A bag contains 10 marbles: 4are green, 2are red, and 4 are blue. Carmen chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue?

b)

A - wins at both games

[tex]P(A)=0.3\cdot0.4=0.12[/tex]

c)

A - wins at just one of the games

[tex]P(A)=0.3\cdot0.6+0.7\cdot0.4=0.18+0.28=0.46[/tex]

Answer:

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]-3x^2-2x+6=0[/tex]            .... (1)

If a quadratic equation is defined as

[tex]ax^2+bx+c=0[/tex]            .... (2)

then the quadratic formula is

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

On comparing (1) and (2), we get

[tex]a=-3,b=-2,c=6[/tex]

Substitute [tex]a=-3,b=-2,c=6[/tex] in the above formula.

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]

Therefore, the correct substitution of the values a, b, and c in the quadratic formula is [tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex].

Answer:

1. 7

2. 25

3. 2/3

4. 132/425

Step-by-step explanation:

Probability is the likelihood of an event occurring and it can be computed by:

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}[/tex]

1. So when you are given a probability of 7/9:

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{7}{9}[/tex]

So the answer is 7.

2. Given the probability is 14/25:

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{25}[/tex]

The number of possible outcomes is 25.

3. You have 14 favorable outcomes out of 21 possible outcomes.

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{21}\div \dfrac{7}{7}=\dfrac{2}{3}[/tex]

The answer is 2/3.

The least likely even would be the smallest fraction. If you want to do this the easy way, just change them all to decimal and find the value with the least.

17/35 = 0.49

5/13 = 0.38

132/425 = 0.31

1/2 = 0.5

Since 132/425 = 0.31 is the smallest, then it is the least likely probability.

[tex]_7P_5=\dfrac{7!}{(7-5)!}=\dfrac{7!}{2!}=3\cdot4\cdot5\cdot6\cdot7=2520\\_7C_5=\dfrac{7!}{5!2!}=\dfrac{6\cdot7}{2}=21\\\\\\_7P_5> {_7C_5}[/tex]

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

[tex]_nP_k[/tex] is always greater than [tex]_nC_k[/tex]. And it's greater [tex]k![/tex] times.

[tex]\dfrac{_nP_k}{_nC_k}=\dfrac{\dfrac{n!}{(n-k)!}}{\dfrac{n!}{k!(n-k)!}}=\dfrac{n!}{(n-k)!}\cdot \dfrac{k!(n-k)!}{n!}=k![/tex]

Answer:

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

Step-by-step explanation:

Let

x -----> the altitude of a commercial aircraft

we know that

The expression " A minimum altitude of 29,000 feet" is equal to

[tex]x\geq 29,000[/tex]

All real numbers greater than or equal to 29,000 ft

The expression " A maximum altitude of 41,000 feet" is equal to

[tex]x\leq 41,000[/tex]

All real numbers less than or equal to 41,000 ft

therefore

The compound inequality is equal to

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft

The solution is the interval ------> [29,000,41,000]

Answer:

A

Step-by-step explanation:

x^2+10x+21

(x+3)(x+7)= 0

x^2+7x+3x+21= x^2+10x+21

x+3-3= 0-3

x+7-7= 0-7

Answers are :

x= -3 , x= -7

Answer:

x=-7,-3

Step-by-step explanation:

Simplifying it, convert it to a radical form, and evaluate it.. Either way it all equals to a simple whole number, which is '4',

well, except when you convert the expression to radical form using the formula 'a^x/n=n√a^x' then it'll be '^3√8^2'.

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

4

Step-by-step explanation:

8 ^ (2/3)

The 2 means squared and the 3 means root

8^2  ^ (1/3)

Rewriting 8 as 2^3

2^3 ^ (2/3)

We know a^ b^c = a^ (b*c)

2 ^ (3*2/3)

2^ 2

4

OR

8 ^ (2/3)

The 2 means squared and the 3 means root

8^2  ^ (1/3)

64 ^ 1/3

We know 4*4*4 = 64

(4*4*4)^ 1/3

4

Answer:

a = 13 and b = 12-5i

Step-by-step explanation:

We need a common denominator

3+2i         5-i

---------- + ---------

3-2i          2+3i

(3+2i) (2+3i)         (5-i)(3-2i)

