A fifth grade teacher is designing a game based on one of her favorite children's books. While reading the book she counted the number of white cats, black cats, and brown cats that appear in the illustrations. The table below summarizes her data. (Use the data box in the picture :D)

The teacher wants to use a probability model to simulate the counting of cats. She wants the probability of counting a cat of a certain color to match the frequency of white, black and brown cats in the book.

Select all the probability *devices* that would best represent the observed probabilities from the table shown.

A)Spinner
B)Color Cube
C)Bags or Marble
D)Front View and Rear View

Please help :D

The linear approximation of [tex]f(x) = x^2 at x = 3.5 is f(3.5)[/tex]  ≈ 9.5.

To write a linear approximation (equation of the tangent) and use it to approximate the value of a function, we can follow these steps:

Choose a point on the function where you want to approximate the value.

Let's call this point (a, f(a)).

Find the slope of the tangent line at that point using the derivative of the function at that point.

The slope of the tangent line is equal to the derivative of the function at that point, which is denoted by f'(a).

Write the equation of the tangent line using the point-slope form, which is given by: y - f(a) = f'(a)(x - a)

Use this equation to approximate the value of the function at a nearby point.

Plug in the value of x that is close to a into the equation and solve for y. The resulting y-value will be an approximation of the value of the function at the nearby point.

For example, suppose we want to approximate the value of [tex]f(x) = x^2 at x = 3.[/tex]

We can follow these steps:

Choose the point (3, f(3)) = (3, 9) on the function.

Find the slope of the tangent line at x = 3 using the derivative: f'(x) = 2x, so f'(3) = 6.

Write the equation of the tangent line using the point-slope form: y - 9 = 6(x - 3), which simplifies to y = 6x - 9.

Use this equation to approximate the value of f(x) at x = 3.5: f(3.5) ≈ 6(3.5) - 9 = 9.5.

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Answer:

17

Step-by-step explanation:

The midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

therefore 2(x+5) = 3x-7

distribute

2x+10 = 3x-7

subtract 2x from both sides

2x+10 -2x = 3x-7 -2x

x-7 = 10

add 7 to both sides

x- 7 +7 = 10 + 7

x = 17

Answer:

Step-by-step explanation:

I think you are in 11th grade

we can use the theorem midpoint theorem.

as the mid-point theorem,

2(x+5)=3x-7

2x+10=3x-7

x=17

I really love your profile picture, is it real?

The location of point P within line segment AB is (8.333, - 6.667).

Herein we find the a line segment whose endpoints are A(x, y) = (10.2, - 6) and B(x, y) = (4.6, - 8), in which we must locate the point P. This can be done by following line segment AB:

P(x, y) = A(x, y) + (2 / 6) · [B(x, y) - A(x, y)]

P(x, y) = (10.2, - 6) + (2 / 6) · [(4.6, - 8) - (10.2, - 6)]

P(x, y) = (10.2, - 6) + (1 / 3) · (- 5.6, - 2)

P(x, y) = (10.2, - 6) + (- 1.867, - 0.667)

P(x, y) = (8.333, - 6.667)

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Answer:

Kailey flipping heads: 3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipping tails: 9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

Step-by-step explanation:

Kailey flipped heads 15 times and tails 5 times.

First, find the total amount of times that Kailey flipped the coin.

15+5=20

Kailey flipped the coin 20 times.

Out of those 20 times, she flipped heads 15 times. We can rewrite this as:

[tex]\frac{15}{20}[/tex]

and simplify it:

[tex]\frac{3}{4}[/tex]

3/4 as a decimal is 0.75, and to find the percentage, simply multiply the decimal form by 100.

We can find that 3/4 as a percentage is 75%.

So, the probability of Kailey flipping heads is:

3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipped heads 11 times and tails 9 times.

Let's find how many times she flipped the coin.

11+9=20

Olivia flipped the coin 20 times.

Out of 20 times, Olivia flipped tails 9 times.

