find the height of a cylindrical water vessel of diameter 1.4m if it holds 770L of water?​

Answer:

The formula for radioactive decay is:

N = N₀ * (1/2)^(t/T)

where:

N₀ = initial amount

N = remaining amount

t = time elapsed

T = half-life

Let's plug in the given values:

N₀ = 20 g

N = 15 g

T = 1620 years

15 = 20 * (1/2)^(t/1620)

Dividing both sides by 20:

0.75 = (1/2)^(t/1620)

Taking the logarithm base 1/2 of both sides:

log(0.75) = t/1620 * log(1/2)

Solving for t:

t = log(0.75) / log(1/2) * 1620

t ≈ 623 years

Therefore, it will take approximately 623 years for a 20 g sample of Radium to decay to 15 g.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

7^2+8^2 does NOT equal 9^2

A. (7,8,9)


Did the test just now.

Answer:

A

Step-by-step explanation:

Assume that the budget is n.

Now we are given that 120% of the budget is equal to $60.

This means that:

60 = 1.2n

Solve the equation for n to know the budget:

60 = 1.2n

n = 60 / 1.2 = 50

Based on the above calculations, Jada's budget is 50$

Answer:

58.8

Step-by-step explanation:

Answer:

a) 60 students

b) 50%

c) Yes

Step-by-step explanation:

a) Looking at the graph, we can see that on the column for 20-24 words, the number of students is 30, and for 25-29 words, the number of students is also 30. When you add the total up (30+30) you get 60 students.

b) there were 120 students, and a total of 60 students between 20-29.

60/120=0.5 or 50%.

50% of students spelled between 20 and 29 words correctly.

c) Yes, there is a normal distribution that is mostly symmetric because the center is the highest point, and the two sides fall down in a bell shape.  (a symmetric identifier is a bell shape)

And , the Y's variance is \(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)To find the mode of Y, we need to find the value of y that maximizes the joint probability density function\(f_X, Y(x,y).\)

To do this, we can fix x to be a particular value and then find the value of y that maximizes \(f_X, Y(x,y).\)

For any fixed x between 0 and 2, the function\(f_X, Y(x,y)\) is maximized at y = 1, since this is the only value of y that depends on x and maximizes the function\(cx^2y.\) Therefore, the mode of Y is 1.

To find the value of c that makes this a valid probability density function, we need to ensure that the integral of \(f_X, Y(x,y)\)over the entire sky-plane is equal to 1. We can set up the integral as follows:

integral from 0 to 2 of (integral from 0 to 2 of cx^2y dy) dx

= integral from 0 to \(2 of [c*x^2/2 * y^2]\)evaluated from 0 to 2 dx

= integral from 0 to 2 of \(c*x^2 x2d\)

= [2c/3 * x^3] evaluated from 0 to 2

= (16c/3)

For this to equal 1, we must have c = 3/16. Therefore, the valid probability density function is:

f_X,Y(x,y) = { (3/16)x^2y, 0 <= x <= 2, 0 <= y <= 2; 0, otherwise }

To find the expected value of Y, we need to integrate Y times the joint probability density function f_X, Y(x,y) over the entire xy-plane:

E[Y] = integral from 0 to 2 of (integral from 0 to 2 of y*f_X, Y(x,y) dy) dx

= integral from 0 to 2 of \([(3/16)*x^2/2 * y^2]\) evaluated from 0 to 2 dx

= integral from 0 to 2 of (3/16)*x^2 dx

= [3/16 * x^3/3] evaluated from 0 to 2

= 1

Therefore, the expected value of Y is 1.

To find the variance of Y, we first need to find the second moment of Y by integrating Y^2 times the joint probability density function f_X, Y(x,y) over the entire xy-plane:

E[Y^2] = integral from 0 to 2 of (integral from 0 to 2 of y^2*f_X, Y(x, y) dy) dx

= integral from \(0 to 2 of [(3/16)*x^2/3 * y^3]\) evaluated from 0 to 2 dx

= integral from \(0 to 2 of (3/8)*x^2 dx\)

= \([3/8 * x^3/3]\) evaluated from 0 to 2

= 2

And , the Y's variance is

\(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)

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Answer:

3/4

Step-by-step explanation:

Tan A = opp/adj

Tan A = 30/40

= 3/4

we know taht

the explicit formula for an arithmetic sequence is equal to

In this problem we have that

we know that

the distance betwee consecutive numbers is 6

that means

the common difference is d=6

substitute the value of d in the first equation

Equete both equations

Answer:

Its B square pyramid

Step-by-step explanation:

Because

Answer:

Cici O i itcivouvitci cc tfurx

Step-by-step explanation:

vhihciycyivovitcu

Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

Answer:

I think it's 4 gigabytes

Step-by-step explanation:

He only wants to pay 65$ and he already spends 45$ on his phone already. So you only have 20 dollars until his grand totaly of 65$ so 5x4= 20 so he can only use 4 gigabytes. Does that make sense? Hope I helped eheh

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Answer:

10 weeks

Step-by-step explanation: 100÷10=10

big brain

Answer:

9 week and 4 days

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

I hope this helps you!

