Use the given probability value to determine whether the sample results could easily occur by​ chance, then form a conclusion.
A study on the enhancing effect of coffee on​ long-term memory found that 35 participants given 200 mg of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine.
a. There was a probability of 0.049 that the difference between the coffee group and the placebo group was due to chance. What do you​ conclude?
b. A group given a higher dose of 300 mg performed better than the 200 mg​ group, with a probability of 0.75 that this difference is due to chance. What do you​ conclude?
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Part 1
a. The probability shows that the sample results
▼
could not
could
have easily occurred by chance. It appears that there
▼
is
is not
sufficient evidence to conclude that 200 mg of caffeine does have an effect on memory.

Step-by-step explanation:

volume = π · r^2 · h

volume = π · 3^2 · 5

volume = π · 9 · 5

volume = π · 45

Answer : 45π

Answer:

Step-by-step explanation:

Yes, the length and width dimensions of the two rectangular boxes are similar.

Two objects are considered similar if they have the same shape, but not necessarily the same size. The ratio of the corresponding sides of two similar objects is called the scale factor.

For the first rectangular box, the ratio of length to width is 10/8, which can be simplified to 5/4.

For the second rectangular box, the ratio of length to width is 15/12, which can be simplified to 5/4 as well.

Since the ratio of the corresponding sides of the two boxes is the same, namely 5/4, we can conclude that the length and width dimensions of the two rectangular boxes are similar.

We can state this by responding to the provided question Hence, the triangle longer limb is around 351.42 in length.

A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.

In a triangle with three legs measuring 30, 60, and 90, the shorter leg is half as long as the hypotenuse while the larger leg is sqrt3 times as long.

Let's name the larger leg's length "x" for simplicity. Thus, we are aware of:

The shorter leg measures 203 in length.

The hypotenuse measures 406 times the length of the shorter leg.

Using the proportion of the hypotenuse and leg lengths in a 30-60-90 triangle, we may find:

x = sqrt3 times ($) 203 = 351.42$

Hence, the longer limb is around 351.42 in length.

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The Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.

A trapezoid is a quadrilateral having two parallel bases and one set of other sides called legs.

To estimate the distance traveled by the Panther I, we need to approximate the area under the velocity curve between 0 and 25.7 seconds. We can divide the area into trapezoids using the data given in the table.

The first trapezoid has a height of 30 mph and a base of 1.8 seconds. The second trapezoid has a height of 40 mph and a base of 1.3 seconds (the difference between 3.1 and 1.8).

Continuing in this way, we get the following table:

Speed       Height

Range    (mph) Base (s)  Area (mph * s)

0-30  30           1.8               54

30-40 40           1.3               52

40-50 50           1.1            55

50-60 60           1.3              78

60-70 70           1.9            133

70-80 80           1.8             144

80-90 90            2.3            207

90-100 100           3.1            310

100-120 120          6.3            756

120-130 130           4.8            624

To find the total area, we add up the areas of all the trapezoids:

54 + 52 + 55 + 78 + 133 + 144 + 207 + 310 + 756 + 624 = 2413

Therefore, the Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.

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Answer:

1/9 and 1/2 one is greater then

Step-by-step explanation:

so if u look at it you will know that 1/2 is less then and 1/9 is greater then.

The time spent on country driving is 25/44 hour

From the question, we have the following parameters that can be used in our computation:

Total time = 3/4

City driving = 2/11

Given that 2/11 hour was spent on city driving, we can find the time spent on country driving as follows:

Time spent on country driving = Total driving time - Time spent on city driving

Time spent on country driving = 3/4 hour - 2/11 hour

So, we have

Time spent on country driving = 25/44

Hence, the time spent is 25/44

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Answer:

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

In this case, we have two similar regular hexagons. Let x be the side length of the smaller hexagon, and y be the side length of the larger hexagon. Then, we have:

Area of smaller hexagon / Area of larger hexagon = (x^2 * 6 * sqrt(3)) / (y^2 * 6 * sqrt(3)) = x^2 / y^2

We are given the areas of the two hexagons:

x^2 * 6 * sqrt(3) = 16 * sqrt(3)

y^2 * 6 * sqrt(3) = 25 * sqrt(3)

Dividing the second equation by the first equation, we get:

(y^2 * 6 * sqrt(3)) / (x^2 * 6 * sqrt(3)) = 25 * sqrt(3) / (16 * sqrt(3))

Simplifying this expression gives:

y^2 / x^2 = 25 / 16

Taking the square root of both sides, we get:

y / x = 5 / 4

Therefore, the scale factor from the smaller hexagon to the larger hexagon is 5/4.

The measure of side AC of the right triangle is 7.2 units.

The figure in the image is the of a right triangle.

To solve for the measure of side AC, we use trigonometric ratio.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Tangent = Opposite / Adjacent

tan( A ) = BC / AC

Plug in the values and solve for side AC.

tan( 51° ) = 8.9 / AC

AC = 8.9 / tan( 51° )

AC = 8.9 / 1.234897

AC = 7.2

Therefore, side AC has a value of 7.2 units.

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Answer:

-16

Step-by-step explanation:

The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:

28 men.

The number of men is obtained applying the proportions in the context of the problem.

The rule of three is given as follows:

n/48 = 8/6 x 7/16.

(the time is inverse proportional to the number of men, hence the fractions are inverted).

Thus:

n/48 = 56/96

Applying cross multiplication, the number of men is obtained as follows:

96n = 48 x 56

n = 48 x 56/96

n = 28 men.

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Answer:

The percent of Dan's average did he score during this game is 11.11%

What percent of Dan's average did he score during this game?

Dan's score in the high school basketball team during last game= 18 points

Dan's score in the high school basketball team during this season = 20 points

Percent of Dan's score during this game = (20 - 18) / 18 × 100

= 2/18 × 100

= 11.11%

In conclusion, Dan scored an average percentage of 11.11% during this game.

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According to the information we can infer that sentence is completed with the words mathematical procedure.

To complete the sentence we must identify the central idea and establish the right words to complete it. In this case, it is referring to a mathematical procedure then we could infer that these are the words that complete the sentence. Then the complete sentence would be like this:

Note: This question is incomplete. Here is the complete information:

Complementary information:

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The maximum height of the ball is given as follows:

92 feet.

The quadratic function modelling the height of the ball is given as follows:

h(t) = -16t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 75, h(0) = 4.

Hence the equation is:

h(t) = -16t² + 75t + 4.

The coefficients are given as follows:

a = -16, b = 75, c = 4.

As the quadratic equation is concave down, the maximum height is at the vertex.

The t-coordinate of the vertex is given as follows:

t = -b/2a

b = -75/-32

b = 2.34375s.

Hence the maximum height is of:

h(2.34375) = -16(2.34375)² + 75(2.34375) + 4.

h(2.34375) = 92 feet.

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The equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is option (B) [tex]6x^3z[/tex] . The expression [tex]\sqrt{36x^6z^2[/tex]  represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2.

What is square root ?

Square root is a mathematical operation that, when applied to a non-negative number, returns another non-negative number that, when multiplied by itself, gives the original number as a result.

The expression [tex]\sqrt{36x^6z^2[/tex]  represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2. To simplify this expression, we can use the following rules of exponents and radicals:

[tex]\sqrt{(a * b)} = \sqrt{a} *\sqrt{b[/tex]

[tex]\sqrt{(a^2)} = a[/tex]  for all non-negative values of a

Using these rules, we can write:

[tex]\sqrt{36x^6z^2 }= \sqrt{(36 * x^6 * z^2)[/tex]

[tex]= \sqrt{(6^2 * (x^3)^2 * z^2)[/tex] (grouping factors with perfect square roots)

[tex]= 6 * x^3 * z[/tex]  (simplifying the square root of the perfect square 6^2)

Therefore, the equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is [tex]6x^3z[/tex]. This means that the square root of [tex]36x^6z^2[/tex] is equal to 6 times the product of x raised to the power of 3 and z.

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9. The discriminant is 33. And the roots are real and distinct.

10. The discriminant is 4. And the roots are real and distinct.

11. The discriminant is -23. And the roots are imaginary roots.

12. The discriminant is -4. And the roots are imaginary roots.

What is the discriminant?

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

9. 2x² + 3x - 3 = 0, the discriminant is given as,

D = 3² - 4 × 2 × (-3)

D = 33

Roots are real and distinct.

10. 4x² - 6x + 2 = y, the discriminant is given as,

D = (-6)² - 4 × 4 × (2)

D = 4

Roots are real and distinct.

11. 0 = x² - 3x + 8, the discriminant is given as,

D = (-3)² - 4 × 1 × (8)

D = - 23

Roots are imaginary.

12. y = 5x² + 4x + 1​, the discriminant is given as,

D = (4)² - 4 × 5 × (1)

D = -4

Roots are imaginary.

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Answer:

67.97%

Step-by-step explanation:

Answer:

67.97%

Step-by-step explanation:

In the polynomial function given, the value of the limit as it approached infinity is 5/3

To evaluate this limit, we need to determine the behavior of the function as x approaches infinity. To do this, we can use the fact that for any polynomial p(x) and q(x) of the same degree, the limit of p(x)/q(x) as x approaches infinity is equal to the ratio of the leading coefficients.

In this case, both the numerator and denominator are polynomials of degree 2, so we can apply this property. The leading coefficient of the numerator is 6 and the leading coefficient of the denominator is 7. Therefore, the limit as x approaches infinity of the given expression is:

lim [ (6x² - 5) / (7x² + x - 3)]

x → ∞ = 5/3

Therefore, the limit of the given expression as x approaches infinity is equal to 5/3.

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The dot notation of the recurring decimal is 51.674674674674.....

Recurrent decimal, often known as recurring decimal, is a decimal number made up only of digits that repeat after the decimal at regular intervals. As an illustration, 46.374374374, 517.338383, etc. Depending on the sort of digits that follow the decimal point—whether they are recurring, non-repeating, ending, or unending—decimals can be divided into many groups (infinite digits after the decimal point).

Here the given recurring decimal is 51.674,

To write into dot notation , we need to write repeated numbers after digits. Then,

=> 51.674674674674....

Hence the dot notation of the recurring decimal is 51.674674674674.....

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Answer:

The answer you are looking for is 1.5x10^1 or 0.15

Step-by-step explanation:

To find the answer I used PEMDAS. (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction).

So I looked at the Parenthesis first, and then I looked for the exponents which were [tex]10^{-13}[/tex], also [tex]10^{11}[/tex].

When put in the calculator 0.0000000000001, and the second exponent was 100000000000.

Then having to multiply 0.0000000000001 by 6 gave me 0.00000000000006 and also multiplying 2.5 with 100000000000 gave me 250000000000.

Finally multiplying the final results with each other gave me 0.15 and in scientific notation, 1.5x10^1

I hope this was helpful!

The width of the canyon in the given image is 70 ft wide.

To find the width of the canyon, we can visually extend side DC and AE to form two sides of a rectangle.

Given that side DC is the same as side AE (80 ft), we can use this same reasoning to determine that the width is the sum of side AB and side BC, which is 35 + 35.

This gives us a width of 70 ft.

In a rectangle, the longer side is known as the length and the shorter side is known as the width.

Therefore, using the sum of side AB and side BC, we get a width of 70 ft for the canyon.

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It satisfies the vertical line test and represents a function.

What is function ?

Function can be defined in which it relates an input to output.

Based on the image you provided, it seems to represent a function since each input value (x-value) corresponds to a unique output value (y-value) and there is only one output value for each input value.

To verify if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. However, in this graph, for any vertical line drawn, it only intersects the graph at one point.

Hence, it satisfies the vertical line test and represents a function.

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Answer:

[tex]y = 4d + 8\\[/tex]

Step-by-step explanation:

Since d is the number of large drinks, and there is always a constant of 1 large popcorn, we go to (0, 8). This concludes that since we start off with the cost of 8 dollars with no large drink but a large popcorn, the popcorn will stay a constant cost of $8. (the equation for this scenario is as shown):

y = md + 8

y (total cost)

m (coefficient - in this sense the cost of the drinks.)

d (amount of drinks)

8 (the constant of 8 represents the cost of one large popcorn consistently)

Now, lets find the cost of the dink.

Go to (1, 12).

$12 dollars is the total cost, with one drink and one large popcorn bought.

We have already discussed that we will have a constant of 8 because no matter the amount of drinks we will get, we would have bought 1 large popcorn at $8.

Therefore, we must subtract 8 dollars from 12.

12 - 8 = 4

From the total cost of everything we bought (2 things) and subtracting it with the cost one of the things we bought, we get the cost of the other thing.

each drink will cost $4.

Therefore, with all the variables and their listed meanings, this will be our given equation:

y = 4d + 8

Answer:

Its answer number 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\tt y+4+3\left(y+2\right)[/tex]

Expand by distributing terms:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\boxed{\tt y+3y}+\boxed{\tt 4+6}[/tex]

[tex]\tt y+3y=\underline{\bf 4y}[/tex]

[tex]\tt 4+6=\underline{\bf 10}[/tex]

⇒ [tex]\underline{\bf 4y+10}[/tex]

Therefore, A. 4y + 10 is our answer!

_______________________

Hope this helps! :)

Answer:

4y+10

Step-by-step explanation:

у + 4 + 3(y + 2) =

y + 4 + 3y + 6

y + 10 + 3y

4y +10

Answer:

x - 5

Step-by-step explanation:

Okay to write this problem as an expression it would be x -5. x represents James and -5 represents less than.

Answer:

x-5

Step-by-step explanation:

we don't know how much James has but we know it is $5 less so what ever the original amount is we are putting as x for now and we will subtract 5 because it is $5 less making our x-5.

The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

Using the formula obtained from Pythagoras' theorem, distance can be computed.

The distance formula in coordinate geometry is:

(P, Q) = √ (x2 – x1)² + (y2 – y1)².

Given points: (5, 4) and (−3, −1)

d = √ (-3 - 5)² + (4 + 1)²

d = √ 64 + 25

d = √ 89

d = 9.43

Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

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a. A ⋁ G: Elvis is alive or Elvis gained weight.

b. ~(A ⋀ G): Elvis is not both alive and gained weight.

c. G → ~A: If Elvis gained weight, then Elvis is not alive.

d. A ↔ ~G: Elvis is alive if and only if Elvis did not gain weight.

According to the Cartesian plane graph, it can be inferred that the circle was rotated and translated (option B).

To identify the movements that were made to circle 1 to become 2 we must carefully observe the graph. Once we have analyzed this graph we can infer the movements that were made to the circle. In this case, the rotation was performed because it can be seen that it was rotated having the coordinate (-1.5, 0.5) as a reference or point of rotation.

However, it was also translated because it was shifted a bit down and to the left. So the correct answer would be option B.

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Answer: rotation and translation

Step-by-step explanation: I took the quiz