------------------ + --------------------

(3-2i) (2+3i)          (2+3i) (3-2i)

Foil the numerators

6 +4i+9i+6i^2 +15-3i-10i+2i^2        

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

         (2+3i) (3-2i)

Combine like terms

21 +8i^2          

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

(2+3i) (3-2i)

We know that i^2 = -1

21 +8(-1)        

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

(2+3i) (3-2i)

21 -8        

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

(2+3i) (3-2i)

13        

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

(2+3i) (3-2i)

Foil the denominator

13

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

6 +9i -4i -6i^2

Combine like terms

13

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

6+ 5i -6(-1)

13

----------

12 +5i

We know have

13

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

12 + 5i

Multiply by the conjugate

13               ( 12-5i)

------------- * -------------

12 + 5i         12 -5i

13 (12-5i)

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

144 +25

13(12-5i)

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

169

12-5i

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

13

The parentheses are (12-5i)/13

We need the reciprocal to make the equation become 1

which is 13/ 12-5i

a = 13 and b = 12-5i

Answer:

a = 13

b= 12-5i

Step-by-step explanation:

Simplify the values and i squared will be -1

To find the height of the football after 1.2 seconds, we substitute t with 1.2 in the polynomial −16t2 + 32t + 3, simplifying to 18.36 feet, which corresponds to answer option C.

The student asked to find the height of a kicked football after 1.2 seconds, with the height given by the polynomial −16t2 + 32t + 3, where t is the time in seconds. To solve for the height after 1.2 seconds, we substitute t with 1.2 in the polynomial, which gives us:

−16(1.2)2 + 32(1.2) + 3

Calculating this gives:

−16(1.44) + 38.4 + 3

−23.04 + 38.4 + 3

15.36 + 3

18.36 feet.

Therefore, after 1.2 seconds, the height of the football is 18.36 feet, making the correct answer option C.

Answer:

[tex]330\ kg[/tex]

Step-by-step explanation:

Remember that

1 kg=1,000 g

1 m= 100 cm

The volume of the granite countertop in cubic centimeters is equal to

[tex]V=(100)(300)(4)\ cm^{3}[/tex]

The density in kg per cubic centimeter is equal to

[tex]D=2.75(\frac{1}{1,000}) \frac{kg}{cm^{3}}[/tex]

Multiply the density by the volume

[tex]2.75(\frac{1}{1,000})(100)(300)(4)[/tex]

[tex]2.75(120)=330\ kg[/tex]

Answer:

0.75 inches

Step-by-step explanation:

The value that has z=2 is 2 standard deviations from the mean. The value that has z=1 is 1 standard deviation from the mean. The difference between these two values is 1 standard deviation:

1 standard deviation = 3.75 in - 3 in = 0.75 in

Answer:

0.75

Step-by-step explanation:

We're given pairs (A,B) and asked if we have

enough calcium,

5A + 4B >= 24

enough iron

4A + 6B >= 15

and enough vitamins

7A + 4B >= 15

We check each constraint on each pair; if we find any false we can stop for that pair.

(A,B)=(1,4)

5(1)+4(4)=21   under 24, NO CHECK

(A,B)=(1,5)

5(1) + 4(5) = 25, bigger than 24, good

4(1) + 6(5) = 34, bigger than 15, good

7(1) + 4(5) = 27, bigger than 15, good   CHECK

(A,B)=(2,3)

5(2)+4(3)=22, NO CHECK

(A,B)=(3,2)

5(3)+4(2)=23, NO CHECK

(A,B)=(4,1)

5(4) + 4(1) = 24, ok

4(4) + 6(1) = 22, ok

7(4) + 4(1) = 32, ok, CHECK

Answer:

(1,5),  (4,1)

Step-by-step explanation:

Let's check the possible answers and see if they will Steve to meet his requirements:

We'll start by looking if each answer (dose) will provide enough calcium first.  If it does, we'll get iron and vitamins if needed.

a) (1,4)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (4)

24 ≤ 5 + 16

24 ≤ 21

NO!

b) (1,5)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (5)

24 ≤ 25   YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(1) + 6(5)

15 ≤ 34 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (1) + 4 (5)

16 ≤ 27  YES

YES, YES, YES...

c) (2,3)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (2) + 4 (3)

24 ≤ 22 NO!

d) (3,2)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (3) + 4 (2)

24 ≤ 23 NO!

e) (4,1)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (4) + 4 (1)

24 ≤ 24   YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(4) + 6(1)

15 ≤ 22 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (4) + 4 (1)

16 ≤ 32 YES

YES, YES, YES...