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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The equivalent exponential equations are given as follows:

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

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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Answer:

Step-by-step explanation:

It is likely that Sharon's calculated mean time is the better estimate of the actual mean time for the whole class. This is because she collected data from a larger sample of the class (10 students) than Gerald (4 students). A larger sample size generally results in a more accurate estimate of the population mean.

It is more likely for the mean time calculated by Sharon to be better estimate than that of Gerald.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Given,

Mean time to complete the assignment taken from 4 students by Gerald = 38 minutes.

Mean time to complete the assignment taken from 10 students by Sharon = 32 minutes

Population size = 30 students

When the sample size is more closer to the population size, the sample mean would be more closer to the actual mean.

So Sharon's estimate is a better option.

Hence the estimate value of mean calculated by Sharon is more likely to be closer to the actual mean.

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Answer:

3(12 + 7)

Step-by-step explanation:

To find the GCF of 36 and 21, list out their factors.

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

21: 1, 3, 7, 21

The greatest factor which both numbers share is 3.

Therefore, you can factor 36 + 21 as 3(12 + 7)

Answer:

I can't understand your equation. Please rewrite it.

Step-by-step explanation:

Answer:

(1;1)

Step-by-step explanation:

1. if y=2x-1, then it is possible to substitute 2x-1 into the 2d equation:

5x-4(2x-1)=1, ⇒ 5x-8x+4=1, ⇔ -3x=-3, ⇔ x= 1;

2. if x=1, then y=2x-1=2-1= 1.

3. the required pair is (1;1)

Answer:

x = { - 2, \(\frac{1}{4}\) }

Step-by-step explanation:

8x² + 7x = 4x² + 2 ( subtract 4x² from both sides )

4x² + 7x = 2 ( subtract 2 from both sides )

4x² + 7x - 2 = 0 ← in standard form

to factor

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 2 = - 8 and sum = + 7

the factors are + 8 and - 1

use these factors to split the x- term

4x² + 8x - x - 2 = 0 ( factor the first/second and third/fourth terms )

4x(x + 2) - 1(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(4x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ( subtract 2 from each side )

x = - 2

----------

4x - 1 = 0 ( add 1 to both sides )

4x = 1 ( divide both sides by 4 )

x = \(\frac{1}{4}\)

solutions are { - 2, \(\frac{1}{4}\) }

Answer:

60

Step-by-step explanation:

\(45 \div \dfrac34=\dfrac{45}{1} \div \dfrac34=\dfrac{45}{1} \times \dfrac43=\dfrac{45\times 4}{1\times 3} =\dfrac{180}{3}=60\)

Answer:

60

Step-by-step explanation:

45:3/4=x:1

\(x = \frac{45 \times 1} { \frac{3}{4} } \\ x = 45 \times \frac{4}{3} \\ x = 60\)

The distance Mr. Jackson drove from when he got in his car to when he got home is 200.5 km.

Given:

The odometer reading when Mr.Jackson got in his car = 187,198.9 km

The odometer reading when Mr.Jackson got home = 187,399.4 km

An odometer is a device used to calculate the distance traveled by a vehicle.

To determine the distance Mr.Jackson drove we subtract the odometer readings from when he got home minus when he got into his car.

⇒ (187,399.4 - 187,198.9) km

⇒ 200.5 km

Therefore, Mr. Jackson drove 220.5 km from when he got in his car to when he got home.

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Answer:

m=0

Step-by-step explanation:

the slope is calculated using two points on the line and the formula

m = (y2 - y1) ÷ (x2 - x1)

where

x1 and y1 are the coordinates of point 1

x2 and y2 are the coordinates of point 2

for example, you can take

point 1 = (x1;y1) = (-2;3)

point 2 = (x2;y2) = (-1;3)

then your slope is

m = (3 - 3) ÷ (-1 - (-2)) = 0

notice that x1 is always at the left of x2 on the x axis

and it makes sense that your slope is 0 because for each x your y is the same

Answer:

the total of rugs is 8

Step-by-step explanation:

6 for $22 means he sold 6 of them and made $132

then take 168 - 132 and we get 36

the rest are 16 each so 2 rugs was the maximum.

Answer:

.25 per orange

Step-by-step explanation:

2.5/10=.25

Answer:

x≥2 and x<2 : ∅

x≥2 or x<2 : All real numbers

x≤2 and x≥2 : 2

Step-by-step explanation:

the first one must follow both conditions, so no number would work.

the second one works with any number, so all real numbers.

the third one has only one condition that works, 2