This can be rewritten as:

[tex]\frac{9}{20}[/tex]

This fraction is already in simplest form.

To find what 9/20 is as a decimal, divide 9 by 20. You'll get 0.45.

Now, multiply 0.45 by 100 to find the percent. You'll get 45%.

So, the probability of Olivia flipping tails is:

9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

The area of the composite figure is 84.85 square units

The area of the composite figure is solved by breaking it up and adding together

To find the area of a semicircle of diameter 8, we first need to find the radius of the semicircle, which is half of the diameter:

radius = diameter / 2 = 8 / 2 = 4

area of semicircle = (1/2) * pi * radius^2

= (1/2) * pi * 4^2

= 8 pi

Now, let's find the area of the parallelogram. The area of a parallelogram is given by the formula:

area of parallelogram = base * height

In this case, the base is 10 and the height is 6, so we have:

area of parallelogram = 10 * 6

= 60

total area = area of semicircle + area of parallelogram

= 8 pi + 60

= 60 + 8 pi (in exact form) or approximately 84.85 (rounded to two decimal places)

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The correct equations for x = - 2 and x = 2 are,

⇒ x² - 4 = 0

⇒ 4x² = 16

We have to given that;

Find the equations which are true for x = - 2 and x = 2.

Now, We can simplify as;

⇒ x² - 4 = 0

⇒ x² = 4

⇒ x = ± 2

⇒ x² = - 4

⇒ x = ±2i

⇒ 3x² + 12 = 0

⇒ x² + 4 = 0

⇒ x = ±2i

⇒ 4x² = 16

⇒ x² = 4

⇒ x = ±2

⇒ 2 (x - 2)² = 0

⇒ (x - 2)² = 0

⇒ x = 2, 2

Thus, The correct equations for x = - 2 and x = 2 are,

⇒ x² - 4 = 0

⇒ 4x² = 16

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Answer:

x = 7.5

Step-by-step explanation:

3(x + 4.5) = 36

Distributive property

3x + 13.5 = 36

Isolate the x, Subtract 13.5 from both sides

3x = 22.5

Divide both sides by 3

x = 7.5

The value of x is given as follows:

x = 5.

The midsegment of a triangle is the line segment that connects the midpoint of two sides of the triangle. The Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to the third side of the triangle, and its length is equal to half the length of the third side.

Thus the equation relating the lengths in this problem is given as follows:

3x + 11 = 2(x + 8)

3x + 11 = 2x + 16

x = 5.

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Answer: 252cm^2

Step-by-step explanation:

Find height of parallelogram using the triangle.

[tex]a^2+b^2=c^2\\(9)^2+b^2=(15)^2\\b^2=114\\b=12[/tex]

Now that we have the height, we can fnd the area of the parallelogram using A=bh.

A = (12)(21)

A =252cm^2

By triangle inequality theorem  7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.

We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

For example, is a, b and c be sides of triangle then a + b ≥ c.

Here, the sides of triangle are:  7.7 cm, 4.0 cm, 1.7 cm

Let  a = 7.7 cm,

b = 4.0 cm,

c = 1.7 cm

consider the sum of sides b and c.

b + c = 4. 0 + 1.7

b + c = 5.7 cm

which is not greater than 7.7 cm (length of side  'a')

This means that, by triangle inequality theorem  7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.

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The complete question is:

Could 7.7 cm,4.0 cm, 1.7 cm be the side lengths of a triangle?

Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.

Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.

To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:

-270 + 360 = 90

Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).

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Answer:

x=7.9*tan(54°)=10.87

The surface area will be equal to 1,017.9 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

Given that:-

The surface area of the cylinder will be calculated as:-

SA = 2 πrl

SA = 2 π x 9 x 18

SA = 1,017.9 square feet

Therefore surface area will be equal to 1,017.9 square feet.

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The surface area of the given cylinder is 486π m² or 1526m².

