A rate of change must be positive

The volume of the cylinder can be obtained from the calculation as  1356 \(cm^3\)

We know that the volume of the cylinder is;

π (pi) is a mathematical constant approximately equal to 3.14159

r is the radius of the cylinder's base (the distance from the center to the edge of the circular base)

h is the height of the cylinder (the distance between the bases)

By substituting the appropriate values for the radius and height into the formula, you can calculate the volume of the cylinder.

V = π\(r^2\)h

V = 3.14 *\((12/2)^2\) * 12

h = 1356 \(cm^3\)

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Answer:

2\(\sqrt{13}\)

Step-by-step explanation:

Use the distance formula and plug in the values

d=(3−(−3))2+(2−6)2√  

d=(6)2+(−4)2√

d=36+16√

d=\(\sqrt{52}\)

d= 2\(\sqrt{13}\)

Answer:

\(\frac{51}{8} \:or \: 6\frac{3}{8}\)

Step-by-step explanation:

solution given:

\(\frac{3}{4} *8\frac{1}{2}\)

let make mixed fraction to normal fraction

\(8\frac{1}{2} =\frac{8*2+1}{2} =\frac{17}{2}\)

replace \(\frac{17}{2}\)

we have

\(\frac{3}{4} *\frac{17}{2}\)

in multplication fraction, we multiply numerator to numerator and denominator to denominator.

\(\frac{3}{4} *\frac{17}{2}=\frac{3*17}{4*2} =\frac{51}{8}\)

again

in mixed fraction =\(6\frac{3}{8}\)

Answer:

Step-by-step explanation:

C

The area of the circular shaped pizza is A = 254.5 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the pizza be r = 9 cm

The area A of a circle with radius r is given by the formula:

A = πr²

Substituting the given radius of 9 cm, we get:

A = π(9 cm)²

A = π(81 cm²)

A ≈ 254.47 cm²

Rounding to one decimal place, we get:

A ≈ 254.5 cm²

Hence , the area of the circular pizza with a radius of 9 cm is approximately 254.5 cm²

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Answer:

2, - 3, 18

Step-by-step explanation:

1). \(\sqrt[3]{1-x}\) = - 1

( \(\sqrt[3]{1-x}\) )³ = ( - 1)³

1 - x = - 1 ⇒ x = 2

2). \(\sqrt{x^2 +7}\) = 4

( \(\sqrt{x^2 +7}\) )² = 4²

x² + 7 = 16 ⇒ x = ± 3 ; x = - 3

3). \((x-2)^{\frac{1}{4} }\) = 2

\([(x-2)^{\frac{1}{4} }] ^{4}\) = \(2^{4}\)

x - 2 = 16

x = 18

Answer:

\(Red = \frac{10}{37}\)

Step-by-step explanation:

Given

\(Red:Yellow = 2 : 3\)

\(Yellow: Blue = 5 : 4\)

Required

Determine the fraction of Red

First, we need to link the given ratios.

Since yellow is present in both ratios, we start by making the ratio of yellow equal in both ratios

Multiply this ratio by 5

\(Red:Yellow = 2 : 3\)

This becomes

\(Red:Yellow = 10 :15\)

Similarly, multiply this ratio by 3

\(Yellow: Blue = 5 : 4\)

This becomes

\(Yellow:Blue =15:12\)

At this point, we have:

\(Red:Yellow = 10 :15\) and \(Yellow:Blue =15:12\)

Combine

\(Red:Yellow:Blue = 10:15:12\)

The fraction is then calculated as:

\(Red = \frac{Red}{Red +Yellow + Blue}\)

This gives

\(Red = \frac{10}{10+15+12}\)

\(Red = \frac{10}{37}\)

Answer:

$3.75

Step-by-step explanation:

Cost of one shirt = $12.25

cost of two shirt = 2*Cost of one shirt= 2*$12.25 = $25

cost of necklace = $8.50

cost of pair of shoes = $22.75

Total cost for the shopping = cost of two shirt+cost of necklace+ cost of pair of shoes

Total cost for the shopping = $25 + $8.50+ $22.75 = $56.25

Given that Maddy had done total shopping worth $56.25 but she gave cashier all her birthday money which is equal  to $60.

Then , cashier will return all the money from $60 exceeding $56.25

change returned to money = money given to cashier - total cost for shopping

change returned to Maddy = $60 - $56.25 = $3.75

Thus, Maddy got Back $3.75

Answer:

C). 38

Step-by-step explanation:

The range is the measurement of the difference between values in a data set. To find the range, subtract the lowest value from the greatest value.

