Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer:

1/15 or 0.0667

Step-by-step explanation:

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chatgpt

red marble on the first draw is 2/6, or 1/3

red marble on the second draw, given that the first marble was red, is 1/5

(1/3) * (1/5) = 1/15

The quadratic equation in the given graph can be written as:

y = -3*(x + 2)^2 + 4

We can see a quadratic equation that opens downwards and we can see that the vertex is at (-2, 4), then if the leading coefficient is a, we can write this as:

y = a*(x + 2)^2 + 4

We can also see that the parabola passes through (0, -8) replacing these values we will get:

-8= a*(0 + 2)^2 + 4

-8 - 4 = a*4

-12/4 = a

-3 = a

Then the quadratic equation is

y = -3*(x + 2)^2 + 4

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Answer: 1.5283

Step-by-step explanation:

When saying something like log base 8 of 24, we know that this means 8 to the power of what is equal to 24. The answer is 1.5283. If you would like to round sine it is the approximate value, do it.

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Answer:

16864

Step-by-step explanation:

16694 + 170 = 16864

The equation that describes the weight of the dog as a function of time is

y = 5x + 1.

We have,

To determine the equation that will describe the dog's weight, we can use the formula for linear interpolation:

y = mx + b

where y is the weight of the dog in kg, x is the number of months since birth, m is the rate of increase of the dog's weight every month in kg/month, and b is the initial weight of the dog in kg.

From the problem, we know that the initial weight of the dog is 1 kg and the monthly average weight gain is 5 kg.

Therefore, we can substitute these values into the formula:

y = 5x + 1

This equation describes the weight of the dog as a function of time.

To predict the dog's weight after five months, we can simply substitute

x = 5 into the equation:

y = 5(5) + 1 = 26 kg

Therefore, we can predict that the dog will weigh 26 kg after five months.

To represent this graphically, we can plot the equation y = 5x + 1 on a coordinate system with time (x-axis) and weight (y-axis).

We can then plot the predicted weight of the dog after five months

(x=5, y=26) as a point on the graph.

The resulting graph will be a straight line with a positive slope of 5, passing through the point (0,1) and the predicted point (5,26).

Thus,

The equation that describes the weight of the dog as a function of time is

y = 5x + 1.

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In the given diagram, the total surface area of the composite figure is 361.28 square yards

From the question, we are to calculate the total surface area of the given composite shape

In the composite shape, we have a cone and a hemisphere

The total surface area of the composite figure = Surface area of the hemisphere + Curved surface area of the cone

Surface area of the hemisphere = 2πr²

Where r is the radius

Curved surface area of a cone = πrl

Where r is the radius

and l is the slant height

In the given diagram,

Using the Pythagorean theorem,

l² = 12² + 5²

l² = 144 + 25

l² = 169

l = √169

l = 13 yd

Radius of cone and hemisphere = 5 yd

Total surface area of the composite figure = 2πr² + πrl

Substituting the parameters

Total surface area of the composite figure = 2π(5)² + π(5)(13)

Total surface area of the composite figure = 50π + 65π

Total surface area of the composite figure = 115π

Total surface area of the composite figure = 361.28 yd²

Hence,

The total surface area is 361.28 square yards

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let's firstly convert tyhe mixed fraction to an improper fraction.

[tex]\stackrel{mixed}{37\frac{5}{7}}\implies \cfrac{37\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{264}{7}} \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=\frac{264}{7} \end{cases}\implies \cfrac{264}{7}=2\pi r\implies \cfrac{264}{7}=2\cdot \cfrac{22}{7}\cdot r \\\\\\ \cfrac{264}{7}=\cfrac{44r}{7}\implies 264=44r\implies \cfrac{264}{44}=r\implies 6=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6 \end{cases}\implies A=\pi (6)^2\implies A=\cfrac{22}{7}\cdot 6^2 \\\\\\ A=\cfrac{22}{7}\cdot 36\implies A=\cfrac{792}{7}\implies A=113\frac{1}{7}[/tex]

Answer:3.14

Step-by-step explanation:This is the only number that I know that corresponds with the Pie symbol.

Answer:

<

Step-by-step explanation:

multiply 1/3 by 10 = 10/30

multiply 6/15 by 2 = 12/30

6/15 is greater

The value of the function f(1/2) for the f(x) = 2 / 5 x- 5 / 2 is equal to -2.3.

Function is equal to,

f(x) = 2 / 5 x- 5 / 2

To get the value of f ( 1 / 2 ) .

Substitute the value of x equals to ( 1 / 2 ) we get,

f(x) = (2 / 5 ) x- ( 5 / 2 )

This implies,

f ( 1 / 2 ) = ( 2 /5 ) × ( 1 / 2 ) - ( 5 / 2 )

⇒ f ( 1 / 2 ) = ( 1 / 5 ) - ( 5 / 2 )

Take the least common multiple of 5 and 2 we get,

least common multiple of 5 and 2 is 10.

⇒ f ( 1 / 2 ) = ( 2  - 25 ) / 10

⇒ f ( 1 / 2 ) = -23 /10

⇒ f ( 1 / 2 ) = -2.3

Therefore, the value of f(1/2) for the given function is equal to -2.3.

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The above question is incomplete, the complete question is:

Consider the function: ƒ(x) = 2/5 x- 5/2 find the value of f( 1/2)?