Answer:

h = 32.25.

Step-by-step explanation:

h^2 = 28^2 + 16^2 (Pythagoras theorem).

h = √1040

h = 32.25.

Using the Pythagorean theorem, the length of the hypotenuse in a right triangle with legs of lengths 28 and 16, rounded to the nearest hundredth, is 32.25.

The question asks for the length of the hypotenuse in a right triangle with legs of lengths 28 and 16. To find this, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). Thus, according to the equation a² + b² = c², we substitute the given values to find the hypotenuse length.

Using the given lengths:

a = 28

b = 16

We calculate:

c = √(28² + 16²)

c = √(784 + 256)

c = √(1040)

c = 32.249

Rounded to the nearest hundredth, the length of the hypotenuse is therefore 32.25.

Answer:

The area of the polygon = 216.4 mm²

Step-by-step explanation:

* Lets talk about the regular polygon

- In the regular polygon all sides are equal in length

- In the regular polygon all interior angles are equal in measures

- When the center of the polygon joining with its vertices, all the

 triangle formed are congruent

- The measure of each vertex angle in each triangle is 360°/n ,

  where n is the number of its sides

* Lets solve the problem

- The polygon has 9 sides

- We can divide it into 9 isosceles triangles all of them congruent,

 if we join its center by all vertices

- The two equal sides in each triangle is 8.65 mm

∵ The measure of the vertex angle of the triangle = 360°/n

∵ n = 9

∴ The measure of the vertex angle = 360/9 = 40°

- We can use the area of the triangle by using the sine rule

∵ Area of the triangle = 1/2 (side) × (side) × sin (the including angle)

∵ Side = 8.65 mm

∵ The including angle is 40°

∴ The area of each triangle = 1/2 (8.65) × (8.65) × sin (40)°

∴ The area of each triangle = 24.04748 mm²

- To find the area of the polygon multiply the area of one triangle

 by the number of the triangles

∵ The polygon consists of 9 congruent triangles

- Congruent triangles have equal areas

∵ Area of the 9 triangles are equal

∴ The area of the polygon = 9 × area of one triangle

∵ Area of one triangle = 24.04748 mm²

∴ The area of the polygon = 9 × 24.04748 = 216.42739 mm²

* The area of the polygon = 216.4 mm²

Answer

[tex]216.4 {mm}^{2} [/tex]

Explanation

The regular polygon has 9 sides.

Each central angle is

[tex] \frac{360}{n} = \frac{360}{9} = 40 \degree[/tex]

The area of each isosceles triangle is

[tex] \frac{1}{2} {r}^{2} \sin( \theta) [/tex]

We substitute the radius and the central angle to get:

[tex] \frac{1}{2} \times {8.65}^{2} \times \sin(40) = 24.05 {mm}^{2} [/tex]

We multiply by 9 to get the area of the regular polygon

[tex]9 \times 24.05 = 216.4 {mm}^{2} [/tex]

Answer:

I believe it's the statement is always true.

Step-by-step explanation:

test it by substituting x = an odd number:

x=1

so

x = 1 odd number

x + 2 = 1+2 = 3 odd

x + 6 = 1 + 6 = 7 odd

x + 10 = 1+10=11 odd

Answer:

the statement is always true.

Answer:

93%

Step-by-step explanation:

1 + 3 + 21 + 35 = 60 = 100%

21 + 35 = 56 = x%

60 = 100%

56 = x%

60x = 56 * 100

x = 56* 100 / 60

x = 2*23*2*2*5*5 / 2*2*3*5

x = 23*2*5/3

x = 93%

To find the percent of soldiers in the new army unit, you divide the number of soldiers in the unit by the total number of soldiers in the army and multiply by 100. However, the question doesn't provide the total number of soldiers in the army, making it impossible to calculate this percentage.

