What is 3 In3-In9 expressed as a single natural logarithim

Answer:

Step-by-step explanation:

In this problem we have independent events, that is, the event "picking a girl" doesn't affect an "picking a boy", also, picking picking a girl doesn't affect the probability of the other subjects.

So, the probability when the first girl is being picked is:

[tex]P_{1}=\frac{7 \ girls}{9 \ students}[/tex]

Because among the total 9 students, there are 7 girls.

Now, after picking one girl, there remains 6 girls and 8 students to be picked. So, the probability of the second girl would be:

[tex]P_{2}=\frac{6 \ girls}{8 \ students}[/tex]

Then, the probability of the third girl:

[tex]P_{3}=\frac{5 \ girls}{7 \ students}[/tex]

The fourth girl probability:

[tex]P_{3}=\frac{4 \ girls}{6 \ students}[/tex]

Therefore, the probability of picking all 4 girls would be the product of each probability, because events are independent (we use product when they are independent):

[tex]P=\frac{7 \ girls}{9 \ students} \times \frac{6 \ girls}{8 \ students} \times \frac{5 \ girls}{7 \ students} \times \frac{4 \ girls}{6 \ students}\\P=\frac{5}{18}=0.28 \ (or \  28\%)[/tex]

Therefore, there's 28% probability that every student in the group is a girl.

The probability that everyone in the group is a girl is 0.2778

The distribution of the students is given as:

Boys = 2

Girls = 7

Total = 9

The selection of the 4 girls at random is:

So, the probability that all students are girls is:

P = 7/9 * 6/8 * 5/7 * 4/6

Evaluate

P = 0.2778

Hence, the probability that everyone in the group is a girl is 0.2778

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Answer:

12-6u

Step-by-step explanation:

To remove the parenthesis, we must multiply the number on the outside to each value within the parenthesis

This means that

[tex]6(2-u)\\\\6*2-6*u\\\\12-6u[/tex]

The distributive property is used to remove parentheses by multiplying each term within the parentheses by the number outside. Thus, the expression 6(2 - u) becomes 12 - 6u.

The distributive property is a mathematical principle that shows how to expand an expression involving brackets (or parentheses). To use the distributive property to remove the parentheses in the expression, you multiply the number outside the parentheses by each term inside the parentheses individually. Let's apply this to the expression you provided, 6(2 - u).

First, multiply 6 by 2. This results in 12. Next, multiply 6 by -u. This gives -6u. Therefore, the expression 6(2 - u) without parentheses, using the distributive property, is 12 - 6u.

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Answer:

20 units³

Step-by-step explanation:

Since all dimensions are being reduced by 1/3, that means that the total volume will decrease by 1/3 * 1/3 * 1/3 = 1/27 the size of its original.

That means that the new volume is 1/27 * 540 = 20 units³

Answer:

B

Step-by-step explanation:

We know 2.2 pounds = 1 kg, hence,

44 pounds / 2.2 = 20 kg (weight of child in kg)

Now, since 40 mg is administered per kg, the child would need 40 * 20 = 800 mg PER DAY

Since this is going to be taken per 4 dose, each dose would need to be 800/4 = 200 mg

Answer choice B is right.

Answer:482.7972

Step-by-step explanation:

Make two equations representing the position of each animal, p and k, for the puppy and kitten respectively.

p=25t and k=180+20t  

The puppy will catch the kitten when p=k so we can say:

25t=180+20t  subtract 20t from both sides

5t=180  divide both sides by 5

t=36

So the puppy will catch the kitten after 36 seconds.

Answer:

36

Step-by-step explanation:

Answer:  1st, 3rd  and 5th answers are correct

Step-by-step explanation:

Answer:

A) The theoretical probability of spinning any one of the five colors is 20%.

C) The theoretical probability of spinning green is equal to the experimental probability of spinning green.

E) If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Step-by-step explanation:

Let's find the probability of each events.

Probability of a event = The number of favorable outcomes / The total number of possible outcomes.

Here the total number of possible outcomes = 10.

Probability of getting blue = 1/10 = 0.10

Probability of getting green = 2/10 = 1/5= 0.20 = 20%

Probability of getting red = 0/10 = 0

Probability of getting orange = 4/10 = 0.40

Probability of getting yellow = 3/10 = 0.30

The above are the experimental probability.

The theoretical probability of getting green = 1/5 = 0.20 = 20%

By looking at the results, the following statements are true.

A) The theoretical probability of spinning any one of the five colors is 20%.

C) The theoretical probability of spinning green is equal to the experimental probability of spinning green.

E) If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Answer:

$60

Step-by-step explanation:

I got this bc 12*30=360 and 360-300=60

Answer: 60 dollars

Step-by-step explanation: For every 5 dollars Tom loans he has to pay 1 dollar plus the amount he loaned. If 30 times 12 is 360 and the original cost is 300 then he payed 60 dollars for the finance charge.