The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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Answer:

The correct operator for the exponential expression 3^5 ? 4^6 is > (greater than), because we can compare the values of the two exponents:

3^5 = 243

4^6 = 4096

Since 4096 is greater than 243, we can write:

3^5 < 4^6

or

4^6 > 3^5

Therefore, the correct operator for the exponential expression 3^5 ? 4^6 is > (greater than).

It takes the object 3(3/4) seconds to travel the full distance of the trip.

We have,

The object moves at a constant speed, so we can use the formula:

distance = speed x time

Let d be the full distance of the trip, and t be the time it takes the object to travel that distance.

We can write the proportion as:

(1/20) / (3/4) = d / t

Simplifying the left-hand side:

(1/20) x (4/3) = d / t

1/5 = d / t

Now, we can solve for t by multiplying both sides by 5:

t x (1/5) = d x (1/5)

t = d/5

Now,

The time it takes the object to travel the full distance of the trip is equal to the distance divided by 5.

So, the object takes 5 times as long to travel the full distance as it takes to travel 1/20 of the distance.

And,

The time it takes the object to travel the full distance is:

t = (5 x 3/4) seconds

t = 15/4 seconds

t = 3 3/4 seconds

Therefore,

It takes the object 3 3/4 seconds to travel the full distance of the trip.

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The complete question:

An object moves in a straight line at a constant speed. The object moves 1/20 of the way in 3/4 of a second. At that speed, how many seconds does it take the object to travel the full distance of the trip?

Answer:

Plot the points on the graphing calculator. Then generate an exponential regression equation.

[tex]y = 698.379( {1.131}^{x} )[/tex]

So a = 698.379 and b = 1.131 (to three decimal places).

Answer:

4, 2

Step-by-step explanation:

the mode is the data sets that occur most frequently

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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The smallest number of edges that would need be duplicated to eulerize the graph is 10.

Given that a graph has 20 vertices.

In order for a graph to be eulerized, it has to added an edge to each vertex having odd valence.

Here total number of vertices = 20

So, the smallest number of edges that would need be duplicated to eulerize the graph is half of the total number of vertices.

Number of edges = 20/2 = 10

Hence it is needed 10 edges to eulerize the graph.

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The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.

We have,

The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.

a)

Potential problem:

Age can be a confounding variable, affecting the occurrence of injuries due to muscle damage. Solution: Randomly assign people to stretch or not stretch after exercising without considering their age.

Improved design:

The researcher selects 400 people who exercise on a regular basis. The people are randomly assigned to stretch after exercising or to not stretch. The people's occurrence of injuries due to muscle damage is monitored.

b)

Potential problem:

The people in the two groups may not be comparable, leading to a biased result. Solution: Randomly assign people to stretch or not stretch after exercising.

Improved design:

The researcher randomly selects 150 people who exercise on a regular basis. Half of them are assigned to stretch after exercising, and the other half are assigned to not stretch. The number of injuries due to muscle damage is monitored for both groups.

Thus,

The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.

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Answer:

We don't know the initial value of the principal but we do know that the accumulated value is double (twice) the principal. It takes 9.9 years for money to double if invested at 7% continuous investment

If in a triangle ABC, right angle is at C, BA is hypotenuse, the length of side BC is 5√7 units.

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. Therefore, in triangle ABC, side BA is the longest side, and it is also the hypotenuse.

Using the Pythagorean theorem, we can find the length of the third side BC. The theorem states that the square of the hypotenuse (BA²) is equal to the sum of the squares of the other two sides (BC² + CA²).

BA² = BC² + CA²

16² = BC² + 9²

256 = BC² + 81

BC² = 256 - 81

BC² = 175

BC = √175

BC = 5√7

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Answer: The area left for development in the field outside the playground is C)1024ft^2

Step-by-step explanation:

We know  that area of rectangle formula is,

Area =  square unit

The total area of the field is the area of the large rectangle, which is:

=>

The area of the playground is the area of the smaller rectangle, which is:

=>

Therefore, the area left for development outside the playground is:

=>

Answer:

136.95

Step-by-step explanation:

hope u understand

The equation for the temperature at 11PM as required is; T(11) = T(5) - 18°F.

The solution as required in the task content is; T(11) = -4°F.

It follows from the task content that the temperature at 11PM is to be determined from the given information.

On this note, we have that; the equation which represents the situation is;

T(11) = T(5) - 18°F where, the temperature at 5pm T(5) = 14°F.

T (11) = 14°F - 18°F

T (11) = -4°F.

Ultimately, the temperature at 11PM is; -4°F.

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The total cost of your eulerization is 111.

We can Eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

We have to add all the edges to get the total cost

10+15+20+4+9+3+17+14+19

111

Hence, the total cost of your eulerization is 111.

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The polar coordinates of the point (-9, 4) are approximately (9.85, -24.04°).

To find the polar coordinates (r,θ) corresponding to the rectangular coordinates (-9, 4), we can use the following formulas:

r = sqrt(x^2 + y^2)

θ = arctan(y/x)

Substituting the values x = -9 and y = 4, we get:

r = sqrt((-9)^2 + 4^2)

= sqrt(81 + 16)

= sqrt(97) ≈ 9.85

θ = arctan(4/-9)

= -0.42 radians

≈ -24.04 degrees

Therefore, the polar coordinates of the point (-9, 4) are approximately (9.85, -24.04°).

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