You have $350 in your bank account. One weekend, you spend 20% of your money on new
clothes. The next weekend you work to earn some money and increase your savings by 20%.
How much money do you have in your account now?

We can expect approximately 144 students in Chloe's school to own pets. The answer is 144.

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

Based on the simulation results, we can count the number of times the number cube landed on digits 1, 2, 3, and 4, which represent the number of students who own pets. We add up these counts and divide by the total number of rolls (25) to get the proportion of rolls that resulted in a student owning a pet:

(5+1+4+4+3+3+2+2+2+1+5+2+1) / 25 = 0.6

So, approximately 60% of the rolls resulted in a student owning a pet. If we assume this proportion holds for the entire school, we can estimate the number of students who own pets out of the total number of students in the school:

Number of students who own pets = Proportion of students who own pets * Total number of students

Number of students who own pets = 0.6 * 240 = 144

Therefore, we can expect approximately 144 students in Chloe's school to own pets. The answer is 144.

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Triangle ABC is similar to triangle ADE by AA test of similarity

Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.

here, we have,

There are different types of similarity test by which we can prove the similarity of triangles.

We are given that BC is parallel to Line DE

As the lines are parallel the respective angle are corresponding angles

hence Angle D = Angle B

And Angle E = Angle C

And both triangle have angle A as common angle

By AA test of similarity we can say that the two triangles are similar

Hence by AA test similarity the two triangles are similar

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Answer:

9.42 or 3pi

Step-by-step explanation:

equation of a circle is 2*pi*r

2r is d which is 3 so the answer would be 3pi which equals about 9.42

Answer:

Step-by-step explanation:

The formula you need for this is

\(A(t)=P(1+\frac{r}{n})^{nt}\)

where A(t) is the final amount after the compounding is done, P is the initial investment, r is the interest rate in decimal form, n is the number of times per year that the money is compounded, and t is the time in years. Filling in accordingly:

\(1708=1170(1+\frac{r}{4})^{(4)(6)}\)

First things first. Simplify by division and then multiply the n by the t to get the exponent:

Divide 1708 by 1170 to get the equation:

\(1.45982906=(1+\frac{r}{4})^{24}\)

Undo the 24th power by taking the 24th root of both sides to get:

\(1.015888202=1+\frac{r}{4}\) Now subtract 1 from both sides to get

\(.0158882024=\frac{r}{4}\) Multiply both sides by 4 to finish it off and get that

r = .0635528 but since we want the percentage, we move the decimal 2 places to the right and round to r = 6.4% which is choice A.

We are given the following equation

We are asked to solve the equation for y.

Solving for y means that we have to separate the variable y.

Step 1:

Subtract 3x from both sides of the equation

Answer:

5 sqrt(11)

Step-by-step explanation:

sqrt(99) + sqrt(44)

sqrt(9*11) + sqrt(4*11)

sqrt(9)sqrt(11) + sqrt( 4) sqrt(11)

3sqrt(11) + 2 sqrt(11)

5 sqrt(11)

The probability p that exactly two of the n people in the party will have the same birthday is given by the expression:

\($p=1 - \frac{(365!)}{(365-n)!365^n\times(n-1)!}$\)

where n represents the number of people at a party, and the probability of each person having the same birthday is considered to be 1/365 for each person.

Let's see how to derive the above expression using the concept of probability.

If n is the total number of people at the party, then the probability that none of them have the same birthday is given by:

\($\frac{365}{365} \times \frac{364}{365} \times \frac{363}{365} \times ...\times\frac{(365-n+1)}{365}$\)

$= \frac{_{365}P_{n}}{365^n}$where $_{365}P_{n}$ \($= \frac{_{365}P_{n}}{365^n}$where $_{365}P_{n}$\) denotes the number of permutations of n distinct objects chosen from a set of 365 distinct objects.

Now, let's calculate the probability that at least two people will have the same birthday. We can do this by subtracting the probability that no two people have the same birthday from 1.

\($p = 1 - \frac{_{365}P_{n}}{365^n}$\)

Next, we can simplify this expression further by using the formula for n-1 objects to be distributed among r bins:

\($\frac{(n-1)!}{(r-1)!(n-r)!}$\\\)

In this case, we want to distribute n people into 365 bins (each representing a unique birthday). Since we only care about the case where exactly 2 people share the same birthday, we can choose the 2 people first in \($^nC_{2}$\) ways, and then distribute the remaining n-2 people into 365 bins in \($365^{n-2}$\) ways.

Therefore, the probability that exactly 2 people will have the same birthday is given by:

\($p = \ ^{n}C_{2} \times \frac{(365^{n-2})}{365^n}$\)

\($= \frac{n!}{2!(n-2)!} \times \frac{1}{365^2}$\)

\($= \frac{n(n-1)}{2} \times \frac{1}{365^2}$\)

Substituting this value in the previous expression, we get:

\($p = 1 - \frac{(365!)}{(365-n)!365^n\times(n-1)!}$\)

Therefore, the probability p that exactly two of the n people in the party will have the same birthday is given by:

\($p=1 - \frac{(365!)}{(365-n)!365^n\times(n-1)!}$\)

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Answer:

B. 31°; 106° and 43°.

Step-by-step explanation:

1) the rule is:

(5x-7)+(3x+1)+(11x-4)=180°;

2) if to solve this equation, then x=10°;

3) if x=10, then after the substitution the answer is 43;31;106.

