There are 10 students in a class: 5 boys and 5 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

Answer

x = 3, y = -1

Step-by-step explanation:

i used substitution because i find that easier most times so here goes:

x + 6y = -3

    - 6y

x = -6y -3

now we have an "x=" to plug into the "y=" we will get ina second

2x + 3y = 3

-2x

3y = -2x + 3

divide the whole thing by 3 to get y by itself. you get:

y = -2/3x + 1

now plug in what you got for x, which was (-6y-3), into the x. so:

y = -2/3(-6y - 3) + 1

now you multiply the -2/3 by the -6y and the -3. when you distribute that you get

y = 4y + 2 + 1

then combine like terms by adding 2 + 1 to get 3 and subtracting the y on the right from the 4y on the left to get

= 3y + 3

since you cant have an empty side of the equal sign, move the 3y over to the left side by subtracting it. you get

-3y = 3    now divide everything by -3 to get y = -1

now you have your y variable so now just plug that into the original equation to get x + 3

HOPE THIS HELPS!!!

if you have more questions or didnt understand something, please let me know!! ill explain it!!

l - length

19 ft - width

62 ft - perimeter

l + l + 19 + 19 = 2l + 38 - perimeter

The equation:

2l + 38 = 62    subtract 38 from both sides

2l = 24     divide both sides by 2

l = 12 ft

Answer: 4 years

Step-by-step explanation:

A(0) has to be amount at start. Assume that's 5mg

Then A(t) = 5×(0.5)^(0.25t) = 5×2^(-t/4),

(also known as 5 exp(-λ t) with λ = ln(2)/4, incidentally).

We need to such that A(t) = 2.5mg, or 2^(-t/4) is 1/2, which happens when -t/4 is -1, or t is 4.

The exponential function given can be used to model how radioactivity decays. Solving this function for when half the material remains, we find it takes approximately 2.8 years for half of the radioactive material to decay.

The amount of radioactive material remaining in a container over time can be modelled by the exponential decay function given in the question: A(t) = 5(0.5)0.25t. Here, A(t) stands for the amount left after time t, and the function gives a general rule for how radioactivity decays over time. Specifically, this rule tells us that after 1 year (t=1), approximately 74% of the radioactive material remains.

However, you're asking for the time it takes for half of the original material to remain. To solve this, we need to set A(t) to half its initial value, which is 2.5 milligrams: 2.5 = 5(0.5)0.25t. This translates to a simple equation 0.5 = (0.5)0.25t. Solving for t, we find that approximately 2.8 years are needed for half of the material to remain. Please note, this relies on the assumptions and limitations of the exponential decay model.

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Answer:

Number of​ restaurant-purchased meals eaten in a​ restaurant = 70

Number of​ restaurant-purchased meals eaten in a​ car = 22

Number of​ restaurant-purchased meals eaten in a​ home = 60

Step-by-step explanation:

Let the number of people that will eat in a restaurant be R.

Let the number of people that will eat in a car be C.

Let the number of people that will eat in a home be H.

From the information given in the problem we have,

R+C+H = 152 ____equation (1)

C+H-R = 12 ____equation (2)

R = H+10 ____equation (3)

1) Plugging in R=H+10 from equation 3 into the equation 2, we get

C+H-R=12

=> C+H-(H+10)=12

=> C+H-H-10=12

2) Cancelling out +H and -H, we get

C-10=12

3) Add 10 to both sides

C-10+10=12+10

4) Cancelling out -10 and +10, we get

C=22

5) Plugin C=22 in equation 1, we have

R+C+H = 152

=> R+22+H=152

Subtract 22 from both sides,

R+22+H-22=152-22

Cancelling out +22 and -22 from the left side, we get

R+H=130 ____let it be equation (4)

6) Plugin C=22 in equation 2, we have

C+H-R = 12

22+H-R = 12

Subtracting 22 from both the sides, we get

22+H-R-22 = 12-22

Cancelling out +22 and -22 from the left side,

H-R = -10 ____let it be equation (5)

7) Adding equation 4 and equation 5, we get

(R+H)+(H-R) = 130 + (-10)

