Volume of Cylinders, Cones, and Spheres

1
2
The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?
○ 3² cm³
π
O 87 cm³
○ 64 cm³
O 167 cm³

The fraction to the garden that would probably remain for his other crops would be = 5/24

The portion of the garden in which potatoes are being planted = 2/3

The portion of the garden in which carrots are being planted = 1/8

Therefore,the fraction of the garden that is left without plants = X

But;

The whole garden is represented as 1.

That is;

1 = 2/3+1/8 +X

Make X the subject of formula;

X = 1 - (⅔+⅛)

X = 1-(19/24)

X = 1-19/24

X= 5/24.

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The mean of the measurements is 23.3 g.
The standard deviation of the measurements is 0.65 g.

The range of the measurements is 1.9 g

The percent relative standard deviation of the measurements is 2.77%.

What is the mean, range, standard deviation, percent relative standard deviation?

Mean: The mean is the average of all the measurements. To find the mean, add up all the measurements and divide by the number of measurements:

(23.4 + 23.9 + 22.6 + 24.5 + 23.0 + 23.6) / 6 = 23.3

So, the mean of the measurements is 23.3 g.

Range: The range is the difference between the largest and smallest measurements. To find the range, subtract the smallest measurement from the largest measurement:

24.5 g - 22.6 g = 1.9 g

So, the range of the measurements is 1.9 g.

Standard Deviation: The standard deviation is a measure of the spread of the data around the mean. To find the standard deviation, we first calculate the difference between each measurement and the mean, square each difference, and then average the squared differences. The square root of this average gives us the standard deviation.

(23.4 - 23.3)^2 + (23.9 - 23.3)^2 + (22.6 - 23.3)^2 + (24.5 - 23.3)^2 + (23.0 - 23.3)^2 + (23.6 - 23.3)^2 = 0.09 + 0.16 + 0.49 + 1.16 + 0.09 + 0.16 = 2.55

2.55 / 6 = 0.425

√0.425 = 0.65

So, the standard deviation of the measurements is 0.65 g.

Percent Relative Standard Deviation (RSD): The percent RSD is the standard deviation expressed as a percentage of the mean. To find the percent RSD, divide the standard deviation by the mean and multiply by 100:

0.65 g / 23.3 g * 100 = 2.77%

So, the percent relative standard deviation of the measurements is 2.77%.

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The expression which is equivalent to (p - q)(x) is (x²-1) - 5(x-1) .

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

Since  p(x) = x² - 1 and g(x) = 5(x-1)

(p - q)(x) can be found by subtracting g(x) = 5(x-1) from p(x) = x² - 1. That is:

(p - q)(x) = (x²-1) - 5(x-1)

Thus,  (x²-1) - 5(x-1) is equivalent to (p - q)(x).

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The discriminant is -2n - 24.

The equation has 2 real solutions.

The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula b^2 - 4ac.

So, for the equation -3n^2 - 2n - 6 = 0, a = -3, b = -2, and c = -6.

Plugging these values into the formula, we get:

(-2)^2 - 4 * -3 * -6 = 4 + 72 = 76

So the discriminant is 76, which is greater than zero, so the equation has 2 real solutions.

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Answer:

The integrating factor, u(t), for the initial value problem t* dy/dt+3y=8t with y(1)=8 is u(t) = e^(3t). The solution to this equation is y(t) = 8e^(-3t)+2te^(-3t).

Step-by-step explanation:

The integrating factor, u(t), for the given initial value problem t(dy/dt)+4y=3t with y(1)=8 is u(t) = e^(4∫t dt) = e^(2t^2).

Using this integrating factor, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)+Ce^(-2t^2), where C is a constant of integration. Since y(1)=8, we can solve for C and find that C=-7/4. Therefore, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)-7/4e^(-2t^2).

We are asked the solve the following differential equation, [tex]t\frac{dy}{dt}+3y=8t[/tex].  This is an ordinary, linear, first-order DE. We need it in the form [tex]\frac{dy}{dt}+P(t)y=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex], which is the integrating factor.

[tex]\Longrightarrow t\frac{dy}{dt}+3y=8t[/tex], multiply everything by t.

[tex]\Longrightarrow \frac{dy}{dt}+(\frac{3}{t} )y=8[/tex]

We now have the correct form for solving a linear, first-order DE.

Find [tex]\mu(t)[/tex].