From the figure, given height of the cylinder (h) = 18m

Given radius of the cylinder (r) = 9m

To find out the surface area of the cylinder the formula s = 2πr² + 2πrh

By substituting the given radius and height of the cylinder in the above equation we get the required surface area value.

s = 2πr² + 2πrh

s = (2 x π x (9)²) + (2 x π x 9 x 18)

s = (2 x π x 81) + (324π)

s = 162π + 324π

s = 486π m²

s = 486 x 3.14......           (since, π = 3.14....)

s = 1526m²

From the above explanation, we can conclude that the surface area of the given cylinder is equal to 486π m² or 1526m².

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Answer:

2c + 3d = 24. For c = 4.25 and d = 3.75, we have 2(4.25) + 3(3.75) = 8.5 + 11.25 = 19.75

and

c^2 + d^2 = 24. For c = 4.25 and d = 3.75, we have 4.25^2 + 3.75^2 = 18.0625 + 14.0625 = 32.125

Step-by-step explanation:

There are many possible algebraic expressions involving c and d that are worth 24, but two possibilities are:

2c + 3d = 24. For c = 4.25 and d = 3.75, we have 2(4.25) + 3(3.75) = 8.5 + 11.25 = 19.75, which is not equal to 24. Therefore, this expression is not true for the given values of c and d.

c^2 + d^2 = 24. For c = 4.25 and d = 3.75, we have 4.25^2 + 3.75^2 = 18.0625 + 14.0625 = 32.125, which is not equal to 24. Therefore, this expression is also not true for the given values of c and d.

It is important to note that there are many

Hello and Greetings Brainly users.

This is an exercise in "Equation of the line that passes through two points". The equation of a line is a mathematical formula used to describe a straight line in a Cartesian plane.

To find the equation of a line that passes through two points, you must first calculate the slope using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the given points. Then, the point-slope form of the equation of the line is used to obtain the equation of the line: y - y₁ = m(x - x₁).

By solving this equation, we can obtain the equation of the line that passes through two points. If the slope of the line is zero, as in the case of two points lying on the same horizontal line, then the equation of the line is simply a horizontal line at y = k, where k is the y-coordinate of the points.

Applying the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where m is the slope of the line.

We find that the points are:

x₁ = 6 ,   y₁ = 4

x₂ = -5 , y₂ = 4

We substitute the data in the formula and solve:

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 4)/(-5-6)

m = 0/-11

m = 0

Now, we can use the point-slope form of the equation of the line to obtain the equation of the line:

Where m = 0 and (x₁, y₁) is one of the two given points. We can choose any of the two points, but for this we will choose (6,4).

So, substituting the values we have, we have:

y - 4 = 0(x - 6)

Simplifying, we arrive at:

y - 4 = 0

y = 4

The equation of the line that passes through the points (6,4) and (-5,4) is y = 4 , since it is a horizontal straight line through the values of y = 4.

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Answer:

1. The parameter of interest is the proportion of students in the school who think of their parents or guardians as “strict”. A statistic that the students could use to estimate the parameter is the proportion of students in their sample who think of their parents or guardians as “strict”.

2. The best design for this study is a sample survey. An experiment would involve manipulating the parents' behavior and observing the effect on the students, which is not ethical. An observational study would only observe the behavior without manipulation, but it is not clear what behavior to observe in this case.

3. Here are three questions that could provide objective data related to strictness:

4. An appropriate method for obtaining a sample of 100 students is random sampling. The students could assign each student in the school a number, and then use a random number generator to select 100 numbers. They could then survey the students corresponding to those numbers. Another method could be stratified sampling, where the students divide the school into groups based on grade level, and then randomly sample a proportionate number of students from each group.

Answer: B and D.

