The answer to question 18 and 19

Answer:

6 cm

Step-by-step explanation:

Volume of the given cylinder is calculated using the formula
V = π r ² l

r = radius of the cylinder = diameter/2

Here r = 4/2 = 2 cm

V = 150 cm³

and we are asked to calculate l

Plugging in known values
150 = π · 2³ · l

switch side:
π · 2³ · l = 150

π · 8 · l = 150

l = 150/8π

= 5.96831 cm

To the nearest centimeter we would round this up to 6 cm (Answer)

The percentage error in the volume calculation is estimated to be 24%.

The formula for the volume of a sphere is V = (4/3)πr³

where;

Since the diameter is given as 50 ± 4 cm, the radius can be calculated as:

r = (1/2)d = (1/2)(50 ± 4) cm = 25 ± 2 cm

The percentage error in the radius is:

Δr/r = (2 cm) / (25 cm) = 0.08

This means that the radius measurement has an error of 8%.

Using the formula for the volume of a sphere, we can calculate the volume as:

V = (4/3)π(25 ± 2)³ = (4/3)π(27 ± 18) × 10³ cm³

The percentage error in the volume calculation can be found by:

ΔV/V = (Δr/r) × 3

ΔV/V = 0.08 × 3 = 0.24 = 24%

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The area of the triangle in this coordinate plane will be 36 square units. Then the correct option is A.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

[tex]\text{A} = (\dfrac{1}{2} ) \times h\times b[/tex]

From the graph, the length of the height of the triangle is 9 units and the length of the base of the triangle is 8 units. Then the area is given as,

[tex]\text{A} = (\dfrac{1}{2} ) \times 9\times 8[/tex]

[tex]\text{A = 36 square units}[/tex]

The area of the triangle in this coordinate plane will be 36 square units. Then the correct option is A.

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Answer: x[tex]\neq[/tex]6

Step-by-step explanation

The inverse function is f^-1(x)=1/x-4+6  and the domain is x[tex]\neq[/tex]6

Express f(x) as y

Swap the positions of x and y

Add 6 to both sides

Multiply both sides by y-4

Divide both sides by x + 6

Add 4 to both sides

Rewrite as: f-1(x)=1/x+6-4

Hence, the inverse function is 4  and the domain is x[tex]\neq[/tex]6

Answer:

[tex] \rm \: a. \: \displaystyle \int \rm \: (3 {x}^{2} + 4x)dx[/tex]

[tex] = \displaystyle \int \rm 3 {x}^{2} dx + \displaystyle \int \rm4x \: dx[/tex]

[tex] \rm = 3 \displaystyle \int \rm {x}^{2} \: dx + 4\displaystyle \int \rm \: x \: dx[/tex]

[tex] \rm \: = 3 \times \dfrac{ {x}^{3} }{3} + 4 \dfrac{ {x}^{2} }{2} + c[/tex]

[tex] \boxed{\rm = {x}^{3} + 2 {x}^{2} + c}[/tex]

[tex]b. \displaystyle \int \rm \bigg( \dfrac{1}{ {t}^{2} } + \sqrt{t} \bigg)dt[/tex]

[tex] = \displaystyle \int \rm \frac{1}{ {t}^{2} } dt + \displaystyle \int \rm \sqrt{t} \: dt[/tex]

[tex] = \displaystyle \int \rm \: {t}^{ - 2} dt \: +\displaystyle \int \rm {t}^{ \frac{1}{2} } dt[/tex]

[tex] \rm \: = \dfrac{ {t}^{ - 1} }{ - 1} + \frac{ {t}^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ [/tex]

[tex] \rm = - \dfrac{1}{t} + \dfrac{2}{3} {t}^{ \frac{3}{2} } + c \\ [/tex]

[ In Second question I used dt instead of dx ]

Option (b) correctly represent the graph f(x) = 1/2 (x-3)² -6, we can find by coordinate geometry.

What is Coordinate geometry?

A coordinate system in geometry is a method for    determining the precise location    of points or other    geometrical objects on a manifold, such as Euclidean space, using one (1) or more    numbers, or coordinates.

