure out how many caps and t-shirt were sold.

- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)

Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )

B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500

YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!

C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.

So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.

Answer: C

Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.

First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.

Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.

So, (8,5) is a valid solution in the context of the situation.

Answer:

350 pairs

Step-by-step explanation:

If the ratio of Athletics, Boots, and Dress shoes is 5 to 2 to 3, it means that for every 2 pairs of Boots they have 5 pairs of Athletics shoes and 3 pairs of dress shoes.

So, if they have 70 pairs of boots, we can calculate the number of Athletics as:

[tex]\frac{5*70}{2} =175[/tex]

And if they have 70 pairs of boots, the number of dress shoes are:

[tex]\frac{3*70}{2}=105[/tex]

Finally, they have 70 pairs of boots, 175 pairs of athletics, and 105 pairs of dress shoes. It means that they have 350 pairs in total.

70 + 175 + 105 = 350

Answer:

The probability that a randomly selected student is female or a physics major is 0.65.

Step-by-step explanation:

Note: This question is not complete. A complete is therefore provided before answering the question as follows:

A physics class has 40 students. Of these, 14 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is_______.

The Step-by-step explanation is therefore provided now as follows:

The probability that a randomly selected student is female or a physics major can be calculated using the following formula:

P(PM or F) = P(PM) + P(F) - P(PMF)

Where;

P(PM or F) = Probability of student selected is Physics Major or Female = ?

P(PM) = Probability of student selected is Physics Major = Number of Physics Major / Total number of students in the Physics class = 14 / 40 = 0.35

P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45

P(PMF) = Probability of student selected is Physics Major and Female = Number Physics Major that female in the Physics class / Total number students in the Physics class = 6 / 40 = 0.15

Substituting the values into equation (1), we have:

P(PM or F) = 0.35 + 0.45 - 0.15 = 0.65

Therefore, the probability that a randomly selected student is female or a physics major is 0.65.

Answer:

what is the physics question

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}[/tex]

Domain:

[tex]x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3[/tex]

solution:

[tex]\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}[/tex]

use (a - b)(a + b) = a² - b²

[tex]\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}[/tex]

multiply both sides by (x - 3) ≠ 0

[tex]\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}[/tex]

cancel (x - 3)

[tex]\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3[/tex]

subtract [tex]\frac{4(x-3)}{x}[/tex] from both sides

[tex]\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}[/tex]

cross multiply

[tex](4)(x)=(x+3)(-x+12)[/tex]

use FOIL

[tex]4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36[/tex]

subtract 4x from both sides

[tex]0=-x^2+12x-3x+36-4x[/tex]

combine like terms

[tex]0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36[/tex]

change the signs

[tex]x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0[/tex]

The product is 0 if one of the factors is 0. Therefore:

[tex]x-9=0\ \vee\ x+4=0[/tex]

[tex]x-9=0[/tex]            add 9 to both sides

[tex]x=9\in D[/tex]

[tex]x+4=0[/tex]          subtract 4 from both sides

[tex]x=-4\in D[/tex]

The lowest common denominator is lcm(5, 3), which is 15.

The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].

Answer:

The price before tip was 35

Step-by-step explanation:

Let x = original amount

x * 20% = 7

Change to decimal form

x * .20 = 7

Divide each side by .20

x*.20/.20 = 7/.20

x =35

Answer:

C. surface area of 5 rectangular prisms.

Step-by-step explanation:

The table in the given figure as shown above has a rectangular flat top that has a solid shape of rectangular prism.

It also has 4 legs that are also rectangular in shape. The legs are rectangular prisms.

To determine the quantity of paint Kimberly would need, she needs to make use of the surface area of the table.

The surface area of the table = surface area of the top + surface area of the 4 legs = surface area of 5 rectangular prisms.

Answer:

C

Step-by-step explanation:

Answer:

-6.

Step-by-step explanation:

The equation is y = -7x - 6.

The initial value is found when x = 0.

y = -7(0) - 6

y = 0 - 6

y = -6

Hope this helps!

Rewriting the Equation:

Answer:

7x+y=-33

Step-by-step explanation:

1.) Combine Like Terms: y=-7x-33

2.) Move the variable to the left side and use the inverse operation:

y+7x=-33

3.) Reorder terms using commutative property since x comes before y:

7x+y=-33

If you want to find the function then tell me.

Answer:

16

Step-by-step explanation:

6*2 = 12

12 + 4 = 16

Answer:

x=3

Step-by-step explanation:

Use the Pythagorean Theorem to write an equation.

x^2+y^2=z^2

Substitute values from the problem.

x^2 + 6^2 = 9^2

Solve for what you know.

x^2 + 36 = 81

Square root it.

x+6=9

Subtract 6 from both sides.

x=3

In the future, if you see a right triangle with an unknown side, and the other two sides are either 3, 6, or 9, you know that the other one is the missing value out of 3/6/9. This is called a 3/6/9 triangle.

Answer:

Step-by-step explanation:

Hypotenuse (h) = 9

base (b) = X

Perpendicular (p) = 6

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]

[tex] {b}^{2} = {(9)}^{2} - {(6)}^{2} [/tex]

[tex] {b}^{2} = 81 - 36[/tex]

[tex] {b}^{2} = 45[/tex]

[tex]b = \sqrt{45} [/tex]

[tex]b = 6.7[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

We have the measure of both angles as  55 degrees and 35 degrees

Step-by-step explanation:

We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.

We now set up an equation using the information we are given about the problem.

From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:

x =2y -15 -------- equation 1

similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:

x + y + 90 = 180

x+ y = 90 ------------- equation 2

we can now solve the two equations simultaneously as

x -2y =-15

x+ y = 90

from this, we have that

x = 55 and y = 35

We have the measure of both angles as  55 degrees and 35 degrees