There are 52 cards in a deck. Each card contains a letter or a number. Theo selects a card at random, records the letter or number, and puts the card back in the deck. The results of his first six trials are: 5, Ace, 2, 8, Queen, and 9. Using Theo's results, how many number cards will he select in 24 trials?​

Answer:

2 boxes

Step-by-step explanation:

do 16 times 2 you get 32 so there are 32 green crayons 32/9 9 times 3 is 36 which is over 32 so you cant fill 3 boxes 9 times 2 equals 27 so the answer would be she can fill 2 boxes

Answer: x=0.9,−0.9

Step-by-step explanation:

The arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

Any equation of the form \(\rm ax^2+bx+c=0\)  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)

The equation:

h = −8t(2t−6)

To find the total number of seconds the arrow will be in the air:

Plug h = 0

−8t(2t−6) = 0

t(2t−6) = 0

t = 0   or    t = 6/2

t = 0  or   t = 3 seconds

Thus, the arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

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Answer:

The points  -3, 5 and 8 are included in the solution set

Step-by-step explanation:

2 ≤ |x-3| ≤ 6

x-3 ≥ 2 or x-3 ≤ -2       -->      x ≥ 5 or x ≤ 1

-6 ≤ x-3 ≤ 6   -->  -3 ≤ x ≤ 9

-9  and -5 are smaller than -3 so they don't hold for the second inequality. -3  fits in both. but 0 and 2 don't fit in the first one.

then 5 does and 8 is included too.

The points  -3, 5 and 8 are included in the solution set

When 2, 325 is rounded to the nearest thousand, the result would be 2, 000.

To round a number to the nearest thousand, identify the place value of the rounding digit, which is the thousandth place (the third digit from the right).

Then, look at the digit to the right of the rounding digit. If this digit is 5 or greater, then round up the rounding digit by adding one to it. If the digit is less than 5, keep the rounding digit as it is.

The number 2, 325 would therefore be rounded to 2, 000 because the digit " 3 " is less than 5.

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Answer:

18

Step-by-step explanation:

count

The number of students measured in this sample is 18.

The number of students measured is the number of heights that were acquired for the sample.

Looking at the question, the number of heights acquired were 18 which means that there were 18 students.

Knowing the number of students is important as it can help you calculate things such as mean:

Mean = Sum of heights / Number of students

= (75 + 72 + 72 + 73 + 74 + 65 + 69 + 74 + 70 + 70 + 71 + 75 + 71 + 75 + 69 + 75 + 78 + 70) / 18

= 72.11

In conclusion, the number of students measured is 18.

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The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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Answer:

The dimensions of a rectangular prism are 21 in. by 20 in. by 19 in.

To find:

The volume of the rectangular prism.

Solution:

Let the length, breadth and height are 21 in, 20 in and 19 in respectively.

Volume of the rectangular prism is

\(V=Length\times Breadth\times Height\)

\(V=21\times 20\times 19\)

\(V=7980\)

Therefore, the volume of the rectangular prism is 7980 cubic inches.

Answer:

16

Step-by-step explanation:

first term/(1-ratio)

8/(1-1/2)

8/1/2 = 16

Here are the steps to simplify the expression \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x} \\\):

1. Combine like terms that have the same radical term \(\sf\:\sqrt{3x} \\\):

\(\sf\:(5x - 2x - x)\sqrt{3x} \\\)

2. Simplify the coefficients:

\(\sf\:2x\sqrt{3x} \\\)

Therefore, \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x}\) simplifies to \(\sf 2x\sqrt{3x} \\\).

If Sanjay bought 14 T-shirts, he paid $133.

Given:

Equation=c = 9.5t

Number of T-shirt=14

Where:

c=Total cost

t=Number of T-shirts

Hence:

Total cost=9.5t

Total cost= 9.5(14)

Total cost=$133

Therefore If Sanjay bought 14 T-shirts, he paid $133.

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Daniel will not going to get a bag

why?

lets read the statement, a part of it

person who donates more than $5 to charity

the key word here is more,

daniel donates exact 5 dollars,

so he will not get a bag

Courtney cant get a bag, because she donates even less,

to get a bag you need to donate, according to the statement , 5 dollars or more,

so for example, you need to donate 5.01 dollars to get a bag

Answer:

6 3/10 / 5 1/4 = 1.2

Step-by-step explanation:

Answer:

1 2/10, 12/10, or 1.2

Step-by-step explanation:

6 3/10 as a fraction is 63/10

5 1/4 as a fraction is 21/4

63/10 ÷ 21/4

=63/10 • 21/4

=1 2/10

Answer:  C. quadrilateral

Step-by-step explanation:

Trapezoid means one side must be parallel, which does not exist in the image so A & D are ruled out.