2, 5, 19, 7, -5, 33, 26, 15, 12

-5, 2, 5, 7, 12, 15, 19, 26, 33

Lowest value,

⇒ -5

Greatest value,

⇒ 33

33 - (-5)

⇒ 38

Hence, the range/answer is 38. ⇒ option c.

The equation which represents a linear function for the variable y is y=12r-5. Option B is the correct option.

Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

y=mx+c

Here, m is the slope of the line represented by the function and c is the y intercept.

The equation given in the problem are,

2ry+y= 9

y=12r-5

3y+r2+t=0

4r+2(y-1)=0

The second option is similar to the standard linear function.

Hence, the equation which represents a linear function for the variable y is y=12r-5. Option B is the correct option.

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Answer:

x = 2.2

Step-by-step explanation:

-0.45x + 0.33 = -0.66

-0.45x = -0.99

x = 2.2

Brainly plz :))

Answeits only 5 points

Step-by-step explanation:

Answer:

a lot

Step-by-step explanation:

994

Answer:

0.897

Step-by-step explanation:

Brahmagupta formula for quadratic equation \(ax^2+bx=c\) is

\(x=\dfrac{\sqrt{4ac+b^2}-b}{2a}\)

It involved only one solution.

The given equation is

\(3x^2+4x=6\)

Here, a=3, b=4 and c=6. Put these values in the above formula.

\(x=\dfrac{\sqrt{4(3)(6)+(4)^2}-4}{2(3)}\)

\(x=\dfrac{\sqrt{4(3)(6)+(4)^2}-4}{2(3)}\)

\(x=\dfrac{\sqrt{72+16}-4}{6}\)

\(x=\dfrac{\sqrt{88}-4}{6}\)

\(x\approx \dfrac{5.38}{6}\)

\(x\approx 0.897\)

Therefore, the required solution is 0.897.

The graph of f(x) = (x - 3)² is the red one, g(x) = (x + 3)² + 3 is blue one and h(x) = -(x - 3)² - 4 is green one.

Function f(x) = (x - 3)²:

The graph of f(x) is a upward-opening parabola with its vertex at (3, 0). It is symmetrical with respect to the vertical line x = 3. The graph touches the x-axis at x = 3.

Function g(x) = (x + 3)² + 3:

The graph of g(x) is also an upward-opening parabola with its vertex at (-3, 3). It is symmetrical with respect to the vertical line x = -3. The graph is shifted 3 units upward compared to the graph of f(x) = (x - 3)².

Function h(x) = -(x - 3)² - 4:

The graph of h(x) is a downward-opening parabola with its vertex at (3, -4). It is symmetrical with respect to the vertical line x = 3. The graph is reflected and shifted 4 units downward compared to the graph of f(x) = (x - 3)².

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

y = 4

Step-by-step explanation:

Using the slope, m = 5, and the given point, (1, -6), plug in these values into the point-slope formula:  

y - y1 = m(x - x1)

y - (-6) = 5(x - 1)

y + 6 = 5x - 5

Subtract 6 on both sides of the equation to isolate y:

y + 6 - 6  = 5x - 5 - 6

y= 5x - 11

Therefore, the linear equation in slope-intercept form is y = 5x - 11.  

To find the value of the y-coordinate in point (3, y ):

Plug in the value of x = 3 into the equation, y = 5x - 11

y= 5x - 11

y= 5(3) - 11

y = 15 - 11

y = 4

Therefore, the value of the y-coordinate in point (3, y) is 4.

The measure of angle B is, 67°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Interior angles are,

⇒ ∠ C = 83°

⇒ ∠ B = 6x + 7

An exterior angle is,

⇒ ∠ A = 15x

Now, We know that;

The sum of two interior angles in a triangle is equal to the exterior angle in a triangle.

⇒ 83° + 6x + 7 = 15x

⇒ 90 = 15x - 6x

⇒ 90 = 9x

⇒ x = 10

Thus, The measure of B is,

⇒ m ∠B = 6x + 7

             = 6×10 + 7

             = 60 + 7

             = 67

⇒ m ∠B =  67

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Answer:

338

Step-by-step explanation:

because it right and i said so

Answer:

g(x) = (x -39)^2 +74

Step-by-step explanation:

Given f(x)=x^2, after performing the following transformations: shift upward 74 units and shift 39 units to the right, the new function g(x) = (x -39)^2 +74

In mathematics, a transformation is a feature f, typically with a few geometrical underpinnings, that maps a fixed X to itself, i.e. f: X → X.