In coordinate geometry, many geometric figures    are described using graphs and coordinates. The    coordinate plane must be described in a definition of coordinate geometry. The     intersection of 2 number lines, referred to as axes,     yields the coordinate plane, also known as the coordinate graph, which is a grid system.

In option (b), if we    put x = 7 , we get y = 2.

and , if we    put x =4, we get y = -5.5

Hence, the option (b) is correct.

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The is a striking deviation at the value of 5.5.

This deviation is seen in the form of a cluster of dots that are significantly higher than the rest of the data points. This cluster of dots represents a group of observations that share a similar characteristic or variable that sets them apart from the rest of the data set.
The presence of this deviation at the value of 5.5 indicates that there is a unique factor or characteristic present in this group of observations that is not shared by the rest of the data set. This could be due to a number of factors, such as a different population, different data collection methods, or even measurement error.
It is important to note this deviation when analyzing the data set, as it can have a significant impact on any conclusions drawn from the data.

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The perimeter of the triangle when expressed in simplest form is 12a + 3b + 15

The dimensions of the triangle are given as

3a + 8 4a +2b + 7 5a + b​

Perimeter refers to the total length of the boundary or outer edge of a two-dimensional shape.

The perimeter is measured in linear units such as centimeters, meters, feet, or inches.

The formula for finding the perimeter of a shape depends on the type of shape

For the triangle, we have

Perimeter = 3a + 8 + 4a +2b + 7 + 5a + b​

Evaluate

Perimeter = 12a + 3b + 15

Hence, teh perimeter is 12a + 3b + 15

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Answer:

b

Step-by-step explanation:

The coordinates of its reflection are (4, -10)

A reflection over line is a transformation in which each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line.

Given that point P(4,11) is reflected across the line y=1,

Point P is on x = 4 which will not change after reflection, P is 10 units above line y = 3 so counting down 10 from y = 1, and then we will get on

y = -5'

Hence, the coordinates of reflection of point P = (4, -10)

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The answer is 2/5.

There is an 8/20 chance that the next person will receive a window seat. You simplify that probability to get your answer. 8/20 becomes 2/5. So the answer is 2/5.

The cοοrdinates οf A′ fοr the dilatiοn D1.5(A) is A'(3, 6).

Cοοrdinates are a set οf numbers used tο lοcate the pοsitiοn οf a pοint οr an οbject in a space οr plane. They are typically used tο represent pοints in a Cartesian cοοrdinate system, which is a system that uses twο οr three perpendicular axes tο define the pοsitiοn οf a pοint.

Tο find the cοοrdinates οf the dilatiοn D1/2(△XYZ), we need tο multiply the cοοrdinates οf each vertex οf the triangle by the scale factοr οf 1/2. This will result in a triangle that is half the size οf the οriginal triangle, but with the same shape and prοpοrtiοns.

The given cοοrdinate is A(2, 4).

It's impοrtant tο knοw that a dilatiοn implies a bigger figure than the οriginal. In this case, we have a factοr οf dilatiοn οf 1.5, which means each cοοrdinate must be multiplied by it.

Sο, using the factοr οf dilatiοn, we have

A(2, 4) ⇒ A((2 × 1.5),(4 × 1.5)) ⇒ A'(3, 6)

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Complete question:

The point A has coordinates A(2, 4). What are the coordinates of A′ for the dilation D1.5(A)?

Answer:

A. 24 in, 32 in, 40 in

Step-by-step explanation:

To determine whether a set of measurements could be the side lengths of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides.

Using this theorem, we can check each set of measurements:

A. 24 in, 32 in, 40 in

Here, 40 in is the longest side, so it could be the hypotenuse. If we square the other two sides and add them together, we get:

24^2 + 32^2 = 576 + 1024 = 1600

And if we square the length of the hypotenuse, we get:

40^2 = 1600

So this set of measurements satisfies the Pythagorean theorem and could be the side lengths of a right triangle.

B. 24 in, 36 in, 40 in

Again, 40 in is the longest side and could be the hypotenuse. Squaring and adding the other two sides gives:

24^2 + 36^2 = 576 + 1296 = 1872

And squaring the length of the hypotenuse gives:

40^2 = 1600

So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.