=> R+H+H-R = 130-10

8) Cancelling out R and -R from the left side, we get

2H = 120

9) Dividing both sides by 2, we get

[tex]\frac{2H}{2} = \frac{120}{2}[/tex]

10) Cancelling out the 2's from the left side, we have

H=60

11) Plugging in C=22 and H=60 in the equation 1, we have

R+C+H = 152

=> R+22+60=152

=> R + 82 = 152

12) Subtracting 82 from both the sides, we get

R + 82 -82 = 152 -82

13) Cancelling out +82 and -82 from the left side, we get

R = 70

So, C=22, H=60, R=70

Answer:

68.2% of the data falls within 1 standard deviation of the mean

Step-by-step explanation:

When we look at the curve for standard deviation, 34.1 % falls within 1 standard deviation below the mean  and 34.1 % falls within 1 standard deviation above the mean.

34.1 + 34.1 = 38.2 %

68.2% of the data falls within 1 standard deviation of the mean

Answer:

68%

Step-by-step explanation:

Answer:

± 1/2,±1, ±2,± 5/2, ±4 ,±5 , ±10, ± 20

Step-by-step explanation:

We can use the rational root theorem to find all the possible roots

2x^3+5x^2-8x-20=0  

Let the constant term  be called p and the leading term be called q.  Then the possible roots are the positive and negative roots of the factors of p/q

p = 20

q = 2

Factors of p: 1,2,4,5,10,20

Factors of q: 1,2

Possible roots

    1 ,2,4,5,10,20

±   --------------------------------------------------------

      1,2

So we get

±1, ±2, ±4 ,±5 , ±10 ± 20 ± 1/2± 2/2,±4/2,± 5/2,± 10/2,± 20/2

Simplifying

±1, ±2, ±4 ,±5 , ±10, ± 20, ± 1/2,± 1,±2,± 5/2,± 5,± 10

Eliminating repeats

±1, ±2, ±4 ,±5 , ±10, ± 20 ,± 1/2,± 5/2

Putting them in numerical order

± 1/2,±1, ±2,± 5/2, ±4 ,±5 , ±10, ± 20

Answer:

Its Option 1

Step-by-step explanation:

The possible rational roots will have a numerator that divides 20 (the last number) and a denominator that divides 2 (the coefficient of x^3).

For example 20/2, 10/2 and -1/2  =  10, 5 and -1/2.

The correct answer is the first option.

Melanie drove a total of 500 miles over three days. To determine how many miles she drove each day, we divided total miles by total days. This gives us 166.67 miles or 166 2/3 miles as a mixed number.

The subject of the provided question is related to simple division. Here, Melanie has traveled 500 miles in total over the course of three days, and she drove the same distance each day. Mathematically speaking, to find out how many miles Melanie drove each day, we need to divide the total distance by the number of days. Hence, we divide 500 miles by 3 days.

This comes out to be 166.67 miles, which is the decimal format of the distance traveled by Melanie each day. However, the question asks for the answer to be written as a mixed number. Therefore, 166.67 miles can be expressed as 166 2/3 miles per day, as a mixed number. This is calculated by expressing the decimal .67 as a fraction.

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Answer:

Option a. No; the domain values are at regular intervals and the range values have a common sum 1.

Step-by-step explanation:

x1=3, x2=1, x3=-1, x4=-3

y1=1, y2=2, y3=3, y4=4

x1-x2=3-1→x1-x2=2

y2-y1=2-1→y2-y1=1

x2-x3=1-(-1)=1+1→x2-x3=2

y3-y2=3-2→y3-y2=1

x3-x4=-1-(-3)=-1+3→x3-x4=2

y4-y3=4-3→y4-y3=1

The data doesn't show an exponential function, because the domain values are at regular intervals and the range values have a common sum 1.

Answer:

a

Step-by-step explanation:

Answer:

convenience sample

Step-by-step explanation:

Answer: Convenience Sample

Step-by-step explanation: Biased sample–Parts of the population are favored over others. She only asked people in her office

Answer:

Step-by-step explanation:

42 < 21+3x < 84

21 < 3x < 63

7 < x < 21

The measure of sides of a triangle lies between 7<x<21.

Given that, Tim is making a fence in the shape of a triangle for his livestock.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Let the measure of one side of a triangle be x meters.