Answer:

Step-by-step explanation:

A quadratic equation is an expression that has an x^2 term. Quadratic equations are most commonly expressed as ax^2+bx+c, where a, b and c are coefficients. Coefficients are numerical values. For example, in the expression 2x^2+3x-5, 2 is the coefficient of the x^2 term. Once you have identified the coefficients, you can use a formula to find the x-coordinate and the y-coordinate for the minimum or maximum value of the quadratic equation.

Determine whether the function will have a minimum or a maximum depending on the coefficient of the x^2 term. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum. For example, if you have the function 2x^2+3x-5, the function has a minimum because the x^2 coefficient, 2, is positive.

Divide the coefficient of the x term by twice the coefficient of the x^2 term. In 2x^2+3x-5, you would divide 3, the x coefficient, by 4, twice the x^2 coefficient, to get 0.75.Multiply the Step 2 result by -1 to find the x-coordinate of the minimum or maximum. In 2x^2+3x-5, you would multiply 0.75 by -1 to get -0.75 as the x-coordinate.

Plug in the x-coordinate into the expression to find the y-coordinate of the minimum or maximum. You would plug -0.75 into 2x^2+3x-5 to get 2_(-0.75)^2+3_-0.75-5, which simplifies to -6.125. This means the minimum of this equation would be x=-0.75 and y=-6.125.

If there is not a number before a variable, the coefficient is 1. For example, if your expression is x^2+5x+1, the x^2 coefficient is 1.

Answer:

hcch6z0d7gpxufufuguftrfue6oo7

Answer:

x=m-a/12

the m-a should be over 12 as the numerator but it's hard to type it like that

Step-by-step explanation:

a+12x=m

12x=m-a

x=m-a/12

Answer:

[tex]x = \frac m{12a}[/tex]

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The value of x is [tex]x = \frac m{12a}[/tex].

Answer:

"4" represents that there are 4 rabbit in the beginning.

Step-by-step explanation:

Given that the population of a species of rabbit triples every year. This

can be modeled by function [tex]f\left(x\right)=4\left(3\right)^x[/tex] and [tex]f(5) = 972[/tex].

Now we need to find about what does the 4 represent in the given function.

We know that exponential function is given by [tex]f\left(x\right)=a\left(b\right)^x[/tex]. Where "a" represents the initial amount.

we have a=4 in given function [tex]f\left(x\right)=4\left(3\right)^x[/tex].

So that means "4" represents that there are 4 rabbit in the beginning.

Answer:

Step-by-step explanation:

Use tangent.

[tex]tangent=\dfrac{oppositive}{adjacent}[/tex]

We have

[tex]oppositive=10\\adjacent=8[/tex]

Substitute:

[tex]\tan(z)=\dfrac{10}{8}\\\\\tan(z)=1.25[/tex]

look at the picture

[tex]z\approx51^o[/tex]

Answer:

113.0 inches squared

Step-by-step explanation:

The area of a circle with radius r is given as;

[tex]Area=pi*r*r[/tex]

We plug in the radius given and solve for the area;

[tex]Area=3.14*6*6\\Area=113.04[/tex]

Answer:

Step-by-step explanation:

The graph is done using Desmos. Just by substitution x = 1 will force the graph to go to y = 0, but graphs are not always that good. This one gets 1.111

to get y = 0. I'd use 1 if you had to answer it and a computer will mark it.

Answer:

x= 21/2 = 10.500  

Step-by-step explanation:

2.2      Solve  :    2x-21 = 0  

Add  21  to both sides of the equation :  

                     2x = 21

Divide both sides of the equation by 2:

                    x = 21/2 = 10.500

x = 21/2 = 10.500

The solution of the equation for the unknown value x is decimal number 10.5. Option C is correct.

The solution of an equation is the value of the variable of the equation, for which the equation is satisfied.

To solve an equation for its variable, isolate the variable on one side of the equation using the mathematical operations.

The equation of unknown value x is given as,

4x = 42

This equation has to be solved for x. For this isolate the x divide the equation with 4 both side.

(4x/4)=(42/4)

x=10.5

Hence, the solution of the equation for the unknown value x is decimal number 10.5. Option C is correct.

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Answer:

21

Step-by-step explanation:

There are 144 M&M's in the bag.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Number of red candies = 16

Also it is given that One-ninth of the candies in a bag of M&M's are red

1/9 of the candies in a bag of M&M's are red

Let x be the M&M's candies

So, we can write,

1/9 x = 16

⇒  x = 144

Thus, there are 144 M&M's in the bag.

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Answer:

$17.35/h

Step-by-step explanation:

In order to get the amount per hour he made, you first need to calculate the global amount of money he made.

He was paid $2,900 then he had costs of $1,200, that leaves him a net income of $1,700 ($2,900 - $1,200)

Then he worked a total of 98 hours for that money.

A salary is an amount of money expressed by a period of time.  In this case, we'll use hours.