The question is asking what percent of the soldiers in the newly formed army unit consists of the total personnels. The total number of soldiers in the unit is the sum of staff sergeants, sergeants, PFCs, and PVTs which is 1 + 3 + 21 + 35 = 60 soldiers. The percent of soldiers in the army is the number of soldiers in the unit divided by the total number of soldiers in the army multiplied by 100. However, without the context of the total number of soldiers in the army, it is impossible to calculate this percentage. For example, if the total army size is 600, then the percent of soldiers in this unit would be (60/600)*100 = 10%. The keywords here are

percent

,

total soldiers

, and

army unit

.

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Answer:

Since we have BC ║ DE, we know that:

AB/AD = BC/DE

12/(12 + 4) = BC/12

12/16 = BC/12

BC = (12 · 12)/16 = 9 (in)

Applying the pythagorean, we have:

AB² + BC² = AC²

12² + 9²     = AC²

225           = AC²

AC             = √225 = 15 (in)

Using the information about the parallel lines again, we have:

AC/CE = AB/BD

15/CE = 12/4

CE = (15 · 4)/12 = 5 (in)

So the answer is B

Answer:

n = -174

Step-by-step explanation:

What I did was 696 divided by -4 and got B) n = -174.

Please mark brainliest and have a great day!

Answer:

27%

Step-by-step explanation:

take the number of times it is at 2 cars (16) and divide by the number of surveyed times in total (60). multiply by 100 to show answer as a percent

Answer:

27%

Step-by-step explanation:

We are given the results of survey of one thousand families to determine the distribution of families by their size.

We are to find the probability (to the near percent) that a line has exactly 2 cars in it.

Frequency of 2 cars in a line = 16

Total frequency = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60

P (2 cars in line) = (16 / 60) × 100 = 26.6% ≈ 27%

Answer:

[tex](f + g) (x)=x^2 +x +3[/tex]

[tex](f - g) (x)=-x^2 +5x +1[/tex]

Step-by-step explanation:

We have the following functions:

[tex]f(x)=3x +2\\[/tex] and [tex]g(x) = x^2 -2x +1[/tex]

First we find [tex](f + g) (x)[/tex]

To find [tex](f + g) (x)[/tex] we must add the function f(x) with the function g(x)

[tex](f + g) (x)=3x +2 + x^2 -2x +1[/tex]

[tex](f + g) (x)=x^2 +x +3[/tex]

Now we find [tex](f - g) (x)[/tex]

To find [tex](f - g) (x)[/tex] we must subtract the function f(x) with the function g(x)

[tex](f - g) (x)=3x +2 - (x^2 -2x +1)[/tex]

[tex](f - g) (x)=3x +2 - x^2 +2x -1[/tex]

[tex](f - g) (x)=-x^2 +5x +1[/tex]

Final answer:

To find the total number of votes polled in the election with three candidates and invalid votes, the sum of votes received by each candidate and the invalid votes is calculated. The total number of votes polled is 1,027,601.

Explanation:

The question pertains to vote totals and calculating the overall number of votes polled in an election with three candidates. To solve this, we will perform simple addition of the votes received by each candidate and also include votes that were declared invalid.

Candidate A received 345,983 votes. Candidate B won the election by a margin of 15,967 votes more than Candidate A, which means Candidate B received 345,983 + 15,967 = 361,950 votes. Candidate C received 279,845 votes, and there were 39,823 invalid votes.

To find the total number of votes polled, add together all the votes:

Votes for Candidate A: 345,983

Votes for Candidate B: 361,950 (since Candidate B won by 15,967 votes more than Candidate A)

Votes for Candidate C: 279,845

Invalid votes: 39,823

Adding these together:

345,983 + 361,950 + 279,845 + 39,823 = 1,027,601

Therefore, the total number of votes polled in the election is 1,027,601.

Step-by-step explanation:

The ratio of the perimeters = the scale

P₂ / P₁ = 6 / 4 = 3 / 2

The ratio of the areas = the square of the scale

A₂ / A₁ = (6 / 4)² = (3 / 2)² = 9 / 4

Same for the triangles:

P₂ / P₁ = 6 / 3 = 2

A₂ / A₁ = (6 / 3)² = (2)² = 4

Distance = rate * time

Replace D with f. Instead of writing D(t), write f(t).

f(t) = 65t

Let t = 3.5

f(3.5) = 65(3.5)

f(3.5) = 227.5

Did you follow?