Parallelogram means opposite sides are parallel which does not exist in this image so B is ruled out.

Quadrilateral means that the object contains 4 sides, which the image does so the answer is C.

Answer:

  a) sin(β) = 7/6 is false for any β

  b) angle β is not a real angle

Step-by-step explanation:

You want to use the Sine Law to show that a triangle with sides of lengths 6 and 10 and a smallest angle of 44.5° is impossible.

The Sine Law tells you side lengths are proportional to the sines of their opposite angles.

  sin(β)/10 = sin(44.5°)/6

  sin(β) = 10(0.7)/6

  sin(β) = 7/6

The angle β does not exist. The maximum value of the sine function is 1. There are no angles for which the sine is greater than 1.

The triangle is impossible because angle β cannot exist.

In effect, the angle 44.5° is too large, or side 10 is too long, or side 6 is too short for the figure to be a triangle.

__

Additional comment

In the realm of complex numbers, β ≈ π/2 -0.569618i radians, about (90 -32.64i)°. You cannot draw this complex angle with your real pencil.

a) For any, sin(β) = 1.17 is false.

b) Angle (β) is not a true angle.

In the branch of mathematics known as trigonometry, the relationships between the sides and angles of triangles are examined.

It involves the study of trigonometric functions like sine, cosine, tangent, cotangent, secant, and cosecant that describe the connections between the sides and angles of a right triangle.

(a) Using the Sine Law, we have:

sin(β)/10 = sin(44.5°)/6

Multiplying both sides by 10, we get:

sin(β) = (10/6)sin(44.5°)

sin(β) = 1.17

However, this is impossible since the sine of an angle can never be greater than 1. Therefore, there is no value of β that satisfies the equation, and we cannot find the value of B.

(b) The fact that the sine of β is greater than 1 means that there is no angle whose sine is equal to that value.

Therefore, there is no possible angle for β that can satisfy the given conditions of the triangle.

This means that the triangle is impossible and cannot exist with the given side lengths and angle measures.

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The students need to earn $182 per month in order to accomplish their goals.

Division is the process of dividing a number by a given number.

Given that, the total cost for the class to go to the observatory is $910 and the students need money in 5 months.

To collect $910 in 5 months, students must earn $910/5 per month.

910/5

= 182

Hence, the students need to earn $182 per month in order to accomplish their goals.

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The expected time taken by her to leave the maze is given by the term as 10.6 minutes.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events.

The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. ., ilk.., the a. to, a il, to the a.

Exit 1 lead out in 3 minutes

Exit 2 bring back in 5 minutes

Exit 3 bring back in 7 minutes

Probability of choosing each door is equal .

Therefore,

probability of choosing the 1st door = probability of choosing the 2nd door = probability of choosing the 3rd door = 1/3

Let x = time taken by the woman to leave the room

y = exit he choose

y = {1, 2, 3}

E(x|y = 1) = 3,

E(x|y = 2) = 5/3 + 3/3 = 8/3

E(x|y = 3) = 15/3 = 5

Therefore,

E(x|y = 1, 2, 3) = 3 + 8/3 + 5 = 10.6

Expected time taken by woman to leave the room will be 10.6 minutes.

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Complete question:

A woman is trapped in a room at the center of a maze. The room has three exits. Exit 1 leads outside the maze after 3 minutes, on average. Exit 2 will bring him back to the same room after 5 minutes. Exit 3 will bring him back to the same room after 7 minutes. Assume that every time he makes a choice, he is equally likely to choose any exit. What is the expected time taken by her to leave the maze?

Hint: Let X = time taken by the man to leave the maze from this room. Let Y = exit he chooses first. So Y belongs in { 1,2,3}

Calculate the conditional expectation of time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of time taken to leave the maze.

The next 3 terms of the sequence defined recursively by the formula f(n + 1) = f(n) + 2 are; 1, 3 and 5.

A sequence is defined as an arrangement of numbers in a particular order.