[tex]\Longrightarrow \mu(t)=e^{\int\ {P(t)} \, dt } \Longrightarrow \mu(t)=e^{\int\ {\frac{3}{t} } \, dt }[/tex]

[tex]\Longrightarrow \mu(t)=e^{3\int\ {\frac{1}{t} } \, dt }\Longrightarrow \mu(t)=e^{3ln|t|} \Longrightarrow \mu(t)=e^{ln(t^3)}[/tex]

[tex]\Longrightarrow \mu(t)=t^3[/tex]

Now multiply the entire DE by [tex]\mu(t)[/tex].

[tex]\Longrightarrow t^3[\frac{dy}{dt}+(\frac{3}{t} )y=8][/tex]

[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(t^3)(\frac{3}{t} )y=(t^3)8[/tex]

[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(3t^2)y=(t^3)8[/tex]

Verify that the L.H.S is a product rule of [tex]t^3y[/tex].

Product rule: [tex]\frac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)[/tex]

[tex]\frac{d}{dt}[t^3y]=(t^3)(\frac{dy}{dt} )+(3t^2)(y)[/tex]

It is the product rule, so we can move forward by integrating both sides of the DE.

[tex]\Longrightarrow \int\ {[t^3y]'} \, =\int\ {8t^3} \, dt[/tex]

[tex]\Longrightarrow t^3y=2t^4+C[/tex]

Now using the initial condition to find the arbitrary constant, C.

[tex]t^3y=2t^4+C ;y(1)=8[/tex]

[tex]\Longrightarrow (1)^3(8)=2(1)^4+C[/tex]

[tex]\Longrightarrow 8=2+C[/tex]

[tex]\Longrightarrow 6=C \Longrightarrow C=6[/tex]

Now we have, [tex]t^3y=2t^4+6[/tex], solve for y.

[tex]\Longrightarrow t^3y=2t^4+6[/tex]

[tex]\Longrightarrow y=2\frac{t^4}{t^3} +\frac{6}{t^3}[/tex]

[tex]\Longrightarrow y=2t +6t^{-3}[/tex]

Thus the given differential equation with the initial condition is solved, [tex]y=2t +6t^{-3}[/tex].

Due to length restrictions, we kindly invite to read the explanation below to know how the graph of the quartic function is made. Here is a summary:

Zeros: x = - 0.732, x = 0, x = 1, x = 2.732

Critical values: x = - 0.432 (minimum), x = 0.541 (maximum), x = 2.141 (minimum)

Increasing: - 0.432 < x < 0.541 and x > 2.141

Decreasing: x < - 0.432 and 0.541 < x < 2.141

Herein we find the definition of a quartic function, that is, a polynomial with grade 4, of which we must sketch its graph. This can be done from the understanding of the following information:

Zeros

Let be equal the polynomial to zero. All roots can be found by means of numerical methods:

x⁴ - 3 · x³ + 2 · x = 0

x = - 0.732 or x = 0 or x = 1 or x = 2.732

Critical values

Determine the first derivative, equal it to zero and find the roots of the expression:

4 · x³ - 9 · x² + 2 = 0

x = - 0.432 or x = 0.541 or x = 2.141

Determine the second derivative and evaluate it at each root found in previous step:

f''(x) = 12 · x² - 18 · x + 2

x = - 0.432

f''(- 0.432) = 12.015 (MINIMUM)

x = 0.541

f''(0.541) = - 4.226 (MAXIMUM)

x = 2.141

f''(2.141) = 18.469 (MINIMUM)

Finally, find the coordinates of the quartic function:

f(- 0.432) = - 0.587

f(0.541) = 0.693

f(2.141) = - 4.148

Interval behavior

Use the first derivative find the roots of the following inequalities:

Increasing

4 · x³ - 9 · x² + 2 > 0

- 0.432 < x < 0.541 and x > 2.141

Decreasing

4 · x³ - 9 · x² + 2 < 0

x < - 0.432 and 0.541 < x < 2.141

Finally, we build the sketch with the help of a graphing tool.

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The value of {b} is equivalent to 4.

Given is to find the value of {b}.

The function is not given. Assume that the function is -

y = ρx + b

For the point (0, 4), we can write -

4 = ρ x 0 + b

b = 4

Therefore, the value of {b} is equivalent to 4.

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Westside Carpet charges more per square foot for the carpet

Since the Carpet City charges $5 per square foot for a type of carpet. They charge an additional $95 for installation.

we can write the linear function for Carpet City charges as:

y = 5x + 95

where x is the number of square foot

From the table:

rate for Westside Carpet = 3250/642 = $5.06 per carpet

The the linear function for Westside Carpet is y = 5.06x

Thus, Westside Carpet charges more because 5.06 is greater than 5.

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Answer: Sandra bought 4 pounds of sweet potatoes for $6.40. What is the cost per pound of the sweet potatoes?