One side of the triangle to be two times as along as another side and the third side to be 21 meters long.

Second side =2x meters and the third side =21 meters

Tim wants the perimeter of the triangle to be more than 42 meters and less than 84meters.

Now, 42<x+2x+21<84

21<3x<63

7<x<21

Therefore, the measure of sides of a triangle lies between 7<x<21.

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Answer: (A) 10

Step-by-step explanation:

                Value       Quantity     =  TOTAL Value

dimes:        .10            Q + 5        =    .10(Q = 5)

quarters:    .25               Q           =      .25Q

Dimes + Quarters = $4.00

.10(Q + 5) + .25Q = 4.00

.10Q + .50 + .25Q = 4.00

           .50 + .35Q = 4.00

                    .35Q = 3.50

                          Q = 10

Quarters = 10

Dimes = Q + 5

           = 10 + 5

           = 15

Answer: Option A, she has 10 quarters.

Step-by-step explanation:

We have quarters of $0.25 and dimes of $0.10

We have 5 more dimes than quarters and a total of $4.00

How many quarters Ms. Kincaid has?

Q is the number of quarters and D the number of dimes.

We have the system of equations:

D = Q + 5

Q*$0.25 + D*$0.10 = $4.00

First, we can replace the first equation into the second and solve it for Q.

Q*$0.25 + (5 + Q)*$0.10 = $4.00

Q*($0.25 + $0.10) + $0.50 = Q*($0.35) + $0.50  = $4.00

Q = (4.00 - 0.50)/0.35 = 3.50/0.35 = 10

So she has 10 quarters.

The correct option is A.

Answer:

Two real solutions

Step-by-step explanation:

z=-1.45

z=0.45

Answer:

ANSWER: Two real solutions

Step-by-step explanation:

its z=-1.45

its z=0.45

Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

As per the given information option (A) is correct because it will shift to the right side by one unit when the function of [tex]g(x)[/tex] is [tex]g(x+1)[/tex].

For example:-

[tex]x=2[/tex]

So,

[tex]g(2)\\g(2+1)[/tex]

Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.

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Final answer:

The true statement for the graphs of all functions g(x) is that the graph of g(x + 1) is the graph of g(x) shifted left by 1 unit.

Explanation:

When considering the transformation of the graph of a function g(x) to g(x + 1), we are applying a horizontal shift to the graph. According to the principles of graph transformation, when we add a positive constant to the input of a function, every point on the graph shifts left by that amount. Therefore, the graph of g(x + 1) is the same as the graph of g(x), shifted to the left by 1 unit. This corresponds to the option C, which states that adding 1 to the input of the function shifts the graph to the left by 1 unit.

Answer:

Distributive property

Step-by-step explanation:

Answer: A

Step-by-step explanation:

f(x) = x³ + 4x² + 7x + 6

possible rational roots are ±{1, 2, 3, 6}

Try x = -2

-2 |   1   4   7   6

   |   ↓  -2  -4  -6

       1    2    3   0 ← remainder is 0 so x = -2 is a root  ⇒  (x + 2) = 0

The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.

a=1, b=2, c=3

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

[tex]x=\dfrac{-(2)\pm\sqrt{(2)^2-4(1)(3)} }{2(1)}[/tex]

[tex]x=\dfrac{-2\pm\sqrt{4-12} }{2}[/tex]

[tex]x=\dfrac{-2\pm\sqrt{-8} }{2}[/tex]

[tex]x=\dfrac{-2\pm2i\sqrt{2}}{2}[/tex]

[tex]x = -1 \pm i\sqrt{2}[/tex]

[tex]x = -1 + i\sqrt{2}[/tex]       [tex]x = -1 - i\sqrt{2}[/tex]

[tex]x - (-1 + i\sqrt{2})=0[/tex]       [tex]x - (-1 - i\sqrt{2})=0[/tex]

The factors are:

[tex](x - 2)[x - (-1 + i\sqrt{2})][x - (-1 - i\sqrt{2})][/tex]

Answer:

1) [tex]2s+s\leq18[/tex]

2) 6 years old

Step-by-step explanation:

Let Hannah's age be [tex]h[/tex] and her sister's age be [tex]s[/tex]

It means [tex]h=2s[/tex]

It means the sum is LESS THAN or EQUAL TO 18. So we can write:

[tex]h+s\leq18[/tex]

1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,

[tex]h+s\leq18\\2s+s\leq18[/tex]

2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,

[tex]2s+s\leq18\\3s\leq18\\s\leq\frac{18}{3}\\s\leq6[/tex]

Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.

