There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.


Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11


Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.

The result from project number 11 suggests that the drug may be effective in reducing the size of pancreatic tumors, but it is not sufficient to conclude definitively that the drug is effective using hypothesis.

The p-value of 0.027 indicates that if there were truly no effect of the drug, the probability of observing a result as extreme as or more extreme than what was observed in project number 11 would be 0.027. This suggests that the result is unlikely to have occurred by chance alone. However, it is possible that the result is a false positive or due to chance variation, especially given that 20 research projects were conducted. It would be important to replicate the result in additional studies and consider the overall body of evidence before concluding definitively that the drug is effective.

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The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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Step-by-step explanation:

For question 30, the first choice is not necessarily true. I attached a picture of what *could* be the parallelogram.

The first choice is true ONLY if the parallelogram is a square.

The second choice is not necessarily true either. It is true ONLY if the parallelogram is a rhombus (a square is also a rhombus, just for reference)

But opposite sides of a parallelogram are always equal

So the answer to question 30 are the first and second choices.

For question 31:

remember what I said about how opposite sides of a parallelogram are always equal? Well opposite angles are also always equal.

So angle BKX = angle BWX = angle XWB = 114 degrees

Angle BKW = angle XWK (using parallel lines) = angle XWB - angle BWK = 114 - 22 = 92 degrees

Angle WBX = angle BXK (using parallel lines too) = angle WXK - angle WXB.

Consecutive angles in a parallelogram add up to 180. So angle WXK + angle XWK = 180. angle WXK = 180 - angle XWK = 180 - 114 = 66 degrees.

angle WDB + angle WBX + angle BWK = 180 because it's a triangle

angle WDB + 66 (just figured it out) + 22 (given) = 180 degrees

angle WDB = 180 - 66 - 22 = 92 degrees

I hope I didn't do anything wrong lol

but I prolly did XD

Answer:

angle WDB + angle WBX + angle BWK = 180 because it's a triangle

angle WDB + 66 + 22 (given) = 180 degrees

angle WDB = 180 - 66 - 22 = 92 degrees

Step-by-step explanation:

When E is the region bounded by the spheres then the answer to the triple integral is -π/2 (e⁻¹ - e⁻¹⁶)

To evaluate the triple integral using spherical coordinates, we need to express the volume element dV in terms of spherical coordinates and determine the limits of integration.

In spherical coordinates, the volume element dV is given by:

dV = ρ² sin(φ) dρ dφ dθ

where ρ represents the radial distance, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).

The given region E is bounded by the spheres x² + y² + z² = 1 and x² + y² + z² = 16. These can be expressed in terms of ρ as:

1 ≤ ρ ≤ 4

To determine the limits of integration for φ and θ, we consider the spherical symmetry of the problem. Since the region is bounded by spheres, the limits for both φ and θ will be the full range of [0, π] and [0, 2π], respectively.

Now, let's evaluate the triple integral:

∭E e(-x² - y² - z²) / √(x² + y² + z²) dV

= ∫₀²π ∫₀ᴨ ∫₁⁴ e(-ρ²) / ρ ρ² sin(φ) dρ dφ dθ

= ∫₀²π ∫₀ᴨ ∫₁⁴ e(-ρ²) ρ sin(φ) dρ dφ dθ

Since the integrand does not depend on θ, we can simplify the triple integral:

= ∫₀²π ∫₀ᴨ [-e(-ρ²) cos(φ)]₁⁴ sin(φ) dφ dθ

= ∫₀²π [-e(-ρ²) cos(φ) sin(φ)]₁⁴ dθ

= ∫₀²π [-e(-ρ²) / 4] dθ

= -e(-ρ²) / 4 [θ]₀²π

= -e(-ρ²) / 4 (2π - 0)

= -π/2 (e(-ρ²))

Now, we need to evaluate this expression within the limits of ρ:

= -π/2 ∫₁⁴ e(-ρ²) dρ

To solve this integral, we can use the substitution u = -ρ², which gives du = -2ρ dρ. The limits of integration transform accordingly:

u = -1, u = -16

∫ eu du = eu [u]_{-1}{-16} = e⁻¹ - e⁻¹⁶

Please note that the above expression represents the numerical value of the triple integral.

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The line TU is parallel to QR and SQR is dilated version of STU by a scale factor of 4.

What is midpoint theorem?

The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.

Through the diagram it can be seen that T and U are midpoints of SQ and SR respectively.

And it can also be seen that TU is parallel to QR.

It is given that ST = 2, TQ = 6, SU = 3 and UR = 9

The length of side SQ -

SQ = ST + TQ

SQ = 2+6

SQ = 8

The length of side SR -

SR = SU + UR

SR = 3+9

SR = 12

The measurement of QR = SQ as seen in the diagram.