$1.57

Step-by-step explanation: pls give brainiest

Answer:

The answer to your question is $1.57.

Step-by-step explanation:

To find the cost per pound of sweet potatoes, divide $6.28 by 4.

6.28 ÷ 4= $1.57

I hope this helps and have a wonderful day!

Yes, the given input and output values represent a function, f(x) = x²

What are functions?

In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.

y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x). In other words, for the same x value, there cannot be more than one value for f(x).

If we look at the table, we can see a relationship between the x (input)  and y (output) values.

The output values (y) are the squares of the corresponding input values(x).

Also, there is only one distinct value of y for each x value.

Therefore the given values represent a function, f(x) = x².

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Answer:

The top one is: 1/2x + 6

The bottom one is: -2x + 5

Step-by-step explanation:

The top function:

f(x) = mx + b

m is the slope and b in the y-intercept.  This is what you need to write the function.

The slope is 1/2.  The slope is the rise over the run. If you start at the point (-6,3) and go up one unit and 2 units to the right, you end up back on the line.  This is the slope.  If you follow that pattern, you will cross the y axis at (0,6).  6 is the y intercept.

The bottom function:

The slope is -2.  I you start at the point (1,3) and you go down 2 and one to the right, you will end up back on the line.  2/1 equals 2.

If you follow that pattern going backwards, 2 up and one to the left, you will be at the y-intercept (0,5) 5 is the y-intercept.

Answer: -13

Step-by-step explanation: Here to help! So first, you do 8-12, then you get -4, right? So then, you multiply 2 times -4, then you get -8. After that, you add -5 to -8, so it's -5 + -8, and you get -13.

Answer:

-13

Step-by-step explanation:

-5+2(8-12)

distribute the 2

-5+16-24

add

11-24

subtract

-13

Step-by-step explanation:

To find the total volume of the solution in liters, we need to add the volumes of the two ingredients:

500 mL + 1000 mL = 1500 mL

To convert mL to liters, divide by 1000:

1500 mL / 1000 = 1.5 L

So, the solution is 1.5 liters.

Answer:

17

Step-by-step explanation:

Find the absolute value of -8, which is 8, and add 9 to that, which gives you 17.

Answer:

There will be 312 pennies and 162 nickels that will make up to $11.22 and there are 474 coins altogether.

Step-by-step explanation:

Here,

A penny is worth 1 cent.

A nickel is worth 5 cents.

A dime is worth 10 cents.

A quarter is worth 25 cents.

A dollar is worth 100 cents.

Let there be x pennies and y nickels.

x+y=474

0.01x+0.05y=11.22

Now,

0.01x+0.01y=4.74

0.01x+0.05y=11.22

subtracting both,

-0.04y=-6.48

y=6.48/0.04

y=162 nickels

x+162=474

x=312 pennies

There will be 312 pennies and 162 nickels totaling $11.22, for a total of 474 coins.

Using the data the frequency table is completed as follows

Age             Frequency

20-29               3

30-39                4

40-49                6

50-59               11

60-69               3

70-79                2

80-89                1

The number of times the data is repeated inside a given dataset is referred to as the frequency of the data sets.

A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension. Two or three columns make up a frequency distribution table. All of the results are presented in the first column as individual values or as class intervals.

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The required solution of the differential equation is given as y² = -4logx + 9.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,
Given the differential equation,
Y’+2/x*y=0
Y' = -2/xy
y (dy/dx) = -2/x
ydy = -2/xdx
y²/2 = -2logx + C

From the initial condition y(1)=3
9/2 = -2log1 + c

c = 9/2

Now,
y²/2 = -2logx + 9/2
y² = -4logx + 9

Thus, the required solution of the differential equation is given as y² = -4logx + 9.

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in essence, PEMDAS, but let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} ~\hfill \stackrel{mixed}{1\frac{2}{4}} \implies \cfrac{1\cdot 4+2}{4} \implies \stackrel{improper}{\cfrac{6}{4}} \\\\\\ \stackrel{mixed}{3\frac{6}{8}}\implies \cfrac{3\cdot 8+6}{8}\implies \stackrel{improper}{\cfrac{30}{8}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{23}{3}-\left(\cfrac{6}{4}+\cfrac{30}{8} \right)\implies \cfrac{23}{3}-\left( \cfrac{(2)6~~ + ~~(1)30}{\underset{\textit{using this LCD}}{8}} \right)\implies \cfrac{23}{3}-\left( \cfrac{12+30}{8} \right)[/tex]

[tex]\cfrac{23}{3}-\left( \cfrac{42}{8} \right)\implies \cfrac{23}{3}- \cfrac{42}{8}\implies \cfrac{(8)23~~ - ~~(1)42}{\underset{\textit{using this LCD}}{24}}\implies \cfrac{184-42}{24} \\\\\\ \cfrac{142}{24}\implies \cfrac{2\cdot 71}{2\cdot 12}\implies \cfrac{2}{2}\cdot \cfrac{71}{12}\implies \cfrac{71}{12}\implies 5\frac{11}{12}[/tex]

Therefore, the project progresses and the unitary method wood becomes smoother, finer steel wool (i.e. grades 3, 2, 1, and 0000) can be used to achieve a smoother finish..