Answer:

System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2

Step-by-step explanation:

We are given four systems of equations.  We are asked to find which two sets have the same solution.

We find that in all the 4 systems, first equation 4x-5y =2 remains the same.

I option is wrong because

Equation I + 2times equation 2 in II system

gives 10x-7y =10 but given is 10x-21y =10 hence wrong.

Now compare 2 and 3

In system 2, I equation +2times second equation gives

24x-5y-42y =2+20 or

24x-47y =22

Hence system 2 and 3 are the same set of equations and give the same solution.

Answer:

12 dogs

Step-by-step explanation:

Let d = dogs

c = cats

d = 3c

c+d = 16

Substitute d =3c into the second equation

c+3c = 16

Combine like terms

4c = 16

Divide by 4

4c/4 = 16/4

c = 4

There are 4 cats

We still need to find the number of dogs

d = 3c

d = 3*4

   = 12

There are 12 dogs

Answer:

cats = 4; dogs = 12

Step-by-step explanation:

There are 3 times more dogs than cats.

There are 16 dogs and cats in all.

Let:

dogs = d ; cats = c

Set the system of equations:

d + c = 16

3c = d

Plug in 3c for d (as d = 3c) in the first equation

(3c) + c = 16

Simplify. Combine like terms:

(3c + c) = 16

4c = 16

Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Divide 4 from both sides

(4c)/4 = (16)/4

c = 16/4

c = 4

Plug in 4 for c in one of the equations.

d + c = 16

d + (4) = 16

Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Subtract 4 from both sides

d + 4 (-4) = 16 (-4)

d = 16 - 4

d = 12

Answers: c = 4; d = 12

~

Answer:

88%

Step-by-step explanation:

if she got 3 problems wrong, so she got (25-3)=22problems correct,

22/25=x/100,x=88

The percent of the questions did she get correct will be 88%.

The quantity of anything is stated as though it were a fraction of a hundred.

Kimberly got 3 problems wrong on a test of 25 questions.

Then the number of the correct question will be

⇒ 25 – 3

⇒ 22

Then the percent of the questions did she get correct will be

⇒ (22 / 25) x 100

⇒ 0.88 x 100

⇒ 88%

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Answer:

arc ≈ 25.13 feet

Step-by-step explanation:

arc length = circumference × fraction of circle

= 2 πr × [tex]\frac{\frac{4\pi }{3} }{2\pi }[/tex] ← cancel 2π

= 6 × [tex]\frac{4\pi }{3}[/tex] = 8π ≈ 25.13 feet

Answer: Choice B (1,-2)

note: I'm assuming there is a "less than or equal to" sign as part of the given inequality, rather than a simple "less than" sign (without the "or equal to" part)

============================================

Work Shown:

Plug in x = -2 and y = 4 from the point (x,y) = (-2, 4). Then simplify. If you get a true statement, then this is a solution point

[tex]y - 4x \le -6[/tex]

[tex]4 - 4*(-2) \le -6[/tex]

[tex]4 + 8 \le -6[/tex]

[tex]12 \le -6[/tex]

This statement is false. The value 12 is not to the left of -6 on the number line, nor is 12 equal to -6. So (x,y) = (-2,4) is not a solution

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

Plug in x = 1 and y = -2

[tex]y - 4x \le -6[/tex]

[tex]-2 - 4*(1) \le -6[/tex]

[tex]-2 - 4 \le -6[/tex]

[tex]-6 \le -6[/tex]

This statement is true, but only if the inequality sign is a "less than or equal to" sign. Otherwise, the statement is false because -6 cannot be smaller than itself.