Step-by-step explanation: We can simplify the expression -3.75+ 2(-4x +6.1) - 3.25x as follows:

-3.75+ 2(-4x +6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.25x + 8.45 (combining like terms)

Now, let's check each expression to see if it is equivalent to -11.25x + 8.45:

A. 7x-2x +8.2

= 5x + 8.2

Not equivalent to -11.25x + 8.45

B. 8.45-8x-3.25x

= 8.45 - 11.25x

Equivalent to -11.25x + 8.45

C. -1.75-7.25x=6.1

This is not an expression, it is an equation. It is not equivalent to -11.25x + 8.45.

D. -11.25x +12.2 - 3.75

= -11.25x + 8.45

Equivalent to -11.25x + 8.45

Therefore, the expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x are B and D.

Thus,  the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

To solve this problem, we need to use algebraic equations. Let's start by assigning variables to the unknown quantities. Let x be the number of purses sold and y be the number of blouses sold.

From the problem, we know that the blouses cost $28 each and the purses cost $39 each. Therefore, the total revenue from selling x purses and y blouses is given by:

Revenue = 28y + 39x

We also know that the store sold three times as many blouses as purses. Therefore, we can write:
y = 3x

Now we can substitute y = 3x into the revenue equation and solve for x:
1107 = 28y + 39x
1107 = 28(3x) + 39x
1107 = 84x + 39x
1107 = 123x
x = 9

So the store sold 9 purses. To find the number of blouses, we can use the equation y = 3x:
y = 3x = 3(9) = 27

Therefore, the store sold 27 blouses.

In summary, the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

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The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.573.

Given that the time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.

We know that the exponential probability distribution function is given by

f(x) = λ e^(-λx)

Where λ is the rate parameter of the distribution and is equal to 1/mean in this case. So, λ = 1/14.

Now, we need to find the probability that the arrival time between vehicles is 12 seconds or less. Mathematically, we can express this as:

P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] λ e^(-λx) dx

Integrating this expression, we get:

P(X ≤ 12) = [-e^(-λx)]_[0,12] = -e^(-λ12) + e^(-λ0)

Since e^(-λ×0) is equal to 1, we have:

P(X ≤ 12) = 1 - e^(-λ×12)

Substituting the value of λ, we get:

P(X ≤ 12) = 1 - e^(-12/14)

P(X ≤ 12) ≈ 0.573

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The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds . What is the probability that the arrival time between vehicles is 12 seconds or less?

Answer:

y=2x+3

Step-by-step explanation:

find x

look for points (2,7), (3,9), (0,3)

(x2-x1), (y2-y1)

x - distance from 7 and 9:  (9-7=2)

y - distance from 2 and 3: (3-2=1)  

Rise(y) over run (x) = 2/1=2

so X=2

y=2x

Because we see the line passes the point (0,3) we know the b in y=mx+b = 3

To prove:

try a point

(2,7)

y=mx+b (plug-in)

7=2(x)+3 (isolate x, subtract 3 to 7)

4= 2x (isolate x, divide by 2)

x=2

2=2 ( compare x to original coordinate: (2,7))

Answer:

10 oranges

Step-by-step explanation:

We Know

A grocery store sells a bag of 6 oranges for $4.80

4.80 / 6 = $0.80 for one orange

If Austin spent $8.00 on oranges, how many did he buy?

We Take

8 / 0.80 = 10 oranges

So, he bought 10 oranges.

The final answers are given below

[tex]10.[/tex]L

[tex]11.[/tex] [tex]3[/tex] (the number should be [tex]1,000,000[/tex], which has six zeros)

[tex]00000[/tex]

[tex]12[/tex]  | |

[tex]00000[/tex]

|

[tex]00000[/tex]

[tex]15. 31 16 48 29 53 47 22 37 98 26 2025[/tex]

A number is an arithmetic value that is used to calculate and represent a quantity.

The numbers that are more than [tex]20[/tex] but less than [tex]30[/tex] are [tex]22[/tex] and [tex]26[/tex], so they should be crossed out:

[tex]31 16 48 29 53 47[/tex] X [tex]37 98[/tex] X [tex]2025[/tex]

Therefore the answers are given below.