To finish a task using unitary procedure, multiply this same sum by two after finding the measurements of one tiny slice. To differentiate a coded unit from a specific group or collection of groups, use the unit variable method, which only needs an expression. For instance, 40 pencils could cost. 4,000, which really is equivalent to $1.01 as well as 4000 pounds.

Here,

The information in the graphic that supports the advice to use coarse steel wool at the start of a major wood refinishing project is:

"Grade 4 steel wool is used to remove paint and other materials, while grade 0000 is used for the final finish on fine woodwork."

This suggests that coarse steel wool (i.e. grade 4) is more effective at removing paint and other materials, which is often necessary at the beginning of a wood refinishing project.

As the project progresses and the wood becomes smoother, finer steel wool (i.e. grades 3, 2, 1, and 0000) can be used to achieve a smoother finish..

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Answer:

22.5 g suger!

Step-by-step explanation:

100% is 75 g

10% is 7,5 g

30% is 22.5 g

10% x 3

( 7,5 g x 3 = )

7 x 3 = 21

0.5 x 3 = 1.5

21 + 1.5 = 22.5 g!

The uncorrected creatinine clearance value is 62.7mL/min

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface

Given:

U=76 mg/dL

P= 1.2 mg/dL

Let V= volume of urine in mm/min

V=1430mL/1440min

V=0.99mL/min

Use the formula:

UV/P

=(76 x .99)/1.2=62.7mL/min

The uncorrected creatinine clearance value is 62.7mL/min

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It depends on Jack's personal preference and priorities. If he values having a large collection of comics.

Comics are visual storytelling medium that combines text and images to convey a narrative or illustrate a story. They can come in many forms, including comic books, graphic novels, manga, and webcomics, and often feature characters, settings, and events that are fictional or based on real-life events. Comics can be serious or humorous and can be aimed at a wide range of audiences, from children to adults. The format of comics allows for a unique combination of text and illustration that can create an immersive experience for the reader.

It depends on Jack's personal preference and priorities. If he values having a large collection of comics, he may choose to make a trade with Caroline for three of her comic books. If he values money, he may choose to sell the comic to Brooke for $100. If he values the sentimental attachment to the comic book or the rarity of a signed copy, he may choose to hold onto the comic. Ultimately, the decision is up to Jack and what he values the most.

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Answer: the new points are A=(2,4) B=(2,3) C=(4,6) D(4,2)

Step-by-step explanation:

If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.

Answer:

392

Step-by-step explanation:

...................

(a) To illustrate the information on a Venn diagram:

A Venn diagram is a graphical representation of the relationship between sets of items

This Venn diagram will visually represent the information given in the question and help to answer the questions about the number of students who passed each subject and the number of students who passed exactly one subject.

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Answer: The equation for the area of the garden is x(x - 2) = 48. To find the length, we need to solve for x:

x^2 - 2x - 48 = 0

Using the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4(1)(-48)))/2(1)

x = (2 ± √(4 + 192))/2

x = (2 ± √196)/2

x = (2 ± 14)/2

x = 8 or x = -6

Since the length cannot be negative, the length of the garden is 8 feet.

Step-by-step explanation:

Answer:

The pitcher won 28 games out of 35.

Step-by-step explanation:

A baseball pitcher won 80% of the games he pitched, so the formula to calculate the number of games won is:

G = 80/100 * n

where

G is the number of games won

n is the number of games pitched

We know that the pitcher pitched 35 games, so:

G = 0.8 * 35

G = 28

So, the pitcher won 28 games out of 35.

Answer: 28

Step-by-step explanation: times 35 by 0.80 to get your answer, also not really a collage level question.

PS pls help me by answering one of my questions (:

The length CD of the triangle is 6 units

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

The triangle

Also, we have

AD = 9 and DB = 4

The length CD (x) is then calculated as

x/4 = 9/x

Cross multiply

This gives

x^2 = 36

Take the square roots

x = 6

Hence, the solution is 6

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