The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meters and the diameter of a base of the cylinder is 4 meters. What is the height of the cylinder? Enter your answer, as a simplified fraction, in the box.

Answer:

To find the coordinates of P, we can use the concept of proportional division of line segments. Given that AP:BP = 2:5, it means that the ratio of the length of AP to BP is 2:5.

Let's first find the vector that represents the direction of AB, which is the vector pointing from A to B. We can find this by subtracting the coordinates of A from the coordinates of B:

(10,13) - (-4,-8) = (14, 21)

This is the vector <14,21>

Now, we can find the point P, which is located two fifths of the way from A to B, by multiplying the vector <14,21> by 2/7 and adding the result to the coordinates of A:

P = A + (2/7) * <14,21>

= (-4,-8) + (2/7) * <14,21>

= (-4,-8) + <8,6>

= (4,-2)

So, the coordinates of P are (4,-2)

We can observe that point P is two fifth of the way from A to B.

The solution of Ax = b is unique precisely when Ax = 0 has only the trivial solution, because Ax-b is consistent, its solution set is obtained by translating the solution set of Ax-0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.

The correct answer is an option (b)

Let us assume that the equation Ax = b has a solution.

Now we need to show the solution is unique when Ax = 0 has only the trivial solution.

As we know Ax = 0 represents homogenous equation.

If Ax = b has a solution, it is unique if and only if every column of A is a pivot column. If every column of A is a pivot column, there are no free variables, and therefore the homogeneous equation has only the trivial solution.

Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax=0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax= 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.

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The complete question is:

Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution. Choose the correct answer.

A. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax-0. For Ax-b to be inconsistent, Ax = 0 has only the trivial solution.

B. Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax-0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.

C. Since Ax = b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the trivial solution.

D. Since Ax = b is consistent, then the solution is unique if and only if there is at least one free variable in the corresponding system of equations. This happens if and only if the equation Ax 0 has only the trivial solution.

The greatest number of blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box = 84

Let h represents the height, w represents the width and l represents the length of the box.

The box is 6 units tall, 7 units wide, and 8 units deep.

⇒ h = 6 units, w = 7 units and l = 8  units

The volume of the box would be,

V = l × w × h

V = 6 × 7 × 8

V = 336 cu. units

The four block has  unit-cubes.

The volume of unit each unit cube would be,  1 × 1 × 1 = 1 cubic unit

so, the volume of 4 blocks would be,

V₁ = 4 × 1

V₁ = 4 cu. units

The number of blocks that can be placed in the box would be,

n = V / V₁

n = 336 / 4

n = 84

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The complete question is:

There is an ample supply of identical blocks (as shown). Each block is constructed from four 1 × 1 × 1 unit-cubes glued whole-face to whole-face. What is the greatest number of such blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box?

Answer: The percent of putts that he missed is 60%.

Step-by-step explanation: You divide 27 by 45, and that equals 0.6. After that you multiply 0.6 by 100, which gets it to 60/60%.

Answer: a. The probability of drawing a single card from a 52 card deck that is a diamond or a 10 is 13/52 or 1/4. There are 13 diamonds in a standard deck of 52 cards and 4 of them are 10s. So, the chance of drawing a diamond 10 is 4/52 and the chance of drawing a diamond is 13/52. The probability of drawing a diamond or a 10 is the sum of the individual probabilities, which is (4/52) + (13/52) = 17/52 or 1/3.

b. The probability of drawing a single card from a 52 card deck that is a spade or a queen is 13/52 or 1/4. There are 13 spades in a standard deck of 52 cards and 4 of them are queens. So, the chance of drawing a spade queen is 4/52 and the chance of drawing a spade is 13/52. The probability of drawing a spade or a queen is the sum of the individual probabilities, which is (4/52) + (13/52) = 17/52 or 1/4.

Step-by-step explanation:

The converse of the parallelogram angle theorem is proved.

The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.

Here we have to prove the the converse of the parallelogram angle theorem.

Here we have given that  LM ≅ ON and  LO ≅ MN

Here we have also know that ∠LNO and ∠NLM are alternative and interior angles

Where as the angles ∠OLN and ∠MNL are alternative interior angles

Then according to the reflexive property, it can be written as

=> LN ≅ LN

Then as per the SSS similarity the given triangle is written as,

=> ΔLNO ≅ ΔNLM

Here we have also it can be written as

=> ∠OLN ≅ ∠MNL and  ∠LNO ≅ ∠NLM

Then it can be written as LM || ON and  LO || MN

Then the LMNO is a parallelogram

Complete Question:

Analyzing a Proof Click here to see a proof of the converse of the parallelogram angle theorem. Complete the statements by choosing the correct answer from the proof of theorem.

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The image of the triangle DEF are formed by the following coordinates: D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5).

In this problem we need to apply a rigid transformation known as dilation, whose definition is introduced below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

We need to determine the image of triangle DEF. If we know that D(x, y) = (2, - 2), E(x, y) = (4, - 2), F(x, y) = (1, - 4) and k = 1.5, then the images of the vertices of the triangle:

D'(x, y) = (4, - 2) + 1.5 · [(2, - 2) - (4, - 2)]

D'(x, y) = (4, - 2) + 1.5 · (- 2, 0)

D'(x, y) = (4, - 2) + (- 3, 0)

D'(x, y) = (1, - 2)

E'(x, y) = (4, - 2) + 1.5 · [(4, - 2) - (4, - 2)]

E'(x, y) = (4, - 2)

F'(x, y) = (4, - 2) + 1.5 · [(1, - 4) - (4, - 2)]

F'(x, y) = (4, - 2) + 1.5 · (- 3, - 2)

F'(x, y) = (4, - 2) + (- 4.5, - 3)

F'(x, y) = (- 0.5, - 5)

The coordinates of the image of triangle DEF are D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5)

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Mutually exclusive events are events that have no overlap between them and the sum of the probabilities of all mutually exclusive events is equal to 1.

What is the probability theory?

Probability theory is a branch of mathematics that deals with the study of random phenomena. It provides a mathematical framework for analyzing the likelihood of different outcomes in a given situation, and for making predictions about future events based on past data.

Things that have an equal chance of happening are known as equally likely events or mutually exclusive events. In probability theory, mutually exclusive events are events that cannot happen at the same time; if one event occurs, the other cannot.

In general, mutually exclusive events are events that have no overlap between them and the sum of the probabilities of all mutually exclusive events is equal to 1.

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Approximate volume of the figure formed with the cylinder with a dome of hemispherical shape with diameter 5 inch is equal to 170 cubic inch ( nearest whole number ).

Figure attached.

Diameter of the hemisphere = 5 inch

Height of the cylinder 'h'= 7 inch

Radius of the cylinder and hemisphere is same 'r' = 2.5 inch

Volume of the figure

= Volume of the cylinder + volume of the hemisphere

= πr²h + (2/3)πr³

= πr² [h + (2/3)r ]

Substitute the values we get,

= 3.14 ( 2.5 )² [ 7 + (2/3)2.5 ]

= 3.14 (6.25 ) [ 7 + 1.67 ]

= 170.14

= 170 cubic inch ( nearest whole number )

Therefore, the volume of the given figure of the cylinder with dome in hemispherical shape is equal to 170 cubic inch ( nearest whole number ).

The above question is incomplete, the complete question is:

The figure is made up of a cylinder and a hemisphere.

To the nearest whole number, what is the volume of this figure?

Use 3. 14 to approximate π. Round only your final answer to the nearest whole number. Enter your answer in the box in³ .

A 7 inch cylinder with a dome on top of it that has a 5 inch diameter.

Figure is attached.

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A proportional relationship between x and y is

y/x = 8.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

A table is given below.

To show a proportional relationship:

y/x = k

6/0.75 = 8

So, 1.5 x 8 = 12

And 3 x 8 = 24

So, the complete table is given in the attached image.

Therefore, the complete table is given in the attached image.

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The statement is False. The residuals will not necessarily add up to 0.

The residuals from a linear regression analysis are the differences between the observed values of the dependent variable and the predicted values of the dependent variable. Therefore, the sum of the residuals will depend on the data and the model used. If the model is a perfect fit, then the sum of the residuals will be 0. However, in most cases, the model will not be a perfect fit and the sum of the residuals will not be 0. Therefore, it is not true that the residuals from a linear regression analysis on any possible dataset (with more than 1 observation) will add up to 0.

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The population mean speed for automobiles and trucks on the length of road is equal to or less than 45 mph, which is the null hypothesis (H0) for this claim. This can be expressed mathematically as H0: = 45 mph.

where the population's average speed is represented by.

For this claim, the alternative hypothesis (H1) would be that the average population speed for vehicles and trucks on that section of road is higher than 45 mph. This can be expressed mathematically as H1: > 45 mph.

 A random sample of cars and trucks would be chosen in order to test the assertion, and their speeds would be recorded. The probability of detecting the sample mean speed under the null hypothesis would then be calculated using a statistical test like the t-test.

  Therefore,  the alternative hypothesis is that the population mean speed for vehicles and trucks on the length of road is more than 45 mph, whereas the null hypothesis is that it is equal to or less than 45 mph.

