What is the meaning of "\(\exists p_{1},...,\exists p_{n} (p=p_{1},...,p_{n})\)"?

Answer:

2

Step-by-step explanation:

I think

Answer:

p^(m+n)

Step-by-step explanation:

p^m * p^n

We know that when they are multiplied when the bases are the same, we add the exponents

p^(m+n)

Answer:

See attached

Expressions matching the properties

The associative property:

The commutative property:

Distributive property:

Answer:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Step-by-step explanation:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Answer: x = 8 1/2 i believe

Step-by-step explanation:

Answer: 40 one flavor cakes and 60 other favor of cakes

Step-by-step explanation:

Let x = Number of one flavor of cakes

y = Number of other flavor of cakes

According to the question

\(x+y=100...(i)\\5x+10y= 800...(ii)\)

Divide (ii) by 5 , we get

\(x+2y= 160...(iii)\)

Eliminate (i) from (iii), we get

\(y=60\)

Put this in (i), we get

\(x+60=100\Rightarrow\ x=40\)

Hence, 40 one flavor cakes and 60 other favor of cakes were donated.

The balloons of each color that Marty inflated are:

This is further explained below.

Generally, the equation for the statement is mathematically given as

w= r+225

w - 225 = r

Therefore

w - 116 = b

Where

r + w + b = 1147

(w - 225 )+w +( w - 116)=1147

3w = 1147 + 341

w = 496

In conclusion, For Red

w - 225 = r

496 - 225 = r

r=271

Marty inflate red 271 ballons

For  blue

w - 116 = b

496  - 116 =380

b=380

Marty inflate red 380 ballons

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Answer:

try all the square roots and wichever gets to 0.58(rounded) is your answer

Step-by-step explanation:

The volume of the given cylinder is 11304 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, radius of a cylinder is 20 cm and depth of a cylinder is 9 cm.

We know that, the volume of a cylinder is πr²h.

Now, volume = 3.14×20²×9

= 3.14×400×9

= 11304 cm³

Therefore, the volume of the given cylinder is 11304 cm³.

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Answer:

5089.4cm

Step-by-step explanation:

9² x pi x 20 =5089.3800

The method of multiplication shown is (a) Ancient Egyptian Method

This involves taking the product of at least two factors which could be numbers, expressions or both

From the method shown, we can see that a factor is multiplied by multiples of 2 (i.e. doubling), till it reaches a maximum

This method is associated with the Egyptian.

Hence, the method of multiplication is (a) Ancient Egyptian Method

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a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Answer: I think it is 336x but tries it

Step-by-step explanation:

y = 9x - 7

When x = 8

y = 9.8 - 7

y = 72 - 7

y = 65

When x = 6

y = 9.6 - 7

y = 54 - 7

y = 47

When x = 7

y = 9.7 - 7

y = 63 - 7

y = 56

When x = -8

y = 9.(-8) - 7

y = -72 - 7

y = -79

When x = 4

y = 9.4 - 7

y = 36 - 7

y = 29

The number of tablets that should be taken each day by the patient who needs Synthroid is 1 tablet.

To find the number of tablets of Synthroid that should be taken, you convert the requirements from micrograms ( μg ) to milligrams ( mg).

1 milligram = 1, 000 micrograms ( μg )

25. 0 μg in milligrams is therefore:

= 25 / 1, 000

= 0. 025 mg

This means that the number of tablet to take is:

= Mg requirement / Mg of tablet

= 0. 025 / 0. 025

= 1 tablet

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

Jupiter will travel 2,400 miles in 5 minutes.

Step-by-step explanation:

There is 60 seconds in a minute, so...

8x60=480

480x5= 2400

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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Answer:

-10

Step-by-step explanation:

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

Incorrect statement

Step-by-step explanation:

Its wrong because when we add 2x on both sides we get

2x+7=2x+20

Then, subtract 2x

7=20

This statement is incorrect and therfore wrong

Answer: you cant

Step-by-step explanation:

Answer:

A' = (-4, 7)

B' = (3, 5)

C' = (1, 2)

Step-by-step explanation:

The question is asking you to translate the function by adding 4 to the x-value of each point and 2 to the y-value of each point.

I didn't double-check my math, but since the question is asking for an ordered pair, this should be correct.

The figure consists of a square and 4 semicircles.

From the information given,

length of each side of the square, s = 8

Area of square = s^2

Area of square = 8^2 = 64

diameter of semicircle = 8

radius = diameter/2 = 8/2

radius = 4

Area of semicircle = 1/2 x π x radius^2

Area of each semicircle = 1/2 x π x 4^2 = 8π

Area of 4 semicircles = 4 x 8π = 32π

Area of figure = 64 + 32π

Substituting π = 3.14,

Area of figure = 64 + 32 x 3.14 = 64 + 100.48

Area of figure = 164.5

Answer:

The principal square root of a non-negative real number is the positive square root. For example, the principal square root of 25 is 5, since 5^2 = 25.

When solving radical polynomials, the principal square root is used because it is the most commonly used square root. In many contexts, including mathematical and scientific calculations, the principal square root is the default choice unless otherwise specified. Additionally, when working with radical expressions, we often simplify expressions by taking the principal square root, as it can help us to simplify calculations and express answers more clearly.

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Given: Two inequalities below

Callculate the y intercept for equation 1

Calculate the x-intercept of equation 1

The graph below showed the solution of the inequalities

The graph above showed the solution of inequalities

y>2 with coordinate (0, 2) is a horizontal line with dash lines

The coordinate of y-3x> 6 is a traight line with dash lines

The solution is as shown in the diagram above

Answer:

19 6/8 or 19 3/4

I’m not sure if you want the smallest possible fraction or not. If you don’t know just put the second one. K.

Carol should decide on the average of the two anticipated numbers. She must thus decide to select  \(\frac{13}{24}\).

Probability is an area of mathematics that examines the possibility that a particular event will occur. In most cases, the probability values for the specified experiment are specified between a range of numbers. The values fall in the range of 0 and 1. A negative number cannot be the probability value. Experimental probability, also known as Empirical probability, is based on actual experiments and adequate recordings of the happening of events. For Alice's number, the anticipated value is \(\frac{1}{2}\) and the expected value of Bob's number is \(0.5*[\frac{1}{2} +\frac{2}{3} ]\). Carol should pick the middle between these two projected figures to increase her chances of winning. She must thus choose \(0.5*[\frac{1}{2} + \frac{7}{12} ]\) = \(\frac{13}{24}\). Alternatively, once we recognize that the answer lies in the interval \((\frac{1}{2},\frac{7}{12} )\), it is straight forward that she has chosen the right number.  

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