What are the 4 transformations in maths?

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The encrypted message for "snowfall" using Vigenere cipher with key "blue" is "TYPAGKL".

To use the Vigenere cipher with key "blue" to encrypt the message "snowfall," we follow these steps:

Write the key repeatedly below the plaintext message:

Key:   blueblu

Plain: snowfal

Convert each letter in the plaintext message to a number using a simple substitution, such as A=0, B=1, C=2, etc.:

Key:   blueblu

Plain: snowfal

Nums:  18 13 14 22 5 0 11

Convert each letter in the key to a number using the same substitution:

Key:   blueblu

Nums:  1 11 20 4 1 11 20

Add the corresponding numbers in the plaintext and key, modulo 26 (i.e. wrap around to 0 after 25):

Key:   blueblu

Plain: snowfal

Nums:  18 13 14 22 5 0 11

Key:   1 11 20 4 1 11 20

Enc:   19 24 8 0 6 11 5

Convert the resulting numbers back to letters using the same substitution:

Encrypted message: TYPAGKL

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Answer:

850

Step-by-step explanation:

There are 85 types of trees, if he planted 10 of each that would be 85 x 10. Anything multiplied by 10 is the same thing with a 0 at the end. That would make it 850. I Calculated and it’s also correct.

The correct system of equations is A. x+y=1212 and x-y=518.

Let us assume the two numbers to be x and y. Based on the first statement, the equation will be:

x + y = 1212

Based on the second statement, the equation will be:

x - y = 518

Using the equation to find the value of x and y

Adding these two equations. We get -

2x = 1730

x = 1730 ÷ 2

Performing division

x = 865

Keeping the value of x in first equation to find the value of y

y = 1212 - 865

Performing subtraction

y = 347

Thus, the system of equations that can solve this problem are: x+y=1212 and x-y=518.

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The complete question is attached in figure.

If 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards, the possible outcome is (10, 10, 5). So, correct option is B.

One possible method to approach this problem is to first find the total number of trading cards Royce has in his collection, which is the sum of baseball cards, football cards, and basketball cards:

Total number of cards = 16 + 21 + 13 = 50

Then, we can find half of the total number of cards, which is the number of cards Royce gives to his friend:

Half of total number of cards = 1/2 x 50 = 25

To find possible outcomes of this selection, we can start by considering how many baseball cards Royce can give to his friend. Since he has 16 baseball cards in total, he can give any number of them from 0 to 16, but he cannot give more than 25 cards in total.

Similarly, he can give any number of football cards from 0 to 21 and any number of basketball cards from 0 to 13.

Therefore, possible outcomes of this selection can be represented by the set of triples (x, y, z) where x is the number of baseball cards, y is the number of football cards, and z is the number of basketball cards, such that x + y + z = 25 and 0 ≤ x ≤ 16, 0 ≤ y ≤ 21, and 0 ≤ z ≤ 13.

The possible outcome is (10, 10, 5), which means Royce gives 10 baseball cards, 10 football cards, and 5 basketball cards to his friend.

So, correct option is B.

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Complete question is:

Royce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He chooses half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?

A) (10.20,20)

B) (10, 10, 5)

C) (20, 10, 5)

D) (10, 10, 25)

Answer:

I can help but I need better pic

Answer:

Width: 4 meters. Length: 11 meters

Step-by-step explanation:

If you do it correctly, the length should be 3 more greater than 4*2. 4*2= 8 +3= 11. Your perimeter= 30 meters. 11+11 accounting for both long sides of the rectangle= 22. Accounting for both sides of the width, so 4*2=8 + our 22= 30 meters. Yw.

The length of the rectangle​ width 4 meters and length 11 meters.

If you do it correctly,

The length should be 3 more greater than

P=2(l+w)

L= Length

W = Width

4*2. 4*2= 8 +3= 11.

Your perimeter= 30 meters.

11+11 accounting for both long sides of the rectangle= 22.

Accounting for both sides of the width,

So 4*2=8 + our 22= 30 meters.

Therefore we get the length of a rectangle is  11 meters.

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The function f(x) = x² - 1/x + 1, with domain [0, ∞), does not have an absolute maximum on its domain, but this does not contradict the extreme value theorem.

The extreme value theorem states that if a real-valued function f is continuous on a closed interval [a, b], then f must have both an absolute maximum and an absolute minimum on that interval.

However, the theorem does not apply to functions that have an open interval as their domain, such as f(x) = x² - 1/x + 1 with a domain of [0, ∞).

In this case, f(x) approaches infinity as x approaches 0, but it does not have a maximum value within the given domain. The lack of an absolute maximum for f(x) on [0, ∞) is consistent with the behavior of the function, and it does not violate the extreme value theorem since the domain is not a closed interval.

Therefore, the function f(x) = x² - 1/x + 1, defined on [0, ∞), lacks an absolute maximum, but this does not violate the extreme value theorem.

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Answer: 1.17600521 rad

Step-by-step explanation:

To find the angle (in radians) that the ladder makes with the building, we can use the right triangle formed by the ladder, the building, and the ground. The ladder acts as the hypotenuse of the right triangle, with a length of 13 feet. The height from the ground to the second-floor window is the side opposite the angle we want to find, which has a length of 12 feet.

We can use the sine function to find the angle, θ:

sin(θ) = opposite side / hypotenuse

sin(θ) = 12 / 13

Now, to find the angle θ in radians, we can use the inverse sine function (arcsin):

θ = arcsin(12/13)

Plug the value into a calculator to get the angle in radians:

θ ≈ 1.17600521 rad

Answer:

θ ≈ 1.17600521 rad

Step-by-step explanation:

a)

Solution,

According to fuel gauge,the petrol left is exactly between 1/2 and 3/4 part of the 40 litres.

i.e. Left fuel = (1/2 + 3/4)/2 litres

Here,

1/2 of 40l = 1/2×40l

= 20l

3/4 of 40l = 3/4×40l

= 30l

Then,

Left fuel = (20l + 30l)/2

= 50l/2

= 25l

Consumed fuel = 40l - 25l

= 15l

Therefore,15 litres of petrol is used to travel 240km

b)

Solution,

Consumed fuel = 15l

Distance covered = 240km

Then,

Fuel consumption rate = 240km/15 l

= 16km/l

Therefore,the rate of petrol consumption is 16km/l of his car for this journey

In this scenario, multiple interactions are occurring within a very short period, each with unique dynamics and ramifications for the individuals involved.

The interactions are as follows: John's uncle called his mother to inform her of an outbreak of brucellosis at his farm, which John may have contracted while helping with a difficult labor case of a sow experiencing dystocia. His mother then contacts the hospital's doctor with this information, requesting that they screen John for brucellosis using a quick screening test called the standard tube agglutination (STA) test.

After the doctor receives the request, additional precautions are taken to prevent the spread of Brucella spp. to the lab staff. The STA test is run on John's previously collected and banked serum and CSF samples. Based on the additional history and clinical presentation, a probable diagnosis of brucellosis is made, and John begins treatment with a combination of three antibiotics that are effective against Brucella spp.

The dynamics of these interactions are centered on the shared concern for John's health and safety, and the potential for Brucella spp. to infect other hospital staff, diagnostic lab personnel, and even family members who came into contact with him.

The ramifications for the participants are numerous, from the need for additional laboratory safety precautions to the psychological effects of being diagnosed with a rare disease. Additionally, John's family will need to be informed of the diagnosis and potential risks, and his uncle's farm may face financial losses and reputational damage due to the outbreak of brucellosis.

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Complete Question:  

John has been in the hospital for three days. He is stable but not showing any significant improvement. John’s mom receives a call from her brother, who has a farm a little over 200 miles from them, where he raises pasture-reared pigs. He tells his sister that brucellosis has been diagnosed at his farm, and brucellosis can infect people. He reminds her that over the Thanksgiving holidays when they visited that John helped to pull some stillborn piglets from the birth canal of a sow experiencing a difficult labor (dystocia). Could John have brucellosis? She thanks her brother and immediately goes to find someone to give them this information.

The doctors request that the standard tube agglutination (STA) test for Brucella spp. is run on John’s previously collected and banked serum and CSF samples. The STA is a quick screening test. Currently, there is no growth on any culture plates streaked with CSF from John, but Brucella spp. are slow-growers and it is too early to expect any growth.

The request also alerts the diagnostic laboratory that samples from John may be infected with Brucella spp. and additional precautions should be observed to prevent laboratory personnel from inadvertently becoming infected.

Based on the additional history and clinical presentation, a probably diagnosis of brucellosis is made, and John begins treatment with a combination of three antibiotics demonstrated to be efficacious against Brucella spp.

:: we don't know the antibiotic. most probably common ones

Multiple interactions are occurring in a very short time frame. Discuss the dynamics of these interactions and the ramifications for the participants.