The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.

The probability that the sample mean would be less than 40.6 dollars will be 0.534.

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is given as

z = (x – μ) / σ

The mean cost of a five pound bag of shrimp is 40 dollars, with a standard deviation of 7 dollars.

If a sample of 51 bags of shrimp is randomly selected.

Then the probability that the sample mean would be less than 40.6 dollars will be

z = (40.6 – 40) / 7

z = 0.0857

Then the p-value will be

P(x < 40.6) = P(z < 0.0857)

P(x < 40.6) = 0.534

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Answer:

1/2 cup of chocolate chips

Step-by-step explanation:

Given ratio:

Let x be the unknown amount of chocolate chips:

[tex]\implies \sf \dfrac{1}{3}:2=x:3[/tex]

[tex]\implies \sf \dfrac{\frac{1}{3}}{2}=\dfrac{x}{3}[/tex]

Cross multiply:

[tex]\implies \sf 3 \cdot \dfrac{1}{3}=2 \cdot x[/tex]

[tex]\implies \sf 1=2x[/tex]

[tex]\implies \sf x=\dfrac{1}{2}[/tex]

Therefore, 1/2 a cup of chocolate chips will be needed for 3 cups of flour.

Let that be x

Answer:

Step-by-step explanation:

[tex]x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}[/tex]

The angle θ to the diameter that she should row is; θ = 56.44°

It should be noted that;

a = 90° - θ. Thus;

b = 2θ

For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .

The time required to walk this distance is given by;

t_w = 4θ/5 = 0.8θ

The distance rowed is given by: cos θ = d_r/2.4

d_r = 2.4cos θ while the time needed for it is;

t_r = 2.4cos θ/3.5

t_r = 0.6857θ

Thus, total time is;

T(θ) = t_r + t_w

T(θ) = 0.6857θ + 0.8θ

T(θ) = 1.4857θ

Now we need the critical numbers:

T'(θ) = 1 - 1.2 sin θ

At T'(θ) = 0, we have;

1 - 1.2 sin θ = 0

1/1.2 = sin θ

θ = sin⁻¹(1/1.2)

θ = 56.44°

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Answer:

yes

Step-by-step explanation:

the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.

the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).

so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.

but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.

there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).

but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.

The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

The function is given as:

[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]

To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5

At this domain;

g(x) = -1

So, the value of g(-0.5) is

g(-0.5) = -1

To calculate g(0.3), we make use of the domain -0.5 < x  0.5

At this domain;

g(x) = 0

So, the value of g(0.3) is

g(0.3) = 0

To calculate g(0.5), we make use of the domain 0.5 ≤ x  1.5

At this domain;

g(x) = 1

So, the value of g(0.5) is

g(0.5) = 1

Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

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Answer:

11. always

12. always

13. always

14. never

15. never

16. always

17. always

18. sometimes

19. sometimes

20. never

Step-by-step explanation:

11. A line can be defined by at least two points

12. A plane can be defined by at least three points

13. If two planes intersect, then they form a line at the intersection.

14. If two lines intersect, then they form a point at the intersection (not a segment).

15. A line does not have any endpoints (infinite in both ways).

16. If two planes are not parallel they will always intersect.

17. If two lines are not parallel they will always intersect.

18. Two points are sometimes collinear. It depends on where they are.

19. Two points are sometimes coplanar. It depends on where they are.

20. Ray MN and NM are not the same ray because the end points are different.

Answer:

  no

Step-by-step explanation:

In order for one number (A) to be a factor of another (B), the exponents of the primes in the prime factorization of A cannot exceed those of the prime factorization of B.

__

  A = 2^14 × 3^20

  B = 2^12 × 3^22

The exponent of the factor 2 in A is 14, which exceeds the exponent of the factor 2 in B (12). Therefore, A cannot be a factor of B.

  (3^20)(2^14) is not a factor of (3^22)(2^12)

0.66 inches of material is needed to be cut off to make the volume maximum.

When the second derivative of a function is negative, the function has a maximum point and if the second derivative is positive, the function has a minimum point.

Analysis:

After cut and folded, length = 8-2x

Width = 3-2x

Thickness = x.

Volume of the folded shape = (8-2x)(3-2x)(x)

After expansion, V = 4[tex]x^{3}[/tex]-[tex]22x^{2}[/tex] +24x

for turning point of the function, dv/dx = 0

dv/dx = 12[tex]x^{2}[/tex] -44x + 24

lowest term = 3[tex]x^{2}[/tex] - 11x + 6

3[tex]x^{2}[/tex] - 11x + 6 = 0

3[tex]x^{2}[/tex] - 9x -2x +6 = 0

3x(x-3) -2(x-3) = 0

(3x-2)(x-3) = 0

x = 2/3 or x = 3

To test for maximum point, we differentiate dv/dx again

we have 6x - 11

for x = 3,  6(3) - 11 = 18 - 11 = 7 which is positive x= 3 is a minimum

for x = 2/3 6(2/3) - 11 = 4 - 11 = -7, x = 2/3 is a maximum.

Therefore for maximum volume, the length to be cut out is 2/3 which is 0.66 inches.

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Answer:

[tex] \boxed{f(6) =2 4}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = x² - 2x[/tex]

Solution:

ATP,it is that x = 6. So substitute 6 on the function.

[tex]f(6) = 6 {}^{2} - 2(6)[/tex]

Simplifying using PEMDAS,we obtain:

[tex]f(6) = 6 \times 6- 12[/tex]

[tex]f(6) = 36 - 12[/tex]

[tex] \boxed{f(6) =2 4}[/tex]

Hence,f(6) = 24.

Here, the surface area, in square units, of the triangular prism is 152 units².

We know that the area of any triangle can be calculated as

Area = 1/2 * base * height

The area of any rectangular figure can be calculated as

Area = length * width

Here, the length of the rectangular portion of the prism is 8 units.

The width of the lowermost rectangle is 5 units.

The area of the uppermost rectangle = the area of the lowermost rectangle = 8 * 5 units² = 40 units²

Again the width of the middle rectangle is 6 units.

So, the area of the middle rectangle = 6 * 8 units² = 48 units²

Now, the height and base of the triangles are 4 and 6 respectively.

So, the area of the left-hand side triangle = the area of the right-hand side triangle = 2 * (1/2) * 4 * (6/2) units² = 1 * 4 * 3 units² = 12 units²

Then the area of the triangular prism = area of rectangular portion + area of triangular portion = (2 * 40 + 48) + (2 * 12) units² = (80 + 48) + 24 units² = 128 + 24 units² = 152 units²

Therefore the surface area, in square units, of the triangular prism is 152 units². So, Option C is correct.

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2x + 9 = 5x - 12

2x - 5x = - 1- 9

- 3x = - 21

x = 21/3

x = 7

Y = 60°

Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)

Step-by-step explanation:

Reflecting over y = x maps (x,y) onto (y,x).

The fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Fractions that are between 12/13 and 19/20 such that:

The numerator(N) is one less than the denominator(D).

N =  D - 1

N = (12, 19)

D = (13, 20)

D = 14, N = 13

D = 15, N = 14

D = 16, N = 15

D = 17, N = 16

D = 18, N = 17

D = 19, N = 18

The fractions that are between 12/13 and 19/20:

N/D = {13/14, 14/15, 15/16, 16/17, 17/18, 18/19}

Thus, the fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6

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Answer:

(-2, 1)

Step-by-step explanation:

You can read the solution from graph. The solution is where the two lines intersect. That happens in point (-2, 1).

---

Alternative:

If you want to be sure, you can alway double check by solving the system of equations.

First equation: [tex]y = \frac{1}{2}x + 2[/tex]

Second equation: [tex]y = -\frac{1}{2}x[/tex]

Substituting y in first equation with y from second.

[tex]y = \frac{1}{2}x + 2[/tex]

[tex]-\frac{1}{2}x = \frac{1}{2}x + 2[/tex]

Adding [tex]\frac{1}{2}x[/tex] on both sides.

[tex]-\frac{1}{2}x + \frac{1}{2}x = \frac{1}{2}x + 2 + \frac{1}{2}x[/tex]

[tex]0 = 1x + 2[/tex]

[tex]0 = x + 2[/tex]

[tex]-2 = x[/tex]

Substituting x with -2.

[tex]y = -\frac{1}{2}x[/tex]

[tex]y = -\frac{1}{2}(-2)[/tex]

[tex]y = 1[/tex]

As you see you get the same result as from reading the graph, (-2, 1).

Here....

The length is given 15 feet and the width is 12 feet...Now let's find the Perimeter..

Perimeter = 2 ( l + b )

= 2 ( 15 + 12 )

= 2 × 27

= 54 feet

[tex]...[/tex]

:)...

Answer:

See below

Step-by-step explanation:

129 500     original price

selling price =   2 ( 129 500) - 9000 = 250 000

% change   Questions worded like this are often up for debate as to exactly answer the question

250 000 / 129 500 =  193 %      Selling price was 193% of original price

(250 000 - 129500)/ 129500 =   93 % INCREASE

The graph is attached and all the sub parts have been answered.

A function is  away of relating a dependent variable to an independent variable .

It is given that

Current weight of Rex at 2 months =6 pounds

Let x represents the age in months of Rex

then a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. is

Let y be the current weight of Rex

then

y = 6 + 9(x -2)

The table  that represents Rex’s current weight, in pounds, as a function of his age, in months

2              6

3              15              

4              24

5              33

6              42

7              51

8              59

The graph is plotted for the given data and attached .

If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old

6 + 9*(12-2)

96 pounds.

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A formula is a fact or rule that uses mathematical symbols. It will usually have: an equals sign (=) two or more variables (x, y, etc) that stand in for values we don't know yet.

Example: The formula for finding the volume of a box is:

x = 2y - 7 Formula (relating x and y)

a2 + b2 = c2 Formula (relating a, b and c)

Answer:

300 cupcakes

Step-by-step explanation:

[tex]27 = .09c[/tex]

[tex]c = \frac{27}{.09} = \frac{2700}{9} = 300[/tex]

In total, the bakery sold 300 cupcakes on a certain day.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of cupcakes sold that day.

let, 'x' be the total number of cupcakes sold that day.

Therefore, 9% of 'x' is 27 which is,

(9/100)×x = 27.

0.09x = 27.

x = 27/0.09.

x = 300.

So, The number of cupcakes sold that day is 300.

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Answer: 7

Step-by-step explanation:

As tangents drawn from a common external point to a circle are congruent,

Answer:

Step-by-step explanation:

Answer:

0

Step-by-step explanation:0 times anything is still 0

The equation for the red graph is f(x)=-x^2.

The question is an incomplete graph of a function is missing

For a complete question refer to the graph attached below

we have [tex]g(x)=4-x^2[/tex]

The vertex of the function g(x) is the point (0,4)

The vertex of the function f(x) is the point (0,0)

This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.

So, the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

The translation is 4 units down

The equation of the function f(x) is

[tex]f(x)=g(x)-4[/tex]

[tex]f(x)=(4-x^2)-4[/tex]

[tex]f(x)=-x^2[/tex]

Therefore, The answer is f(x)=-x^2

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Answer:

=8x+14 or

=16x²+56x+49

[tex]\bf{(4x+7)2 }[/tex]

[tex]\bf{=2(4x+7)}[/tex]

[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]

[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]

[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]

Answer: SAS

Step-by-step explanation:

Since [tex]\frac{BC}{CD}=\frac{AC}{CE}=\frac{1}{2}[/tex], and [tex]\angle ACB \cong \angle DCE[/tex] because they are vertical angles, the triangles are similar by SAS

The value of this irrational Expression is 40.77 .

An expression is a mathematical statement consisting of variables , constants and mathematical operators.

The expression given is

7√22 +3√7

√22 = 4.69

√7 = 2.65

32.83 + 7.94

40.77

The value of this irrational Expression is 40.77 .

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The graph is shown in the attached image.