Final answer:

The distance a car travels at 65 mph is a function of time, expressed as f(t) = 65t. Evaluating it for 3.5 hours, the car would travel 227.5 miles.

Explanation:

The distance a car travels at a rate of 65 mph is a function of the time, t, the car travels. This can be expressed mathematically as f(t) = 65t, where f(t) is the distance in miles and t is the time in hours. To evaluate this function for f(3.5), we multiply 65 miles/hour by 3.5 hours.

f(3.5) = 65 miles/hour × 3.5 hours = 227.5 miles

Therefore, a car traveling at a constant speed of 65 mph for 3.5 hours will have traveled 227.5 miles.

Answer:

if a line has a slope equal to zero, then it is horizontal

Step-by-step explanation:

Answer:

If a line does not have zero slope, then it is not a horizontal line.

Step-by-step explanation:

edg

Answer:

4 wrong

Step-by-step explanation:

Just do .84 times 25.

.84(25)=21

That means you got 21 questions right.

Answer:

You missed 4 questions.

Step-by-step explanation:

If you have a 100 questions test with 1 point each and you get and 84% that means you missed 16 questions. Since there was 25 questions on this test that is 1 quarter of 100. Divide the number of questions missed on a 100 questions test by the fraction of the actual test. So by 4. 16 divided by 4 = 4

Answer:

D. not congruent

Step-by-step explanation:

Only two pairs of congruent sides are given to us, when we need either 3 pairs of congruent sides (SSS) or two pairs of congruent sides & 1 pair of congruent angles (SAS), or two pairs of congruent angles & one pair of congruent sides (ASA).

~

Answer:

the functions f(x) and g(x) are equivalent

Step-by-step explanation:

Your full question is attached below

The equations of your problem are

f(x) = √(16^x)

f(x) = √(4^(2x))

f(x) = √(4^(2x)) = √(4^x.4^x)

f(x) = 4^(x)

and

g(x) = ∛64^x

g(x) = ∛4^(3x)

g(x) = ∛4^(3x)  =  ∛4^(x) .4^(x) .4^(x)

g(x) = 4^(x)

Thus, the functions f(x) and g(x) are equivalent

Answer:

  see below for a graph

Step-by-step explanation:

Each of the functions:

will only be graphed in the specified domain. You know that ...

  y = -x

is a line with slope -1 through the origin. It won't go through the origin on your graph, because it stops at x = -2. f(x) is not defined as -(-2) at x=-2, so there will be an open circle at the end of this portion of the graph.

__

You know that

  y = x+2

is a line with slope +1 through the y-intercept (0, 2). It will only be part of your graph for x-values between -2 and 2, inclusive. Because f(x) is defined as x+2 at the end points of this segment, those points will be shown as solid dots.

__

You know that

  y = 5

is a horizontal line. It will be part of your graph for x > 2, and will have an open circle on the end at x=2. f(2) is not defined as 5, but is defined as 4 (see above), which is why the circle is open.

Answer:

√3 + 12 = x

Step-by-step explanation:

Simplify both sides of the equation, isolating the variable.

Answer:

(C)

10

Step-by-step explanation:

Let y = cost of items

Let x = number of items

Total cost  = fixed charge + (cost per item x number of items)

Given:

company A fixed charge = $50 , cost per item = $7

company B fixed charge = $30 , cost per item = $9

For company A,

Total Cost = $50 + ($7 x number of items),

          or

     y = 50 + 7x

Similarly for company B,

Total Cost = $30 + ($9 x number of items),

          or

     y = 30 + 9x

Hence (C) is the correct answer.

For the cost to be the same, Total cost for A = total cost for B

i.e 50 + 7x = 30 + 9x

x = 10 items  (Answer)

The correct system to solve the problem is y=50+7x and y=30+9x. The cost will be the same at both companies when there are 10 items.

The correct system that could be used to solve the problem is (C) y=50+7x and y=30+9x.

To find the number of items where the cost will be the same at both companies, we need to set the two equations equal to each other and solve for x.

50+7x = 30+9x

20 = 2x

x = 10

Therefore, the cost will be the same at both companies when there are 10 items.

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