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

Plug in x = 1 and y = 3

[tex]y - 4x \le -6[/tex]

[tex]3 - 4*(1) \le -6[/tex]

[tex]3 - 4 \le -6[/tex]

[tex]-1 \le -6[/tex]

Like choice A, this is false. So (x,y) = (1,3) is not a solution

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

Plug in x = 2 and y = 3

[tex]y - 4x \le -6[/tex]

[tex]3 - 4*(2) \le -6[/tex]

[tex]3 - 8 \le -6[/tex]

[tex]-5 \le -6[/tex]

We end up with another false statement. So (x,y) = (2,3) isn't a solution either.

Answer:

The triangles are similar, because the angles are congruent and the sides are proportional.

Step-by-step explanation:

The first step to see if the triangles are similar is to see if the angles are the same.

The third angle in the large triangle is

30 + 65+ unknown = 180

95 + unknown = 180

Subtract 95 from each side

unknown = 180-95

unknown = 85

So the angles are the same.

Lets check the ratio of the the sides

14            10

------ = ----------

7                5    

Both simplify to 2/1  so the ratio's are the same.

The triangles are similar because the angles are congruent and the sides are proportional.

Answer:

It would be 90 because if there are 15 soccer people on the team and there are 6 in the packets then each would get 1 and if you multiply 15 times 6 you will get 90.

So the answer would be 90

Answer:

90

Step-by-step explanation:

just do 15x6

Answer: Choice D) approaches y = -4

"x increases without bound" is another way of saying "x heads off to positive infinity". Visually, you follow the graph curve going to the right. As the graph shows, the curve steadily gets closer to the horizontal line y = -4, but it never actually gets there. This line is the horizontal asymptote.

Answer: he has 3000

Step-by-step explanation: just multiply 600 by 5

Answer:

120

Step-by-step explanation:

all you do is 600 x 1/5

but u have to turn 1/5 into a decimal which is .20

so 600 x .20= 120

Answer:

46%  of Xander's friends prefer to stay home on Friday nights.

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

[tex]\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.[/tex]

i.e

Zanders friends prefer to stay home on Friday night = 23

Total numbers of Zanders friends are 50.

Part value = 23

Total value = 50

Put in the formula

[tex]Percentage = \frac{23\times 100}{50}[/tex]

[tex]Percentage = \frac{2300}{50}[/tex]

Percentage = 46%

Therefore 46%  of Xander's friends prefer to stay home on Friday nights.

Answer:

wasdd ada

Step-by-step explanation:

Answer: assuming that this was your equation;

[tex]\frac{1}{16} =64^{4x-3}[/tex]

You answer is x= 7/12

Step-by-step explanation:

First, rewrite 1/16 as 2^-4 and 64^4x-3 as 2^24x-18

This will leave you with;[tex]2^{-4} =2^{24x-18}[/tex]

Since bases are the same, set the exponents equal (eliminate the 2’s);

-4=24x-18

Move 24x to the left to get; -24x-4=-18

Move constant to the right to get -24x=-18+4

Add 4 to -18 to get; -24x=-14

Divide both sides by -24 to get you final answer for x which is 7/12

Hope this helps. Please rate and hit that thanks button. Cheers!

The required value of exponential equation is x =  [tex]\frac{7}{12}[/tex].

Given that,

Exponential equation; [tex]\frac{1}{16} = 64^{4x-3}[/tex]

We have to determine,

The value of x.

According to the question,

To obtain the value of x by solving the exponential equation follow all the steps given below.

Exponential equation;

[tex]\dfrac{1}{16} = 64^{4x-3}[/tex]

Then,

[tex]\dfrac{1}{16} = 64^{4x-3}\\\\\dfrac{1}{2^{4}} = 2^{6(4x-3)}\\\\2^{-4} = 2^{24x-18}\\\\[/tex]

Since, bases are the same, set the exponents equation,

Then,

Equating the power of exponential equation,

[tex]-4 = 24x-18\\\\24x = -4+18\\\\24x = 14\\\\x = \dfrac{14}{24}\\\\x = \dfrac{7}{12}[/tex]

Hence, The required value of exponential equation is [tex]\frac{7}{12}[/tex].

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Add 1,1.5,1.25,2.5, and 3 to get D, or 9 and 1/4.

Answer:

9 and 1/4 hope this helps!!!!!

Answer:

C. 2x^2 - 85 / 13