C. 24 in, 32 in, 48 in

Here, again, we can take 48 in as the hypotenuse. Squaring and adding the other two sides gives:

24^2 + 32^2 = 576 + 1024 = 1600

And squaring the length of the hypotenuse gives:

48^2 = 2304

So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.

D. 20 in, 32 in, 40 in

Once more, we can take 40 in as the hypotenuse. Squaring and adding the other two sides gives:

20^2 + 32^2 = 400 + 1024 = 1424

And squaring the length of the hypotenuse gives:

40^2 = 1600

So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.

In conclusion:

A set of measurements that could be side lengths of a right triangle is A) {24in,32in,40in}. The other sets do not satisfy Pythagorean theorem and cannot be sides of a right triangle.

Hence, in response to the provided question, we can say that As a result, derivatives the integral has a value of -i/2.

In mathematics, the derivative of a function with real variables measures how sensitively the function's value changes in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. einsteinerupload of. Derivatives are rate of change metrics that apply to almost any function.

To use the Cauchy Integral Theorem to evaluate the integral (3z+1)/(z(z-2)2), we must first determine whether the function has any singularities in the region we are integrating across.

We can write the function to find the residue at z=0 as:

A/z + B/(z-2) + C/(z-2)2 = (3z+1)/(z(z-2)2)

3z+1 = A(z-2)^2 + Bz(z-2) + Cz

When we set z=0, we get:

1 = 4A

So, A = 1/4.

Set z=2 in the following equation and its derivative to determine B and C:

9 = 4B + 2C

3 = 4A - 2B - C

B = -1/2 and C = 7/4.

So, A=1/4 is the remnant at z=0, while B=-1/2 is the residue at z=2.

Applying the residue theorem, the integral is as follows:

dz = 2i [Res(z=0) + Res(z=2)] = 3z+1/(z(z-2)2

= 2πi [1/4 - 1/2]

= -πi/2.

As a result, the integral has a value of -i/2.

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Answer:

To determine whether Kyle will arrive in time for the baseball game, we need to calculate how long it will take him to travel the 130 miles to the baseball field.

Using the formula:

distance = rate × time

We can rearrange the formula to solve for time:

time = distance / rate

Plugging in the given values, we get:

time = 130 miles / 50 miles per hour

time = 2.6 hours

This means that it will take Kyle 2.6 hours to travel the 130 miles to the baseball field at the speed limit of 50 miles per hour.

Since Kyle has 2 hours to get to the baseball game, he will not arrive in time if he drives at the speed limit. He would need to drive faster than the speed limit to make it to the game on time. However, it's important to note that speeding is illegal and dangerous, so Kyle should not exceed the speed limit. He may need to consider leaving earlier or finding alternative transportation to ensure that he arrives at the baseball game on time.

Step-by-step explanation:

The chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.

Quantity is the amount or magnitude of something. It can be measured in terms of units, such as length, weight, volume, area, speed, temperature and time. Quantity also refers to the size or number of something, such as the number of items in a package or the number of people in a room. In mathematics, quantity is usually represented by a number or symbol.

In order to calculate the quantity of carrots the chef needs to pull from the walk-in, we can use the following formula:

Quantity Needed = 12 lb / 0.86 (yield percent)

Therefore, the chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.

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The chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.

Quantity is the amount or magnitude of something. It can be measured in terms of units, such as length, weight, volume, area, speed, temperature and time. Quantity also refers to the size or number of something, such as the number of items in a package or the number of people in a room. In mathematics, quantity is usually represented by a number or symbol.

In order to calculate the quantity of carrots the chef needs to pull from the walk-in, we can use the following formula:

Quantity Needed = 12 lb / 0.86 (yield percent)

Therefore, the chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.

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The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.

What is probability ?

Probability cam be defined as ratio of number of  favorable outcomes, total number of outcomes

We can solve this problem by using the central limit theorem. According to the theorem, if we have a large enough sample size, the distribution of sample means will be approximately normal, regardless of the underlying distribution of the population.

The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.

In this case, we have a sample size of 20, which is not very large, but we can still use the central limit theorem as an approximation. The population mean is 48 minutes, and the population standard deviation is 15 minutes. The standard error of the sample mean is:

SE = σ / sqrt(n) = 15 / sqrt(20) = 3.354

To find the probability that the mean completion time for the sample is greater than 60 minutes, we need to standardize the sample mean using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the sample mean.

Plugging in the values, we get:

z = (60 - 48) / 3.354 = 3.57

We can now look up the probability of getting a z-score greater than 3.57 in a standard normal distribution table (or use a calculator). The probability turns out to be very small, approximately 0.0002 or 0.02%.

Therefore, the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.

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Answer:

A. Triangle A= 16cm^2

Step-by-step explanation:

triangle A area=8×4=32

32÷2=16cm^2

triangle B area= 5×6=30

30÷2=15cm^2

so triangle A has the greater area of 16 cm^2

Answer:

A. 16cm2 triangle

Explanation in detail: triangle A area=84=32 32÷2=16cm^2 area of triangle B = 56=30

30÷2=15cm^2 As a result, triangle A has a bigger area of 16 cm2.

Step-by-step explanation:

122°

Step-by-step explanation:

the formula is (n-2)180

n = the number of sides of a polygon

in this case (n-2)180;

=(4-2)180

=(2)180

=360 the total interior angle

add everything and minus them with the total interior angle to get your answer

Answer:

y=4sin(1/2πx)

Step-by-step explanation:

A = 4

Period for y=sin(x) is 2pi

Since the graph shows the period is 4. Then b must be 1/2pi

The set of all real numbers between 1 and 3, including 1 can be represented using set-builder notation as: { x ∈ R | 1 ≤ x ≤ 3 }

set-builder notation:

{ x ∈ R | 1 ≤ x ≤ 3 }

"The set of all x in the set of real numbers such that x is bigger than or equal to 1 and less than or equal to 3" can be understood from this notation. The word "such that" is denoted by the vertical bar "|," and the condition that follows lists the requirements that each element of the set must meet.

When the criteria is "more than or equal to 1" in this instance, the set contains 1. As they also meet the requirement of being "less than or equal to 3," the set also includes all real numbers between 1 and 3. Observe that no numbers outside of the range [1,3] are included in the collection.

In conclusion, the set of all real numbers between 1 and 3, including 1, may be written as x R | 1 x 3 in set-builder notation.

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A. x + y = 3.5 equation is a representation of the TOTAL TIME Mali spent training

An amοunt οf space between twο things οr peοple

The tοtal distance Mali cοvered can be expressed as the sum οf the distance run and the distance biked, which is equal tο 34 miles:

distance run + distance biked = 34

We can express the distance run and the distance biked in terms οf their speeds and the time spent running and biking, respectively:

distance run = 6x (where x is the time spent running in hοurs)

distance biked = 12.5y (where y is the time spent biking in hοurs)

Using the fοrmula distance = rate × time, we can write twο equatiοns fοr the time Mali spent running and biking:

6x + 12.5y = 34 (tοtal time equatiοn)

x + y = 3.5 (tοtal time equatiοn)

Optiοn A, x + y = 3.5, is a representatiοn οf the tοtal time Mali spent training, but οptiοn B, 6x + 12.5y = 34(3.5), is nοt a representatiοn οf the tοtal time Mali spent training, but rather a representatiοn οf the tοtal distance cοvered by Mali in terms οf their speeds and time spent training. Optiοns C, D, and E are nοt cοrrect representatiοns οf the tοtal time Mali spent training either. Therefοre, the cοrrect answer is:

A. x+y = 3.5

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Answer:

-2yz

Step-by-step explanation:

To simplify the expression -5yz + yz + 2yz, we can combine the yz terms that have the same coefficient:

-5yz + yz + 2yz = (-5 + 1 + 2)yz

Simplifying the coefficients gives:

= -2yz

Therefore, the simplified expression is -2yz.

Answer:

[tex]-2yz[/tex]

Step-by-step explanation:

[tex]-5yz + yz + 2yz = (-5 + 1 + 2)yz[/tex]

[tex](-5 + 1 + 2)yz = -2yz[/tex]

Therefore, the simplified expression is:

[tex]-2yz[/tex]

Answer:

Jim was the project leader given that the project has succeeded is approximately 0.57.

The required length of lace = 4.17m and the cos for lace of 4.17m is ₹ 70.65.

Step 1:

Find the radius, r of the circular table.

Given that, Salma wants to put a lace on the edge of a circular table of diameter

Diameter of circle, d=1.5m

Radius of circle, [tex]\text{r}=\dfrac{1.5}{2}\text{m}[/tex]

Step 2:

Find circumference of the circle.

Substitute [tex]\text{r}=\dfrac{1.5}{2}\text{m}[/tex] in formula

[tex]\text{Circumference of the circle}=2\pi r[/tex]

Take [tex]\pi =3.14[/tex]

[tex]=2\times3.14\times\dfrac{1.5}{2}[/tex]

[tex]=3.14\times1.5[/tex]

[tex]=4.71 \ \text{m}[/tex]

[tex]\text{Circumference of circle} = 4.71 \ \text{m}[/tex]

[tex]\text{The length of lace required is 4.71} \ \text{m}[/tex]

Step 3:

Find the cost of rope.

From step 2

[tex]\text{Length of lace required} =\it{4.17} \ \text{m}[/tex]

Given that, of the lace costs ₹ 15

From the above statement, form an equation.

Cost of 1m lace = ₹ 15

Therefore, cost of 4.17m lace

Required length of lace = 4.17m. Cost for lace of 4.17m is₹ 70.65.

By answering the presented question, we may conclude that Evelyn will equation need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.  

Initially, we must determine the entire cost of producing and transporting one mask:

Total cost per mask = $1.25 plus $2.15 for delivery = $3.40

Profit per mask is selling price minus total cost per mask, which equals $5 - $3.40 = $1.60.

As a result, Evelyn will profit $1.60 for each mask she sells. We may use the following calculation to calculate how many masks she needs to sell to recoup her $450 initial project costs:

Total beginning project expenditures / profit per mask = number of masks to sell

Total number of masks to be sold = $450 / $1.60 per mask = 281 masks

Evelyn will need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.

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This same car's purchase amount, which would include tax, is $21,733.

A tax is a compulsory fee / financial charge imposed by a government on a person or an entity in order to raise money for public works projects that provide the greatest infrastructure and facilities.

a. To determine the amount of tax paid, multiply the cost of the car even by applicable sales tax rate.

3% times $21,100 is the amount of tax paid.

Taxes paid = 0.03 times $21,100.

Total tax paid: $633

Hence, $633 in taxes were paid on the vehicle.

b. To get the entire cost of the vehicle, we must add the purchase price and any applicable taxes:

Total price equals automobile price plus tax paid.

Cost in total is $21,100 plus $633.

Cost in total is $21,733

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The unknown angles of the kites are as follows:
m∠1 = 90°

m∠2 = 65°

m∠3 = 90

m∠4 = 65°

m∠5 = 25°

A kite is a quadrilateral that has 90° angles at the point of intersection of the two diagonals. The sum of angles in a kite is 360 degrees.

Therefore, the diagonal of a kite bisect each other at right angle.

Diagonals also bisect each angles.

Using the diagonal theorem of the kite,

m∠1 = 90 degrees

m∠2 = 180 - 25 - 90 = 65 degrees(sum of angles in a triangle)

m∠3 = 90 degrees

m∠4 = 65 degrees(Base angles of an isosceles triangles are congruent)

m∠5 = 25 degrees

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Answer:

A) 1080º

Step-by-step explanation:

I remember learning this in math class. The octagon has 8 interior angles and 8 exteriors angle. The sum of the interior angles of an octagon is 1080º

Answer:

The sum of the interior angles of an octagon can be found using the formula: (n-2) x 180 degrees, where n is the number of sides of the polygon.

For an octagon, n = 8, so the sum of the interior angles is (8-2) x 180 = 6 x 180 = 1080 degrees.

Therefore, the correct answer is A) 1080º.