According to midpoint theorem the mid points line segment TU measures half of its parallel third side of triangle QR.

Now, to find the scale factor -

= QR - TU

= 8 - 4

= 4

Therefore, the scale factor is 2.

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Applying basic unitary method and time conversion, The answer is 3750 calls annually.

The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

The unitary technique is used practically all the time, from problems involving speed, distance, and time to issues with estimating material costs. The technique is applied to determining a product's pricing. It is used to determine how long it takes a person or vehicle to travel a certain distance in an hour.

average length of call= 30 minutes

average travel time=30 minutes

annual working days=250

per day works 8 hours.

call hour in work = 8*60 - 30 = 450minutes.

number of calls made in those hours= 450/30=15 calls daily.

total annual number of calls= 250 * 15 = 3750

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Answer:

Answers below

Step-by-step explanation:

Answer:

hey there you go with the steps , please mark as brainliest

Using visual interpretation of the plot trend, the scatter plot shows positive correlation.

A positive correlation is depicted by a positive slope or trend line on a scatter plot. The trend of the scatter plot slopes upward which establishes a positive association.

If the slope is otherwise negative, such that the trend line slopes downward, then we have a negative association or relationship.

Therefore, the scatter plot shows positive relationship.

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Answer:

50 degrees

Step-by-step explanation:

Line CDF is 180 degrees

76 and 54 and some part of the 180 degrees

1. add 76+54 = 130

2. subtract 180-130 = 50

The change in quantities can be represented as percentage

The percentage decrease in miles driven is 34.83%

The given parameters are:

\(\mathbf{Initial = 22250}\)

\(\mathbf{Final = 14500}\)

The percentage decrease is calculated as:

\(\mathbf{\%Decrease = \frac{Final - Initial}{Initial} \times 100\%}\)

Substitute known values

\(\mathbf{\%Decrease = \frac{14500- 22250}{22250} \times 100\%}\)

\(\mathbf{\%Decrease = \frac{-7750}{22250} \times 100\%}\)

\(\mathbf{\%Decrease = \frac{-775000}{22250} \%}\)

\(\mathbf{\%Decrease = -34.83 \%}\)

The negative sign implies that, the change represents a decrement.

Hence, the percentage decrease in miles driven is 34.83%

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Mr. Ross can choose any dimensions for the length, width, and height as long as their product falls within the given volume range of 4 * 5 * 5 to 6 * 5 * 5 cubic inches.

To help you find the dimensions for Mr. Ross's tool box that can hold between 100 and 150 cubic inches, let's consider the following terms: volume, length, width, and height.

1. Volume: The space occupied by the tool box, which should be between 100 and 150 cubic inches.

2. Length, Width, and Height: The dimensions of the tool box that will determine its volume.

To find the dimensions for the tool box that meets Mr. Ross's requirements, we can use the formula for volume of a rectangular box:

Volume = Length × Width × Height

We need to find the Length, Width, and Height such that 100 ≤ Volume ≤ 150.

Unfortunately, without more specific information about the dimensions Mr. Ross prefers or the shape of the box, we cannot provide an exact set of dimensions. However, he can choose any dimensions for the length, width, and height as long as their product falls within the given volume range of 100 to 150 cubic inches.

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Answer:

Type A cabinets generated was 10

Type B and type C cabinets generated were 35

So, the total cabinets produced is 45

Step-by-step explanation:

It is given that

B = 1 ÷ 2 A + 30

C = 3 ÷ 2A + 20

Now equate these

B = C

1 ÷ 2A + 30 = 3 ÷ 2A + 20

30 - 20 = 3 ÷ 2A - 1 ÷ 2A

10 = A

Now put the A value in any of the above equation

B = 1 ÷ 2A + 30

B = 1 ÷ 2(10) + 30

B = 5 + 30

B = 35

And,

C = 3  ÷ 2A + 20

C = 3 ÷ 2(10) + 20

C = 15 + 20

C = 35

Therefore

Type A cabinets generated was 10

Type B and type C cabinets generated were 35

the total cabinets produced is 45

Answer:

\(\huge\boxed{y+5=3(x-2)}\)

Step-by-step explanation:

The point-slope form of an equation of a line:

\(y-y_1=m(x-x_1)\)

We have

\(m=3;\ (2;\ -5)\to x_1=2;\ y_1=-5\)

Substitute:

\(y-(-5)=3(x-2)\\\\y+5=3(x-2)\)

The equation of the line in a point-slope form that has slope 3 and passes through (2,-5) is y = 3x - 11

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that  line in a point-slope form that has slope 3 and passes through (2,-5)

Therefore, m = 3

Now substituting;

y-y₁ = m(x-x₁)

y- -5 = 3(x- 2)

y = 3x - 6 - 5

y = 3x - 11

Hence, the equation of the line in a point-slope form that has slope 3 and passes through (2,-5) is y = 3x - 11

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The perimeter of the window to the nearest hundredth will be;

⇒ 102.8 cm

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The shape of window is semicircle.