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The null hypothesis (H0) for this statement is that the population mean speed for cars and trucks on the length of the road is equal to or less than 45 mph. H0: = 45 mph is a mathematical expression for this.

where is the average speed of the population.

The alternative hypothesis (H1) for this assertion is that the typical population speed for cars and trucks on that stretch of road is greater than 45 mph. Mathematically, this is represented as H1: > 45 mph.

The population's average speed for cars and trucks travelling the distance of the road is equal to or lower than

To test the claim, a sample of randomly selected cars and trucks would be selected, and their speeds would be recorded. An analytical statistical test like the t-test would then be used to determine the chance of detecting the sample mean speed under the null hypothesis.

The null hypothesis is that the population's mean speed for cars and trucks on the length of the road is equal to or less than 45 mph, whereas the alternative hypothesis is that it is more than 45 mph.

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Answer:

512-358= how manyy miles left

Step-by-step explanation:

The expression that shows how many miles Graham has left to hike would be 512 - 358 = 154 miles.

Answer:

Step-by-step explanation:

well if you 6+2 is 8 that is the one's place then 50+10 is 60 that is the tens place then 300+100 is 400 that is the hundreds place and add 400+60+8 is 468

You Welcome

Answer: The answer is D

Step-by-step explanation: I hope this helps!

Answer:

All parts are below

Step-by-step explanation:

Seeing the first part asking for f(1). The equation f(n) lies above, so right here is plug and play. Since the n was replaced with a 1, we'll go to the table and find n and find 1.

Since it's the first number, looking directly below it is 7. Meaning f(1) = 7

Seeing common ratio... everytime n goes up 1, the value doubles, making r = 2/1 also known as 2

Now that we know f(1) is 7 and r is 2, we can plug it all in

f(n) = f(1) * (r)^n-1

Plugged in, it's f(n) = 7 * 2^1-1. 1-1 = 0. Anything to the power of 0 equals 1, which means 2^0 is 1

Multiplying 7 and 1 gives you 7, so

f(n) = 7

Geometric sequence is that f(n) = f(1) * (r)^n-1

Also known as f(n) = 7 * 2^n-1

For problem #2, try replicating all this and let me know how it goes

Answer:

∞

Step-by-step explanation:

I don’t know just think it out. That is the explaination

Answer: (2,7) does not satisfy the system:

x - 2y ≤ -16

6x - y < 5

We can substitute the point (2,7) into the inequalities and see if they are true:

2 - 2*7 ≤ -16

-10 ≤ -16 which is false

6*2 - 7 < 5

5 < 5 which is also false

Since (2,7) does not satisfy both inequalities of the system, it is the correct answer.

Step-by-step explanation:

The attached figures(a., b., c., d., and e.) define the line of symmetry of the given options.

a) In order to have exactly one vertical and one horizontal line of symmetry, you can shade one square in the first row and one square in the centre column.

b) To have only two lines of symmetry about the diagonals, you can shade two squares that are diagonally opposite from each other.

c) To have only one horizontal line of symmetry, you can shade one square in the centre row.

d) To have only one line of symmetry about a diagonal, you can shade two squares that are on the same diagonal.

e) To have no line of symmetry, you can shade two squares that are not on the same row, column, or diagonal.

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--The given question is incomplete; the complete question is

"Use Figure 2 to answer the problem.

Shade exactly two of the nine smaller squares so that the resulting figure has

a. Only one vertical and one horizontal line of symmetry.

b. Only two lines of symmetry about the diagonals.

c. Only one horizontal line of symmetry.

d. Only one line of symmetry about a diagonal.

e. No line of symmetry."--

The value of x for the expression is 73.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

log (4x + 8) - log 3 = 2

[ log (a/b) = log a - log b ]

So,

log (4x + 8) - log 3 = 2 can be written as,

log (4x + 8)/3 = 2

Taking exponents on both sides.

(4x + 8)/3 = [tex]10^2[/tex]

4x + 8 = 100 x 3

4x + 8 = 300

4x = 292

x = 73

Thus,

The value of x is 73.

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The value of the house before the increase is £1560

Now, According to the question:

Percentage basically means a part per hundred. It can be expressed in fraction form as well as decimal form. For example, if we say 25%, it means 25 out of 100. So, 25% is equivalent to the fraction 25/100 or 0.4 in decimal form.

"Information available from the question"

The value of a house increased by 6% the house then had a value of £26000.

Now, The expression will be :

= 6% of £26000.

= 6/100 × £26000.

= £1560

Hence,  the value of the house before the increase is £1560.

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A longitudinal study is a type of research method used to observe changes in a given behavior or condition of a group of individuals over a period of time.

It is especially useful in resolving the limitation of a traditional correlational study in that it can provide evidence for the direction of a possible causal relationship between the variables. This is because the study is conducted over a period of time, which allows for the observation of changes in the variables over time, and the ability to determine which variable is causing the changes in the other. This can be done through the use of statistical tests, such as regression analysis, which can measure the strength of the correlation and the direction of the relationship. Additionally, longitudinal studies can also help to determine whether the sample size is sufficient, as well as whether the relationship between the variables is statistically significant.

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The required sample size when its 95% error margin is 0.03 with 385 samples.

To estimate the proportion of people who want to purchase tablet PCs that cost more than $700 with a 95% confidence level and an error margin of 0.03, you can use the formula for sample size:

n = (z² * p * (1-p)) / E²

where:

Since we don't know the proportion of people who want to purchase tablet PCs that cost more than $700, you can use a reasonable estimate or a conservative estimate (e.g., 0.50) in the formula.

n = (1.96² * 0.50 * (1 - 0.50)) / (0.03²)

n = 384.16

The sample size required is 385.

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Answer: If a lawyer charges $120 an hour (or any fraction of an hour), how much is a bill for 3 hours and 20 minutes? What is the equation for this problem? answer choices l (x) = 120x l (x) = 120 [x-1] l (x) = 120 [x] l (x) = 120 [x+1]

Thank me later.

There are 384 ways to arrange these given letters as per the given situation.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another.

In this question, we have 2 ways where A and B (AB, BA) are next to each other and 2 ways where C and D (CD, DC) are next to each other.  2 ways where g and h (gh, hg) are next to each other and 2 ways where e and f (ef, fe) are next to each other.

The total number of arrangements is = 4! * 2 * 2 *2*2

The total number of arrangements is = 24 * 16

The total number of arrangements is = 384

Therefore, the Different ways to arrange these letters are 384.

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Kieran can ride at 235 yd per min if he continues at this rate.

Speed is a scalar quantity that refers to "how fast an object is moving."

Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time.

Given that, Kieran is horseback riding. His horse can trot 470 yards in 2 minutes and 1,410 yards in 6 minutes when Kieran is riding.

Here, the question is asking about how fast Kieran riding if he continues at the given rate,

That mean we have to find the speed,

Speed = distance / time

Therefore,

Speed of Kieran = 470 / 2

= 235 yd per min

Speed of Kieran = 1410 / 6

= 235 yd per min

Therefore, we can say kieran us riding for 235 yd in a minute.

Hence, Kieran can ride at 235 yd per min if he continues at this rate.

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Answer:

x = 25

Step-by-step explanation:

Following the Pythagoras' Theorem,

 a² + b² = c²

24² + 7² = c²

         c² = 625

       ∴ c = 25

In this case, since the length of the hypotenuse is x cm, ∴ c = x.

∴ x = 25

Answer:

25

Step-by-step explanation:

According to Pythagoras theorem,

H²=P²+B²

(H-hypotenuse, P-perpendicular, B-Base)

X²=24²+7²

X²=576+49

X²=625

X²=25²

X=25

After solving the polygon, the area of this polygon is 34.5 unit². So the option 2 is correct.

an equilateral triangle is a plane shape with at least three straight sides and angles, and usually five or more.

The total length of all the sides equals the perimeter. Apothem is the term for the segment that connects the midpoint of any perpendicular side to any side's midpoint in a polygon.

Let A(-6, -2), B(-5, 1), C(-1, 4), D(1, 1), E(5, 3), and F(1, -2) are the vertices of polygon.

Divide the shape into 3 triangles and 1 rectangle to get 4 separate forms.

Area of a triangle = 1/2 x base x height

Area of rectangle = length x width

Calculate the areas of each of the four forms, then add them.

The area of Shape 1 from the diagram:

Area of shape 1 = 1/2 × 1 × 3

Area of shape 1 = 1.5

Area of shape 2 = 1/2 × 6 × 3

Area of shape 2 = 9

Area of shape 3 = 1/2 × 3 × 4

Area of shape 3 = 6

Area of shape 4 = 3 × 6

Area of shape 4 = 18

Total Area = 1.5 + 9 + 6 + 18

Total Area = 34.5

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The complete question is given below:

Answer:

Amount = 800000×(1+0.09)2 = 800000×1.1881 = 946480

Amount = 800000×(1+0.1)2 = 800000×1.21 = 960000

The granite countertop costs $555

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

Length = 3 meters

Width = 1 meter

Cost per square meter = $185.00

The cost of the granite counter is then calculated as

Cost = Length * width * Cost per square meter

substitute the known values in the above equation, so, we have the following representation

cost = 3 * 1 * 185

Evaluate

cost = 555

hence, the cost is $555

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