using the definition of compactness (i.e. you should not use the heine-borel theorem), show that the finite union of compact sets is compact.

Answer:

Step-by-step explanation:

Answer:

Area = 40

Perimeter = 26

Step-by-step explanation:

length = 8

width = 5

Area = 8 x 5 = 40

Perimeter = 2(8 + 5) = 26

Answer:

Width: 12 inches

Length: 4 inches

Step-by-step explanation:

To find the width and length, we can solve this algebraically while using the equation \(2(x+x+8)=32\)

Step 1: Simplify both sides of the equation.

Step 2: Subtract 16 from both sides.

Step 3: Divide both sides by 4.

Since x (4) is the length, the width is 12 inches.

Therefore, the width is 12 inches and the length is 4 inches.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

  ~ ren ⚘

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

The differential equation that represents the relationship is

     dT/dt = - k * ( T - T0 ) from the condtion - dT/dt ∝ ( T - T0 ).

Given:

The engine fluid temperature rate of change, dT/dt

- dT/dt ∝ ( T - T0 )   [proportional to the difference of the fluid's instantaneous temperature, T, and the fluid's original temperature, T0.]

The Differential Equation that represents the relationship.

The framework is already set, there is only one thing that changes the proportionality to an equation. And that is a proportionality constant.

Let's call it 'k'

Since this is a directly proportional set up, the constant 'k' will be multiplied to the term of ( T - T0 )

                            - dT/dt = k * ( T - T0 )

And to make this look like a typical equation, multiply both sides by a -1 to get:

                           ∴ dT/dt = - k * ( T - T0 )

As expected, this comes to represent the same thermodynamic effect you'd see in Newton's Law of Cooling; it is expected because most of all fluids exhibit this cooling effect when interacting with other fluids of differing temperatures.

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1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

Answer:

4.44

Step-by-step explanation:

Total NM of ball=18,

black ball=4

p(black,black)=?

p(black,black)=p(b)+p(b)

4/18+4/18=4.44ans

Answer:

Step-by-step explanation:

Total number of marbles:

Probability of black marble:

Without replacement, we have 3 black out of 17 total, then probability of the second black is:

Required probability is:

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

The normal approximation is not suitable as np<5.

Given,

mean = np

It turns out that if np and nq are both at least 5, the normal distribution can be used to approximate the binomial distribution. Additionally, keep in mind that a binomial distribution has a mean of np and variance of npq.

Hence apply the mean formula and get the value for np

n= 12 and p=0.

therefore mean = np

np = n×p

np = 12×0.3×

np = 3.6

np is less than 5.

nq=?

q=1-p

q=1-0.3

q=0.7

∴nq = 12 × 0.7

nq = 8.4

nq is not less than 5

It's remarkable that the normal distribution may accurately represent the binomial distribition when n, np and nq are large.

since here only nq is greater than five and np is less than five, therefore we conclude that normal approximation is not suitable.

Hence np<5 so normal approximation is not suitable.

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Clara can reach a height of 2.57 meters when she jumps.

Given information:

The ceiling in Clara’s basement is 2.75 meters high.

When Clara jumps she is 18 centimeters short of being able to touch the ceiling.

We can start by converting the height of the ceiling and Clara's jump to the same units, either meters or centimeters. Let's convert Clara's jump to meters:

18 centimeters = 0.18 meters

Now we can subtract Clara's jump from the height of the ceiling to find how high she can reach:

2.75 meters - 0.18 meters = 2.57 meters

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Answer:

14+y=3y+2

y-3y=2-14

-2y=-12

y=12÷2

=6

The positive difference between the greatest sum and the least sum in the sample space of the output of the two cubes is 10.

A sample space is a mathematical collection or set of possible outcomes of a random experiment. A sample space is represented by the symbol "S". The possible outcome of an experiment is called the events.

The greatest sum is obtained by adding the largest number on the first cube with the largest number on the second cube. The least number can be obtained by adding the smallest number on the first cube with the smallest number on the second cube.

The possible numbers displayed by the first cube are; 1, 2, 3, 4, 5, 6

The possible numbers displayed by the second cube are also; 1, 2, 3, 4, 5, 6

The positive difference between the greatest sum and the least sum in the sample space is therefore;

12 - 2 = 10

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Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

Step-by-step explanation:

-5(4)+2

-20+2

-18

just put 4 on the place of x

Answer:

\(=-18\)

Step-by-step explanation:

\(g(x)=-5x+2\)

Let's substitute 4 for x and solve.

\(g(4)=-5(4)+2\)

\(g(4)=-20+2\)

\(g(4)=-18\)

This means that when the function of \(g\) is 4, then the \(x\) value is \(-18\)

Hope this helps.

Answer:

1 ticket - $4.25

5 tickets - $21.25

Step-by-step explanation:

12.75/3=4.25 which is one ticket then take the price of one ticket and multiply it by 5, 4.25*5=21.25.

9514 1404 393

Answer:

Step-by-step explanation:

The area of each triangular face is given by the formula ...

  A = 1/2bh

The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...

  A = 1/2(8 cm)(6 cm) = 24 cm²

__

Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...

  A = LW

Bottom face: A = (20 cm)(8 cm) = 160 cm²

Back face: A = (20 cm)(6 cm) = 120 cm²

Sloped face: A = (20 cm)(10 cm) = 200 cm²

__

The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...

  (2×24 + 160 +120 +200) cm² = 528 cm²

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Hello There!

14/5 as a mixed number is

2+4/5

\(S^TE^PS^:\)

First, think about how many times we can stuff 5 into 14.

Turns out the answer is 2. So \(2\) is the whole part. However, we must also have a fraction.

Now that we know that we can stuff 5 into 14 twice, we think about what is left.

5*2=10 And we have 14. So 14-10=4

4 is the numerator of our fraction.

The denominator stays the same.

\(2\frac{4}{5}\)

Hope it helps and please mark Brainliest!

\(GraceRosalia\)

The function has three distinct real zeros.

The correct answer is A.

To determine the statement about the zeros of the graphed function, let's analyze the given information.

We have the following points on the graph:

(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)

Additionally, the function intercepts the x-axis at 1, 4, and 6 units.

To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.

From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.

These three x-values correspond to three distinct real zeros of the function.

The correct statement about the zeros of the graphed function is:

The function has three distinct real zeros.

The correct answer is A.

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After answering the presented question, we can conclude that triangle Therefore, the answer is A. 29 inches, since it falls within this range.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.  

So, for triangle ABC with sides AB, BC, and AC, we have:

\(AB + BC > AC\\16 + 25 > AC\\41 > AC\\BC + AC > AB\\25 + AC > 16\\AC > -9 \\AB + AC > BC\\16 + AC > 25\\AC > 9\\\)

So, the possible lengths of side AC are between 9 and 41 inches.

Therefore, the answer is A. 29 inches, since it falls within this range.

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Answer:

\(\mathbf{y(t) = t + \dfrac{7}{2}t^2 - \dfrac{2}{3}t^3+ ...}\)

Step-by-step explanation:

THe interpretation of the given question is as follows:

y'' + ky +  ry³ = A cos ωt

Let k = 4, r = 3, A = 7 and ω = 8

The objective is to find the first three non zero terms in the Taylor polynomial approximation to the solution with initial values y(0) = 0 ; y' (0) = 1

SO;

y'' + ky " ry³ = A cos ωt

where;

k = 4, r = 3, A = 7 and ω = 8

y(0) = 0 ; y' (0) = 1

y'' + 4y + 3y³ = 7 cos 8t

y'' = - 4y - 3y³ + 7 cos 8t     ---- (1)

∴

y'' (0) = -4y(0) - 3y³(0) + 7 cos (0)

y'' (0) = - 4 × 0 - 3 × 0 + 7

y'' (0) = 7

Differentiating equation (1) with respect to  t ; we have:

y''' = - 4y' - 9y² × y¹ - 56 sin 8t

y''' (0) = -4y'(0) - 9y²(0)× y¹ (0) - 56 sin (0)

y''' (0) = - 4 × 1  - 9 × 0 × 1 - 56 × 0

y''' (0) = - 4

Thus; we have :

y(0) = 0  ; y'(0) = 1  ; y'' (0) = 7 ; y'''(0) = -4

Therefore; the Taylor polynomial approximation to the first three nonzero terms is :

\(y(t) = y(0) + y'(0) t + y''(0) \dfrac{t^2}{2!} + y'''(0) \dfrac{t^3}{3!}+...\)

\(y(t) = 0 + t + 7 \dfrac{t^2}{2!} + \dfrac{-4}{3!} {t^3}+ ...\)

\(\mathbf{y(t) = t + \dfrac{7}{2}t^2 - \dfrac{2}{3}t^3+ ...}\)

Answer:

Infinite Solution!

Step-by-step explanation:

First, We simplify the right side.

Distribute -4, -4x-20=-4x-20

Now we add +4x to both sides, now the equation stands as -20=-20

We know when the solution is same #= same #. We have infinite solution!

Answer:

8.5=161.50;h= 19 hours

Step-by-step explanation:

So its pretty easy all you have to do is multiply 8.5 x 19

The prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.

Using prime factorisation, we shall consider the first five prime numbers which are; 2, 3, 5, 7, and 11.

45 cannot be divided by 2 without a remainder so we use 3;

45/3 = 15

15 can also be divided by 3 so;

15/3 = 5

3 cannot divide 5 without a remainder so we use 5;

5/5 = 1

hence;

45 = 3 × 3 × 5

45 = 3² × 5¹

Therefore, the prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

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The cost function is an illustration of an exponential growth function, and as such the price of product A is increasing

The cost function of product A is given as:

\(C(x) = 72(1.25)^x\)

An exponential function is represented as:

\(C(x) =ab^x\)

Where b is the rate of the function.

When b exceeds 1, then the function represents growth and the value of the function increases.

Hence, the price of product A is increasing

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Answer:

true, they can form a triangle.

Step-by-step explanation:

since, sum of two sides is greater than the third side in any case and the difference between two sides is smaller than the third one in all cases.