[tex]10.[/tex]L

[tex]11.[/tex] [tex]3[/tex] (the number should be [tex]1,000,000[/tex], which has six zeros)

[tex]00000[/tex]

[tex]12[/tex]  | |

[tex]00000[/tex]

|

[tex]00000[/tex]

[tex]15. 31 16 48 29 53 47 22 37 98 26 2025[/tex]

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the area of given figure made from two part Parallelogram and Triangle is 288sq cm

A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal in measure. Parallelograms can have various orientations, but their opposite sides will always be parallel.

A triangle, on the other hand, is a three-sided shape with three angles and three vertices. The sum of the angles in a triangle is always 180 degrees. Triangles can come in various shapes and sizes, such as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), and scalene (all sides and angles are different).

given that

1st part:

Base=6cm

height=8cm

Area=1×Base×Height/2

Area=(1×6×8)cm²/2

Area=24cm²

it have two part so, Area=2×24=48sq cm

2nd part:

if we assume Parallelogram

Area=Base×Height

Area=15cm×8cm

Area=120 sq unit

it have two part so,2×120sq cm

240sq unit

total area of given figure is 48 sq cm+240sq cm=288 sq unit.

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The standard deviation of the mean birth weights for samples of 100 babies is 50 grams.

The standard deviation of the mean birth weights for samples of 100 babies can be calculated using the formula:

Standard deviation of the mean = Standard deviation of the population / sqrt(sample size)

Given that the standard deviation of birth weights for individual babies in the population is 500 grams, and the sample size is 100, we can plug in these values into the formula:

Standard deviation of the mean = 500 / sqrt(100) = 50 grams

Therefore, the standard deviation of the mean birth weights for samples of 100 babies is 50 grams.

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Answer: Im sorry i dont have a picture :( but the awnser to your problem is (168)

Step-by-step explanation:

Answer: Either 58 or 85

Step-by-step explanation:

5 + 8 = 13
8 + 5 = 13

5 x 8 = 40

8 x 5 = 40

The surface area of the prism is 78 square units, which corresponds to option A.

You provided three dimensions: 5 units, 3 units, and 3 units. I assume these are the dimensions of a rectangular prism.

Let's label the dimensions: length (l) = 5 units, width (w) = 3 units, and height (h) = 3 units.

There are two bases, and their areas are equal:

Base Area = l * w = 5 * 3 = 15 square units

There are also three pairs of lateral faces. The areas of the lateral faces are:

Two faces with dimensions l and h: 2 * (l * h) = 2 * (5 * 3) = 30 square units

Two faces with dimensions w and h: 2 * (w * h) = 2 * (3 * 3) = 18 square units

Now, add the areas of all the faces together:

Surface Area = Base Area * 2 + Lateral Area = 15 * 2 + 30 + 18 = 30 + 30 + 18 = 78 square units

So, the surface area of the prism is 78 square units, which corresponds to option A.

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The answer for the given equation is 5x-4.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Some algebraic expressions use the same variables raised to the same exponents for like terms in the equation. Similar phrases remain constant. We initially formulate an expression as the sum of its terms in order to locate the terms and the similar terms in it.

An algebraic expression is considered to be in its simplest form when it doesn't contain any brackets or like terms. We employ the distributive property to add or subtract coefficients that are linked to variables.

according to question,

= -(x+4)+6x

= -x-4+6x

=5x-4

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The sides of the triangle are;

c = 5√2

b = 3√3

A right triangle is a triangle that has a right angle that measures 90 degrees. The hypotenuse, which is the side that faces the right angle, is the longest side. The right triangle's other two sides are referred to as its legs.

1) Cos 45 = 5/c

√2/2 = 5/c

c√2 = 10

c = 10/√2

c = 5√2

2) Tan 30 = b/3

√3/3 = b/3

3√3= 3b

b = 3√3/3

b = 3√3

We have used to concept of the special angles to solve the problem above.

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