So, Jonah earned $1,700 after 98 hours of work:

S = $1,700 / 98 hours = $17.35/h

Answer:

c = 14

Step-by-step explanation:

For this triangle we have to

[tex]a=18.2\\B=62\°\\C=48\°[/tex]

We want to find the length of b

We know that the sum of the internal angles of a triangle is 180 °

then

[tex]A + 62 +48=180\\\\A=180-62-48\\\\A=70\°[/tex]

Now we use the sine theorem to find the length of c:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Therefore:

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}\\\\c=\frac{sin(C)}{\frac{sin(A)}{a}}\\\\c=a*\frac{sin(C)}{sin(A)}\\\\c=(18.2)\frac{sin(48)}{sin(70)}\\\\c=14[/tex]

Answer:

c= 14

Step-by-step explanation:

First, let's find the angle A, because it's easy and because we'll need it.

We know that the sum of the interior angles of a triangle is 180, and we have 2 angles... so we can easily find A:

A = 180 - 62 - 48 = 70 degrees

Now, we can use the law of Sines to find c:

[tex]\frac{c}{sin(C)} = \frac{a}{sin(A)}[/tex]

so...

[tex]c = \frac{a * sin(C)}{sin(A)} = \frac{18.2 * sin(48)}{sin(70)} = 14.39[/tex]

The precise answer is 14.39, but you are asked to round up to the closest whole number... so 14.

Answer

B

Step-by-step explanation:

5-2x<7

subtract 5 on both sides

-2x<2

divide by -2

x>-1

so its B

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-3}\cdot x^3\cdot y^{-4}\implies \cfrac{1}{\begin{matrix} x^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot ~~\begin{matrix} x^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{1}{y^4}\implies \cfrac{1}{y^4}[/tex]

can you tell me what the points are because the graph is somewhat blurry

Answer:

if the scale is 1, then the slope is 1/3

Step-by-step explanation:

Answer:

162.24 ft

Step-by-step explanation:

So you first find the area of one side.

5.2 x 5.2 = 27.4

Then you times it by 6, because a cube has 6 sides.

27.4 x 6 = 162.24 ft

A steel cargo container is shaped like a cube measuring 5.2 ft on each edge. we will need 162.24 ft sq. steel to make this container.

A cube has all sides congruent, so all sides have the same area.

Supposing that the considered cube has a side length (also called edge length) of L units.

Then, its one side's area equals  L^2 sq. units (as each side is a square, so we used the formula for the area of a square).

Since there are 6 such sides in a closed cube, thus, its surface area evaluates to

[tex]S = L^2 + L^2 + ... + L^2 \text{\: (six times)} = 6L^2 \: \rm unit^2[/tex]

A steel cargo container is shaped like a cube measuring 5.2 ft on each edge.

So first we need to find the area of one side.

The area of a square = 5.2 x 5.2

                                   = 27.4

For 6 sides of cube

27.4 x 6 = 162.24 ft sq.

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For this case we must simplify the following expression:

[tex](x ^ {\frac {3} {2}}) ^ 6[/tex]

We have that by definition of properties of powers that is fulfilled:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex]x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9[/tex]

Answer:

[tex](x^{\frac{3}{2}})^6=x^9[/tex]

Final answer:

To simplify the expression [tex](x^{3/2)6[/tex], use the power rule of exponents to get x to the power of 9, which is the simplified form of the expression.

Explanation:

To simplify the expression [tex](x^{3/2)6[/tex], we need to apply the power of a power property, which states that when you raise a power to another power, you multiply the exponents.

So, we have:

[tex](x^{3/2)6[/tex] = [tex]x^{(3/2)\times 6[/tex]

= [tex]x^{3\times 3[/tex]

= x⁹

Therefore, [tex](x^{3/2)6[/tex] simplifies to x⁹.

This means that the expression is equivalent to x raised to the power of 9.

In summary, when you raise x to the power of 3/2 and then raise that result to the power of 6, you end up with x raised to the power of 9.

Answer:

The answer is 84cm^2.

Step-by-step explanation:

To find the area, you need to find the length x width. here is an equation to help:

A=L X W

Lets plug the numbers into the equation:

A=6cm X 14cm

Now, mulitply:

A=84cm^2

hope this helps

84, you multiply 14x6 for the area

Answer: 4(5j+7) = 20j+28

Step-by-step explanation:

Answer: 3 1/4 as an improper fraction could be 13/4. Written as a fraction would be 3 1/4.

Answer:

continous

Step-by-step explanation:

Answer:

Continuous

Step-by-step explanation:

Since the problem has decimals for your t values it will most likely be continuous.

Answer:

B) [tex]f(x)=2(x-7)^2-3[/tex].

Step-by-step explanation:

The vertex form of the equation is given by [tex]f(x)=a(x-h)^2+k[/tex].

We plug in the vertex to obtain:

[tex]f(x)=a(x-7)^2-3[/tex].

Since the graph passes through (5,5) and (9,5), they must satisfy its equation.

[tex]5=a(9-7)^2-3[/tex].

[tex]5+3=4a[/tex].

[tex]8=4a[/tex]

Divide both sides by 4.

[tex]a=2[/tex]

Therefore the equation is:

[tex]f(x)=2(x-7)^2-3[/tex].

Answer:

1527 feet

Step-by-step explanation: