!!TIMED!!PLEASE HELP

Answer:

10 x 10 = 100

20 x 5 = 100

500 - 200 = 300

so 300 rs

Answer:

3 weeks

Step-by-step explanation:

<333333

The Laplace transform of f(t) can be computed when f(t) = { t if 0 < t < 1, 1 if t > 1.

The Laplace transform of f(t) can be computed using the following equation:

\(\large F(s)=\int_{0}^{\infty}e^{-st}f(t)dt\)

Using the given function f(t) = { t if 0 < t < 1, 1 if t > 1.

Hence we have \(\large F(s)=\int_{0}^{\infty}e^{-st}f(t)dt =\int_{0}^{1}e^{-st}t\ dt+\int_{1}^{\infty}e^{-st}\ dt\)

Applying Laplace transform on f(t),

we get \(\large L(f(t))= \int_{0}^{1}e^{-st}t\ dt+\int_{1}^{\infty}e^{-st}\ dt\)

For the first integral \(\large \int_{0}^{1}e^{-st}t\ dt\)

The integration by parts formula is given by \(\large \int u \ dv = uv - \int v \ du\)

Taking,

\(u = t,\\\\ du = 1,\ \\dv = e^{-st} \\ v = -\frac{1}{s}e^{-st\)

we have

\(\large \int_{0}^{1}e^{-st}t\ dt=-\frac{t}{s}e^{-st}\Bigg|_{0}^{1}+\frac{1}{s}\int_{0}^{1}e^{-st}\ dt=-\frac{1}{s}\Bigg[e^{-s}-(1)\Bigg]+\frac{1}{s^2}(1-e^{-s})\)

The second integral,

\(\large \int_{1}^{\infty}e^{-st}\ dt=\frac{1}{s}\Bigg[0- e^{-s}\Bigg]=\frac{1}{s}e^{-s}\)

Thus, the Laplace transform of f(t) is given by,

\(\large L(f(t))= \int_{0}^{1}e^{-st}t\ dt+\int_{1}^{\infty}e^{-st}\ dt =\frac{1}{s^2}(1-e^{-s})-\frac{1}{s}e^{-s}\)

Therefore, \(\large F(s) = L(f(t)) = \frac{1}{s^2}(1-e^{-s})-\frac{1}{s}e^{-s}\),

when f(t) = { t if 0 < t < 1, 1 if t > 1.

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The probability that a sample of 81 painkiller pills has a mean weight less than 345 mg can be found using the properties of the normal distribution.

We are given that the weights of painkiller pills are normally distributed with a mean of 350 mg and a standard deviation of 7 mg. Since we are interested in the mean weight of a sample of 81 pills, we can use the Central Limit Theorem, which states that the sample mean of a large enough sample size will be approximately normally distributed, regardless of the underlying distribution.

To calculate the probability, we need to standardize the sample mean using the Z-score formula:

Z = (X - μ) / (σ / sqrt(n))

Where:

X is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

In this case, X = 345 mg, μ = 350 mg, σ = 7 mg, and n = 81.

Calculating the Z-score:

Z = (345 - 350) / (7 / sqrt(81))

Z = -5 / (7 / 9)

Z ≈ -5 / 0.777

Z ≈ -6.43

To find the probability corresponding to this Z-score, we can refer to the standard normal distribution table or use statistical software. Looking up the Z-score of -6.43 in the table, we find that the probability is extremely close to 0 (approaching 0 but not exactly 0).

The sketch of the density curve for the normal distribution would show a symmetric, bell-shaped curve centered at the mean of 350 mg. The probability we calculated represents the area under the curve to the left of the Z-score -6.43, which corresponds to the probability of the sample mean weight being less than 345 mg.

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The characteristics I notice in top 3 mobile banking vs. online banking. is that:

They are:

The top 3 banking activities done via online banking are:

Therefore, the characteristics I notice in top 3 mobile banking vs. online banking. is that:

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The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

There are a total of 15 people in the group. A committee of size 5 is to be chosen from a group of 7 men and 8 women randomly. Therefore, the sample space for this situation is 15C5 ways to choose 5 people from a total of 15 people. 15C5 = 3003 ways. That means there are 3003 ways to select 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003. That means the probability of selecting any one committee out of 3003 committees is 1/3003.To compute the probability of selecting any given committee, we first need to determine how many possible committees can be formed from the group of 15 people. The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

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Answer:

-5

Step-by-step explanation:

-2x+7>17

-2x>17-7

-2x>10

Divide both sides by -2

-2x<10

-2 -2

x<-5

Note:when dividing with a negative the signs changes

Answer:

Step-by-step explanation:

- 2x + 7 > 17

- 2x > 17 - 7

- 2x > 10

x < 10 ÷ ( - 2 )

x < - 5

x ∈ ( - ∞ , - 5 )

Answer:

it is a kite

Step-by-step explanation:

2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

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Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

15 ÷ 6 \(\frac{2}{3}\) ( change mixed number to an improper fraction )

= 15 ÷ \(\frac{20}{3}\)

• leave first number

• change division to multiplication

• turn fraction ' upside down '

= 15 × \(\frac{3}{20}\) ( cancel 15 and 20 by 5 )

= 3 × \(\frac{3}{4}\)

= \(\frac{9}{4}\)

= 2 \(\frac{1}{4}\) → B

Answer:

The probability of picking a yellow marble is 2/13

Step-by-step explanation:

First of all, we need to know the total number of marbles that are in the bag. To do this, we will have to add up all the marble colors together.

This will give us 6 + 2 +4+ 1 = 13 marbles in total.

The next step is to find the number of yellow marbles in the bag.

We can get this from the question. There are 2 yellow marbles in the bag.

The probability of selecting a yellow marble can be obtained by dividing the number of yellow marbles by the total number of marbles in the bag

This will give us 2/13.

Therefore, the probability of picking a yellow marble is 2/13

Answer: -3x+7

Step-by-step explanation: Good luck! :D

Answer:

-3x+7

Step-by-step explanation:

(5x-8x)+(2+5) Like terms together

(-3)x+7 Combine within each group

-3x+7 Simplify the signs in the product

-3x+7 Is your answer

Hope that helps :)

Roses will have six arrangements, while daisies will have ten.

Each bouquet will contain two flowers.

The highest common factor (HCF) between two or more numbers is two.

Amanda is arranging flowers in accordance with the question. She has 36 tulips, 20 daises, and 16 roses.

Every bouquet must have an equal amount of daisies, a reasonable quantity of roses, and an equal number of tulips.

The least common divisor, which is 2 instead of HCF, which would make it the least amount of arrangements, is the most arrangements she is capable of making.

based on the facts provided;

So,

20 daisies divided by 2 is 10 arrangements.

12 roses divided by 2 is 6 arrangements.

There will be 2 flowers in each kind of arrangements.

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Answer:

\(0\)

Step-by-step explanation:

\((-5)(0)(-x)(y)\\(-5)(-xy)(0)\\5x(-5y)(0)\\\)Anything multiplied by zero is zero:

\(0\)

Answer: 13

Step-by-step explanation:

Answer:

Set B has a greater speed ,because it has greater range

The length of the main diagonal, d, is the square root of 169, which is an integer:

d = √169 = 13

What is diagonal?

A diagonal is a line segment that connects two non-adjacent vertices or points in a polygon or a geometric shape.

To find an example of a three-dimensional rectangular box with integer dimensions and an integer diagonal for which no two of the three-dimensional measurements yield an integer diagonal in their plane, but the length of the main diagonal of the box is an integer, we can use the Pythagorean theorem.

Let's consider the following dimensions for the box: a = 3, b = 4, c = 12. These values are chosen such that a² + b² = 3² + 4² = 9 + 16 = 25, which is a perfect square.

Now, let's calculate the length of the main diagonal, which we'll denote as d, using the Pythagorean theorem:

d² = a² + b² + c²

d² = 3² + 4² + 12²

d² = 9 + 16 + 144

d² = 169

Therefore, the length of the main diagonal, d, is the square root of 169, which is an integer:

d = √169 = 13

So, in this example, the box with dimensions 3, 4, and 12 has an integer main diagonal length of 13. However, when we consider the two-dimensional diagonals within each plane, they do not yield integers.

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Answer:

Each pound of walnuts cost $3.50 and each pound of chocolate chips cost $1.50

Step-by-step explanation:

Let the cost of one pound of walnuts = $w

and the cost of one pound of chocolate chips = $c

Cost of 12 pounds of walnuts and 2 pounds of chocolate chips = $45

12w + 2c = 45 ------(1)

Cost of 3 pounds of walnuts and 5 pounds of chocolate chips = $18

3w + 5c = 18 --------(2)

Multiply equation (2) by 4 then subtract it from equation (1)

(12w + 2c) - (12w + 20c) = 45 - 72

-18c = -27

c = \(\frac{27}{18}\)

c = $1.5

Substitute c = 1.5 in equation (1),

12w + 2(1.5) = 45

12w = 45 - 3

w = \(\frac{42}{12}\)

w = $3.5

Therefore, each pound of walnuts cost $3.5 and each pound of chocolate chips cost $1.5

There are 176,851 ways to store the bikes in four distinct warehouses if the bikes are indistinguishable and the warehouses are distinct.

Let's consider the two scenarios separately:

Scenario 1: Bikes and warehouses are considered distinct.

In this case, each bike and each warehouse is considered distinct. We need to find the number of ways to distribute 100 distinct bikes among 4 distinct warehouses.

To solve this, we can use the concept of stars and bars. Imagine we have 100 stars representing the bikes, and we want to separate them into 4 distinct groups (warehouses) using 3 bars.

The number of ways to distribute the bikes can be calculated as (100 + 3) choose 3:

Number of ways = (100 + 3)C3 = 103C3 = (103 * 102 * 101) / (3 * 2 * 1) = 176,851.

Therefore, there are 176,851 ways to store the bikes in four distinct warehouses if the bikes and warehouses are considered distinct.

Scenario 2: Bikes are indistinguishable, warehouses are distinct.

In this case, the bikes are indistinguishable, but the warehouses are distinct. We need to find the number of ways to distribute 100 identical bikes among 4 distinct warehouses.

This problem can be solved using the concept of stars and bars again. Since the bikes are indistinguishable, the placement of bars doesn't matter.

We can think of it as distributing the 100 bikes into 4 distinct groups (warehouses) using 3 bars. The number of ways to do this can be calculated as (100 + 3) choose 3:

Number of ways = (100 + 3)C3 = 103C3 = (103 * 102 * 101) / (3 * 2 * 1) = 176,851.

Therefore, there are 176,851 ways to store the bikes in four distinct warehouses if the bikes are indistinguishable and the warehouses are distinct.

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Answer:

(- 1, 7 )

Step-by-step explanation:

Given the 2 equations

3x - 4y = - 31 → (1)

- 3x - 3y = - 18 → (2)

Adding the 2 equations term by term will eliminate x, that is

0 - 7y = - 49

- 7y = - 49 ( divide both sides by - 7 )

y = 7

Substitute y = 7 into either of the 2 equations and solve for x

Substituting into (1)

3x - 4(7) = - 31

3x - 28 = - 31 ( add 28 to both sides )

3x = - 3 ( divide both sides by 3 )

x = - 1

solution is (- 1, 7 )

Answer:

-1and 7 hope it helpssss

There are exactly 19 tents for 2-person tents.

According to the question

A group of 202 people went on an overnight camping trip, taking 60 tents with them.

Some of the tents held 2 people each, and the rest held 4 people each.

Let there be x tents for two people and y tents for four people

By writing the statements in mathematical form

We get two equations

2x + 4y = 202-------------(1)

x + y = 60------------------(2)

By solving using substitution method, we get

From equation 2, y = 60 - x

substituting y = 60 - x in equation 1

2x + 4(60 - x) = 202

2x + 240 - 4x = 202

-2x =  202 - 240

2x = 38

x = 38/2

x = 19

y = 60 - x = 60 - 19 = 41

y = 41

Therefore,

By using the equations using substitution method, There are exactly 19 tents for 2-person tents.

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Answer:

D

Step-by-step explanation:

Answer:

D. the distance between A and C

Step-by-step explanation:

|-2| = 2

its the distance between -2 and 0

The given set of functions {f_1(x) = x, f_2(x) = x^2, f_3(x) = 3x - 6x^2} is linearly independent on the interval (-infinity, infinity).

Linear independence of a set of functions means that no function in the set can be expressed as a linear combination of the other functions. In other words, for the set to be linearly independent, the only solution to the equation c_1f_1(x) + c_2f_2(x) + c_3f_3(x) = 0 should be c_1 = c_2 = c_3 = 0, where c_1, c_2, and c_3 are constants.

To determine if the given set is linearly independent, we need to check if there exist non-zero constants c_1, c_2, and c_3 such that c_1f_1(x) + c_2f_2(x) + c_3f_3(x) = 0 for all x in the interval (-infinity, infinity).

By substituting the functions into the equation and equating the coefficients of the terms with the same powers of x, we can solve for c_1, c_2, and c_3. If the only solution is c_1 = c_2 = c_3 = 0, then the set is linearly independent. In this case, the given set is indeed linearly independent as there is no non-zero solution to the equation, confirming that the functions are not dependent on each other.

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The exact length of the curve is:

\(L = 2(17^\frac{2}{3}-1 )\)

We have the values of x and y are:

x = 6 + 3\(t^2\)___eq.(1)

y = 8 + 2\(t^3\)___eq.(2)

We have to find the exact length of the curve.

Now, According to the question:

We have to use the formula for length L of the curve:

\(L=\int\limits^4_0 \sqrt{[x'(t)]^2+[y'(t)]^2} \, dt\)

Now, Differentiate both equations:

x' = 6t

y' = \(6t^2\)

Plug the values in above formula:

\(L=\int\limits^4_0 \sqrt{6^2t^2+6^2t^4} \, dt\)

By pulling 6t out of the square-root,

\(L=\int\limits^4_06t {\sqrt{1+t^2} } \, dt\)

by rewriting a bit further,

\(L=3\int\limits^4_02t ({1+t^2} )^\frac{1}{2} \, dt\)

by General Power Rule,

\(L = 3[\frac{2}{3}(1+t^2)^\frac{3}{2} ]^4_0\)

\(L = 2(17^\frac{2}{3}-1 )\)

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Answer:

y = \(\frac{4}{3}\) x + \(\frac{29}{3}\)

Step-by-step explanation:

assuming you require the equation of the perpendicular line.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{3}{4}\) x - 3 ← is in slope- intercept form

with slope m = - \(\frac{3}{4}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{3}{4} }\) = \(\frac{4}{3}\) , then

y = \(\frac{4}{3}\) x + c ← is the partial equation

to find c substitute (- 2, 7 ) into the partial equation

7 = - \(\frac{8}{3}\) + c ⇒ c = 7 + \(\frac{8}{3}\) = \(\frac{21}{3}\) + \(\frac{8}{3}\) = \(\frac{29}{3}\)

y = \(\frac{4}{3}\) x + \(\frac{29}{3}\) ← equation of perpendicular line

The equation of the line is y = (4x +29)/3

The line y = -3/4x - 3 has a slope of -3/4.  A line perpendicular to -3/4 has a slope of 4/3. So the slope of our new line will be 4/3.

We are told that the line goes through the point (-2, 7).  That is x = -2 and y = 7.  Now that we know a point and a slope, we can use the formula:

y2 - y1 = m(x2 - x1)

where,

x1 = -2

y1 = 7

m = 4/3 [slope]

Substituting in the formula,

y2 - 7 = 4/3(x2 - (-2))

y2 - 7 = 4/3*x2 + 4/3*2

3(y2 - 7) = 4(x2) + 8    

3y2 - 21 = 4(x2) +8

3y2 = 4(x2) + 8 +21

3y2 = 4(x2) +29

y2 = (4(x2) +29)/3          

Therefore, the equation of the line is y = (4x +29)/3

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The completer question is

'Find the equation of the line that is perpendicular to y = -3/4x - 3 and passes through the points (-2,7).'

The true condition about the dependent events, P(B|A) is not equal to P(B).

Dependent events in probability mean events whose occurrence of one affect the probability of occurrence of the other.

Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Also, Two events are said to be independent if the outcome or occurrence of the first does not affect the outcome or occurrence of the second so that the probability is not changed.

For independent events: P(A and B) = P(A) x P(B).

Recall that P(B|A) = P(A and B) / P(A) = P(A) x P(B) / P(A) = P(B).

Therefore, for dependent events, P(B|A) is not equal to P(B).

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Answer:

Option E is correct

Step-by-step explanation:

E. P(B|A) ≠ P(B)

Answer:

22.5 feet

Step-by-step explanation:

volume of a retangular shape: l*w*h

4.5*2.5*2=22.5

Answer:

Step-by-step explanation:

y= 2/3 x - 4

Answer:

p = 200 - 35w

Step-by-step explanation:

Let's represent

Number of weeks = x

Amount of money Jane still owes her parents = p

From the above question, we are told:

Jane borrowed = $200

She agreed to pay = $35 each week. Therefore, the equation that represents the amount of money Jane still owes her parents, p, after w weeks is written as:

p = $200 - $35 × w

p = 200 - 35w

Answer:f

(

x

+

2

)

=

3

x

+

2

Step-by-step explanation: