You are designing a container in the shape of a cylinder. The radius is 5 inches. You want the container to hold at least 725π cubic inches. What is the least possible height of the container?

Answer:

2.4

Step-by-step explanation:

10% of 24

Make the 10% a decimal.

0.10

Multiplication!!!

0.10×24

0.10×24=2.4

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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We will have the following:

So, she will have 4 & 1/2 cups.

answer is g(x)=|x+2|-1

\(answer \\ g(x) = - |x + 2| - 1\\ as \: we \: can \: see \: from \: the \: given \: graph \\ above \: that \: the \: graph \: of \: absolute \\ function \: has \: been \: reflected \: over \: the \\ x \: axis \: \: shifted \: 2 \: units \: left \: and \: 1 \: \\ units \: down. \\ due \: to \: reflection \: there \: is \: a \: negative \\ sign \: shift \: of \: 2 \: units \: left \: is \: given \\ by \: x + 2 \: and \: 1 \: units \: down \: is \: given \\ by \: - 1 \\ hope \: it \: helps\)

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

=1/15

Step-by-step explanation:

The value of x is 30° as per below diagram.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

We know that,

Draw a line segment BG is with CBG equal to 20° on line CE.

So that, (40 + x)  = 70, so that means x = 30°

Therefore, The value of x is 30°

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Complete question here-

Triangle: According to the question the value of x is 30° as per below diagram.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

We know that,
All the angles in a triangle sum → 180°
An isosceles triangle: two equal angles → two equal sides.
Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x)  = 70, so that means x = 30°
Therefore, The value of x is 30°

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Complete question:

Answer:

3,3/2

Step-by-step explanation:

let 10,-6 be x1, y1

-4,-9 be x2, y2

(x1+x2)/2 , (y1+y2)/2

(10-4)/2 , (-6+9)/2

6/2 , 3/2

3 , 3/2

Answer:

(3, -7.5)

Step-by-step explanation:

Use the midpoint formula: (x1 + x2) / 2 , (y1 + y2) / 2

Plug in the points:

(10 - 4) / 2 , (-6 - 9) / 2

6/2 , -15/2

3, -7.5

So, the midpoint will be at (3, -7.5)

Add 7 to both sides.

Add −4 and 7 to get 3.

Multiply both sides by 3, the reciprocal of 1/3 . Since 1/3 is >0, the direction of inequality remains the same.

Multiply 3 and 3 to get 9.

Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

Answer:

y = 1/2x + 3

Step-by-step explanation:

anUm, y = mx + b format. M would be the slope, b is the y intercept. and obviosuly x and y are the x and y components :D

y=mx+b where m is the slope and b is the y intercept, m=1/2 and b=3

y=x/2+3 or more neatly

y=(x+6)/2

Answer:

1 penny

Step-by-step explanation:

It would take 1 penny. A penny is taller than 1 centimeter anyway.

The expression of the length of the arc is  4πb⁵

The circle has a radius of 9b³. An arc subtend an angle at the centre of 80b² degrees. Therefore, the expression for the length of the arc can be solved as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 80b² / 360 × 2 × π × 9b³

length of arc = 144b⁵π / 36

Therefore,

length of arc = 4πb⁵

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The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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This is about hypothesis testing. The various steps required to determine whether elderly dementia patients really do take longer to fall asleep than average are given below.

The stages involved in testing a hypothesis are as follows:

1) First, state your hypotheses.

Elderly dementia sufferers fall asleep in the same length of time as the ordinary person (H0) (μ = 7)

An alternative hypothesis (Ha) is that elderly dementia patients sleep more slowly than the general population (μ  > 7)

2) Determine the degree of importance in step two.

The problem does not specify the degree of relevance (α). Assume that α = 0.05.

3) Calculate the test statistic in step three.

To compare the sample mean to the population mean, we may use a one-sample t-test. The t-test formula is as follows:

t = (x - μ) / (s / √n)

where:

x = sample  mean (7.2)

μ  = population mean  (7)

s =  sample standard  deviation (1.1)

n = sample  size  (8)

Plugging in the values,  we obtain the folowing:

t = (7.2  - 7) / (1.1 / √ 8) = 1.62

4) Determine the crucial value in step four.

We must use the t-distribution to ascertain the critical value because this is a one-tailed test with a sample size of fewer than 30, and the population standard deviation is unknown. n - 1 equals 7 degrees of freedom.

The crucial value is 1.895 when using a t-table with 7 degrees of freedom and a one-tailed test with = 0.05.

Step 5: Make a choice and analyze the outcomes

We are unable to reject the null hypothesis since the computed t-value (1.62) is lower than the critical value (1.895).


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Answer:

y = ⁷/5x + 34/5

Or

y = 1.4x + 6.8

Step-by-step explanation:

To find the equation of the line in the slope-intercept form, y = mx + b, we have to determine the value of:

Slope (m) = change in y/change in x

y-intercept (b) = the y-coordinate of the point where the y-axis is intercepted by the line

Using the two points indicated in the line, (-7, -3) and (-2, 4),

Slope (m) = (4 - (-3))/(-2 - (-7)) = 7/5

m = ⁷/5

To find b, substitute m = ⁷/5 and (x, y) = (-2, 4) into y = mx + b

4 = ⁷/5(-2) + b

4 = -14/5 + b

4 + 14/5 = b

(20 + 14)/5 = b

34/5 = b

b = 34/5

To write the equation, substitute m = ⁷/5 and b = 34/5 into y = mx + b

y = ⁷/5x + 34/5

Or

y = 1.4x + 6.8

Answer:

3/18

Step-by-step explanation:

Answer:

vertex= (0,-4), Axis of symmetry - x= 0,

sorry I don't know the rest and I don't know  if this is even know if this is correct, so good luck I hope someone else can.

Step-by-step explanation:

The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

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Answer: 9 × 4

              9 × 5

              9(4 + 5)

Step-by-step explanation:

36 = 9 × 4

45 = 9 × 5

so, GCF is 9.

36 + 45 = 81

= 9(4 + 5)

= (9 × 4) + (9 × 5)

= 36 + 45

= 81

ALTERNATELY :

36 + 45 = 81

= 9(4 + 5)

= 9 × 9

= 81

Two reasons for the use of measurement tools are:

1. Using reliable and valid measurement tools ensures that the data collected is accurate and trustworthy, providing the researcher with more confidence in their conclusions.

2. Using reliable and valid tools reduces the amount of time needed to develop a new measurement tool, as the researcher can simply adapt an existing tool to meet their research needs. This allows the researcher to focus more of their effort on the other aspects of the project.

1. Using reliable and valid tools can help the researcher reduce the likelihood of bias in their results, as the tools have already been shown to be free of any potential bias. This helps to ensure that the results of the study are as objective as possible.

2. Using reliable and valid tools can also help to minimize the potential for errors and misinterpretation of data, as the tools are already proven to be valid and reliable. This helps to ensure that the results are as accurate as possible.

3. Finally, using reliable and valid tools can help to reduce the amount of effort and resources needed for data collection, as the researcher does not have to spend time and energy developing their own measurement tools. This can help to save time and money in the long run.

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Answer:

\(17/2\)

Step-by-step explanation:

I don't know what the column method is, but I can give you another method of solving.

We know that \(1.5=1~1/2=3/2\), so we really want to find \(10-3/2\).

We know that \(20\) divided by \(2\) is \(10\), so we really want to find \(20/2-3/2\).

We can combine fractions with like denominators, so we really want to find \((20-3)/2\).

We know that \(20-3\) is \(17\), so we really want \(17/2\). We can't simplify \(17/2\) anymore.

So, the answer is \(\boxed{17/2}\) and we're done!

Answer:hbwufvj6y

Step-by-step explanation:

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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Answer:

2y-6

Step-by-step explanation:

(y-3)2=2y-6

The mathematical expression for twice the difference of y and 3 is 2(y - 3); the answer is 2(y - 3).

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete:

The complete question is:

Write the mathematical expression for "Twice the difference of y and 3"

It is given that:

Twice the difference of y and 3

The number is y:

The difference between y and 3:

= (y - 3)

Twice the above number:

= 2(y - 3)

The above expression representing a linear expression; If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.

Thus, the mathematical expression for twice the difference of y and 3 is 2(y - 3); the answer is 2(y - 3).

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The solution to the quadratic equation is given as follows: \(q = -\frac{1}{3}\)

A quadratic function is given according to the following rule:

\(y = ax^2 + bx + c\)

The solutions are:

In which:

\(\Delta = b^2 - 4ac\)

In this problem, the equation is:

9q² + 6q + 1.

The coefficients are a = 9,b = 6, c = 1, hence:

\(\Delta = 6^2 - 4(9)(1) = 0\)

\(q_1 = \frac{-6 + \sqrt{0}}{2(9)} = -\frac{1}{3}\)

\(q_2 = \frac{-6 - \sqrt{0}}{2(9)} = -\frac{1}{3}\)

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