From the question f(n + 1) = f(n) + 2 such that rewriting we have;

f(n) = f(n + 1) - 2

The first is -1, so n = 1 and we derive the next term f(2) as follows;

f(1) = f(1 + 1) - 2 = -1

f(1) = f(2) - 2 = -1

f(2) = 2 - 1 {add 2 to both sides}

f(2) = 1

f(2) = f(2 + 1) - 2 = 1

f(3) = 2 + 1 {add 2 to both sides}

f(3) = 3

f(3) = f(3 + 1) - 2 = 3

f(4) = 3 + 2 {add 2 to both sides}

f(4) = 5

Therefore, we have the next three terms of the sequence to be 1, 3, and 5.

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Answer:

● Whats point slope formula

\(➢ \: formula = y - {y}^{1} = m \: (x - {x}^{1} \\ y = coordinate \: of \: second \: point \\ {y}^{1} \: coordinate \: of \: point \: one \\ m = slope \\ x = coordinate \: of \: second \: point \\ {x}^{1} = coordinate \: of \: point \: one.\)

\(TextFromYourMrEx\)

#CarryOnLearning

Hi!

I can help you with joy! :)

Remember, point-slope form

\(\rm{y-y1=m(x-x1)\)

Where

y1 is the y-coordinate of the point

m is the slope

x1 is the x-coordinate of the point

Hope it helps!

Enjoy your day!

\(\bf{erutaNtneliS\)

Answer:

the collection center should be located at Collection Option (D).

Step-by-step explanation:

To determine the best location for the collection center, you can calculate the average coordinates of the four collection points and choose the location that is closest to this average.

To calculate the average coordinates, you can add the coordinates of each collection point and divide the result by the number of collection points. For example, to find the average X coordinate, you can add the X coordinates of all four collection points and divide by 4. Similarly, to find the average Y coordinate, you can add the Y coordinates of all four collection points and divide by 4.

Using this method, the average coordinates for the four collection points are (5.75,3.25). The collection point that is closest to these average coordinates is Collection Point D, which is located at (7,3). Therefore, the collection center should be located at Collection Point D.

I hope this helps to clarify the process for determining the best location for the collection center. Please let me know if you have any other questions.

Answer:

Option A and B are correct

Step-by-step explanation:

We have to add here

6x+5y=1.

6x-5y=7

sow e will get 12x=8 , x=8/12=2/3

Option A  is correct.

If We substract bottom from furst then

6x+5y=1

-6x+5y=-7

10y=-6

y=-6/10=-3/5

we put y=-3/5 in any equation and find x

6x+5(-3/5)=1

6x=4

x=4/6=2/3

So Option B also correct.

Answer:

I'll setup the problem and you can do the calculations

Step-by-step explanation:

The formula for simple interest:

I = P*r*t

I = interest

P = principle or amount invested

r = interest rate per period (period is a year)

t = number of periods

P = 4920

r = .13

t = 8

if you have questions, send a comment

Here we have been provided with the principal , rate of interest and time period for which the sum of rupees is invested.

Now here we know that simple Interest is calculated by the formula,

Here in this formula,

Putting there values in the formula,

\(\longrightarrow \: \sf{S.I. \: = \: \dfrac{4920 \times 13 \times 8}{100} }\)

\(\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times 8}{10} }\)

\(\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times \cancel{8}}{ \cancel{10}} }\)

\(\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times 4}{ 5} }\)

\(\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 52}{ 5} }\)

\(\longrightarrow \: \sf{S.I. \: = \: \dfrac{25584}{ 5} }\)

\( \longrightarrow \: \sf{S.I. \: = \: \cancel\dfrac{25584}{ 5} }\)

\( \longrightarrow \: \orange{\boxed{\bf{S.I. \: = \: 5116.8}}}\)

\(\underline{\bf{Henceforth, \: interest \: paid \: is \: of \: Rs.5116.8}}\)

Answer:

First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.

Step-by-step explanation:

Answer:

Step-by-step explanation:

81 texts in 9 hours

So you do 81 divided by 9

Which givrs you 9 text an hour

Answer:

It's C

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

Hey there!

\(Answer:\boxed{\text{verticles}}\)

Edge - a line segment where two verticals meet.

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

side 1^2 + side 2 ^2 = hypotenuse ^ 2

18^2 + 20^2 = hypotenuse^2

324 + 400 = 724

hypotenuse^2 = 724

hypotenuse = 26.9072480941474

hypotenuse = 26.9

Step-by-step explanation:

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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