And, The radius of window (r) = 20 cm

Now,

We know that;

The perimeter of semicircle = πr + 2r

Here, The radius of window (r) = 20 cm

So, We get;

The perimeter of the window = πr + 2r

                                             = 3.14 x 20 + 2 x 20

                                             = 62.8 + 40

                                             = 102.8 cm

Thus, The perimeter of the window to the nearest hundredth will be;

⇒ 102.8 cm

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The property of the average of any two odd integers being odd is true for all integers.

This is because the sum of any two odd integers is always an even integer. For example, if we take any two odd integers, say 3 and 7, then the sum of these two is 10, an even integer. Therefore, the average of 3 and 7, which is (3 + 7)/2, is also an even integer, in this case, 5.

Since all even integers are divisible by 2, the average of any two odd integers must be an odd integer.

Therefore, the property is true for all integers.


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Answer:

$1.4 million

Step-by-step explanation:

A P E X

Answer:1.4 million

Step-by-step explanation:

Using an exponential equation, it is found that 4 mg of the substance would still be left after 32 days.

The equation for the amount of the substance y after x half-lifes is given by:

\(y = a(0.5)^x\)

In this problem, the initial mass is of a = 64 mg.

Considering a half-life of 8 days, 32 days is equivalent to x = 32/8 = 4 half-lifes, hence:

\(y = 64(0.5)^4 = 4\)

4 mg of the substance would still be left after 32 days.

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Answer:

TZ = 10 units

UY = 12 units

ZW = 11 units

Step-by-step explanation:

Point Z is the centroid of ΔTUV.

Since, centroid of a triangle is located on each median so that it divides each median in the ratio of 2 : 1

Therefore, TZ = 2(ZX)

TZ = 2(5) = 10 units

UY = UZ + ZY

     = UZ + \(\frac{1}{2}(UZ)\)

     = \(\frac{3}{2}UZ\)

     = \(\frac{3}{2}\times 8\)

     = 12 units

ZW = \(\frac{1}{3}(VW)\)

      = \(\frac{1}{3}(33)\)

      = 11 units

The coordinates of A' and C' will not be the same. The perimeter and area of ΔA'B'C' will be the same. The measure of ∠B' and the slope of A'C' will be the same.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation,

2 units down and 3 units right

The coordinate will change as,(x,y) → (x+3,y-2) so it will change.

The transformation consists only of linear transformation no rotation exists thus area and perimeter will remain the same.

The slope and angle are unchanged irrespective of any transformation.

Hence "A' and C' will not have the same coordinates. The boundaries and surface area of ΔA'B'C' will be identical. The slope of A'C' and the measure of ∠B will be equal.".

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The solution to the expression (7 + 5) + 4 • 13 – 2 is 62

The expression is given as:

(7 + 5) + 4 • 13 – 2

Evaluate the expression in bracket

(7 + 5) + 4 • 13 – 2 = (12) + 4 • 13 – 2

Remove the bracket in the expression

(7 + 5) + 4 • 13 – 2 = 12 + 4 • 13 – 2

Evaluate the product in the expression

(7 + 5) + 4 • 13 – 2 = 12 + 52 – 2

Evaluate the sum in the expression

(7 + 5) + 4 • 13 – 2 = 64– 2

Evaluate the difference in the expression

(7 + 5) + 4 • 13 – 2 = 62

Hence, the solution to the expression (7 + 5) + 4 • 13 – 2 is 62

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Answer:

see below

Step-by-step explanation:

Angles opposite each other when two lines cross. (see attached)

in the attached example, the angle a° and b° are vertical angles.

Step-by-step explanation:

\(

\underline{\bf{Given\::}}

Given:

\underline{\bf{To\:find\::}}

Tofind:

\underline{\bf{Explanation\::}}

Explanation:

\boxed{\bf{\frac{1}{f} =\frac{1}{v} -\frac{1}{u} }}}}

\begin{gathered}\longrightarrow\sf{\dfrac{1}{-10} =\dfrac{1}{v} -\dfrac{1}{-30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-10} +\dfrac{1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{-3+1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\cancel{\dfrac{-2}{30} }}\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-15} }\\\\\\\longrightarrow\sf{v=-15\:cm}\end{gathered}

⟶

−10

1

=

v

1

−

−30

1

⟶

v

1

=

−10

1

+

30

1

⟶

v

1

=

30

−3+1

⟶

v

1

=

30

−2

⟶

v

1

=

−15

1

⟶v=−15cm

\boxed{\bf{M \:A \:G \:N\: I \:F \:I \:C\: A\: T \:I \:O\: N :}}

MAGNIFICATION:

\begin{gathered}\mapsto\sf{m=\dfrac{Height\:of\:image\:(I)}{Height\:of\:object\:(O)} =\dfrac{Distance\:of\:image}{Distance\:of\:object} =\dfrac{v}{u} }\\\\\\\mapsto\sf{m=\cancel{\dfrac{-30}{-15}} }\\\\\\\mapsto\bf{m=2\:cm}\end{gathered}

↦m=

Heightofobject(O)

Heightofimage(I)

=

Distanceofobject

Distanceofimage

=

u

v

↦m=

−15

−30

↦m=2cm

Thus;

The magnification will be 2 cm .

\)

To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.

In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.

If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.

On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.

Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.

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Answer:

184

Step-by-step explanation:

Answer:

E. - 11

Step-by-step explanation:

This is by the simple quantum physics moving by the gravitational carbon dioxide in the air that causes the numbers to evolve into the number 11 while mixed together

One liter of the lotion contains 23 milligrams of the active ingredient.

If the active ingredient in a lotion uses the Strength 23 ppm (parts per million)

Definition of PPM ?

The best approach to describe the degree of performance or chemical concentration in a larger combination is in parts per million, or PPM. This could be used to describe the components of water, the faulty rate of a provider, etc. Being a ratio of two quantities of the same unit, it is theoretically a dimensionless measure that is represented as a percentage and is better suited to representing lesser concentrations of chemicals in gases, liquids, or solids. In its entire form, one part per million (ppm) is written as equation ppm=1/1,000,000=0.0001 /eq% of the whole.

1gm = 1000 mg

1 litre = 1000 ml

So that

1 ppm = 1 mg per liter

1 ppm = 0.998

23 ppm = 23 x 0.998

23 ppm = 22.958 mg / L

It is approximately equal to 23 mg / L

Round off to the nearest whole no 23 p pm = 23 mg / L

Therefore, 23 mg of active ingredient are in 1 liter of the lotion

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Therefore, the zeros of the function f(x) are x = 5 and x = -4.

A polynomial is a mathematical expression consisting of variables and coefficients, combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. It can have one or more terms, and the degree of a polynomial is the highest power of the variable in the expression.

Here,

To find the zeros of the function f(x) = x² - x - 20, we need to solve for x when f(x) = 0:

x² - x - 20 = 0

We can factor the left side of this equation as:

(x - 5)(x + 4) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x:

x - 5 = 0 or x + 4 = 0

Solving for x in each equation gives us:

x = 5 or x = -4

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If the DSM changes to a dimensional approach for diagnosing personality disorders in the future, clinicians will need to adapt their diagnostic practices by using a different framework that emphasizes the continuum of symptoms and traits, rather than categorical diagnoses.

If the DSM (Diagnostic and Statistical Manual of Mental Disorders) transitions to a dimensional approach for personality disorders, clinicians will need to adjust their diagnostic strategies accordingly. Currently, the DSM employs a categorical model, where individuals either meet the criteria for a specific disorder or they do not. However, a dimensional approach would shift the focus towards assessing the severity and variability of symptoms and traits across a spectrum.

To adapt to this change, clinicians will require training and education on the new dimensional framework. They will need to familiarize themselves with the new diagnostic criteria and learn how to assess and measure the various dimensions of personality functioning. This may involve using standardized assessment tools and scales that capture different facets of personality, such as neuroticism, extraversion, or conscientiousness.

Clinicians will also need to develop a nuanced understanding of how these dimensions interact with each other and with other mental health conditions. They will have to consider the interplay between different personality traits and how they contribute to the overall functioning and well-being of individuals. Additionally, treatment planning and interventions may need to be adjusted to align with the dimensional framework, focusing on addressing specific areas of impairment or dysfunction rather than solely targeting categorical diagnoses.

Overall, the shift to a dimensional approach in the DSM for personality disorders would require clinicians to adapt their diagnostic practices by embracing a more nuanced and comprehensive understanding of personality functioning. It would involve incorporating dimensional assessments, updating their knowledge base, and refining treatment approaches to better align with the new framework.

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Answer:

77

Step-by-step explanation:

3.5 ( 11 ) = 38.5

1.9 ( 11 ) = 20.9

1.6 ( 11 ) = 17.6

38.5 + 20.9 + 17.6

= 77

hope this helps