1. There will be $102, 826 in the account in 25 years.

2. The total amount of money you will put into the account is $60, 000

3. The total interest that you would have earned is $42,826.

For us to calculate the future value of the account in 25 years, we shoud use the formula; FV = P x (((1 + r)^nt - 1) / r)

When we insert the values, it will be

FV = 200 x (((1 + 0.04/12)^(12 x 25) - 1) / (0.04/12))

= 102, 825. 9. If we round this up, we should get

$102, 826

For us to calculate the total amount of money you put into the account, we should us the formula;

Total Deposits = Monthly Deposit x Number of Months

If we insert the values it wil be

200 x (25 x 12)

60,000

Lasty, if we are to find the total interest earned:

Total Interest = Future Value - Total Deposits

$102, 826 - 60,000

=  $42,826

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A strategy canvas is a visual framework used to analyze and compare the strategic positioning of different companies or products within an industry.

It is a tool developed by W. Chan Kim and Renée Mauborgne, the creators of the Blue Ocean Strategy, to help organizations identify and create new market spaces by differentiating their offerings.

The strategy canvas consists of two axes: the horizontal axis represents the key factors that the industry competes on, and the vertical axis represents the offering level or degree of offering provided for each factor. By plotting the current state of competing products or companies on the canvas, organizations can gain insights into the competitive landscape and identify areas of opportunity for innovation and differentiation.

The strategy canvas helps visualize the competitive factors that are driving the industry and highlights areas of convergence or similarity among existing offerings. It allows organizations to identify untapped market spaces where they can create unique value propositions and redefine the competitive boundaries.

To use a strategy canvas effectively, organizations need to analyze the key factors that customers value in the industry and assess the relative performance of their offerings compared to competitors. By identifying the factors where they are underperforming and overperforming, organizations can focus on enhancing their value proposition by reallocating resources, investing in areas of differentiation, and eliminating or reducing elements that do not create significant customer value.

A strategy canvas is a powerful tool for strategic analysis and innovation. It helps organizations visualize the competitive landscape, identify areas for differentiation, and create new market spaces by providing a clear understanding of customer preferences and the competitive factors that drive industry success.

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The correct answer is c. Lq divided by μ.

In queuing theory, Lq represents the average number of units waiting in the queue, and μ represents the service rate or the average rate at which units are served by the system. The average time a unit spends in the waiting line can be calculated by dividing Lq (the average number of units waiting) by μ (the service rate).

The formula for the average time a unit spends in the waiting line is given by:

Average Waiting Time = Lq / μ

Therefore, option c. Lq divided by μ is the correct choice.

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Julius is correct that it will take less time for them to mow the lawn when working together.

Both Julius and Marcos have different predictions on how long it will take them to mow the lawn when working together. Marcos believes it will take them 5 hours, while Julius thinks it will take less time. Without any calculations, we can determine who is correct based on the concept of work rates.

When working alone, Julius takes 4 hours to mow the lawn. This means his work rate is 1 lawn per 4 hours. Similarly, Marcos takes 6 hours to mow the lawn alone, so his work rate is 1 lawn per 6 hours.

When working together, their work rates are combined. To find the total work rate, we add their individual work rates: 1/4 + 1/6 = 5/12.

This means that together, Julius and Marcos can mow 5/12 of the lawn in one hour. To mow the entire lawn, they need to complete 1 whole unit of work.

Since their combined work rate is 5/12, it will take them less than 5 hours to finish mowing the lawn. Therefore, Julius is correct in saying that it will take them less time than what Marcos predicted.

In conclusion, Julius is correct that it will take less time for them to mow the lawn when working together.

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The critical number of the given function {g(t) = 3t ㏑t} is t = e⁻¹

Assume f(x) is a function with an open interval (a,b). If c is in the interval (a,b) and either f'(c) =0 or f'(c) does not exist, we say c is a critical number of f(x).

Each local minimum as well as maximum of f(x) must correspond to a critical number of f(x). The opposite is not truly the case: not all critical number of f(x) must correspond to a local maximum as well as minimum of f(x).

Now, as per the question;

It should be noted that the broadest possible domain of {g(t) = 3t ㏑t} is given in the set {t : t > 0} as ㏑t can not be defined for negative numbers of zero.

Now, differentiate the given function with respect to t.

\(g^{\prime}(t)=\frac{d}{d t}(3 t \ln t)\)

Apply the product rule of differentiation;

\(\begin{aligned}&=\left[\frac{d}{d t}(3 t)\right] \ln t+3 t \frac{d}{d t}(\ln t) \\&=3 \ln t+3 t \frac{1}{t} \\&=3 \ln t+3 \\&=3(\ln t+1)\end{aligned}\)

Now, put this value of g'(t) = 0 for finding the critical points.

0 = g'(t)

  = 3(㏑t + 1)

Divide equation by 3.

0 = ㏑t + 1

㏑t = -1

Taking anti log;

t = e⁻¹ (critical value)

Therefore, the critical value obtained for the given function is  t = e⁻¹.

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The complete question is-

how many critical numbers does {g(t) = 3t ㏑t} have? note: critical numbers must be within the domain of the function.

Answer:

Stationery section will be 4 feet wide.

Step-by-step explanation:

Total area of bookstore = 288 sq ft

Area to be devoted to stationery = \(\frac{1}6\) of total area = \(\frac{1}{6} \times 288 = 48\ sq\ ft\)

Length of stationery section = 12 ft

To find:

Width of stationery section = ?

Solution:

First of all, let us have a look at the area of rectangle:

\(A = Length \times Width\)

Here, we are given the length for stationery section and area of stationery section has been calculated above.

And we have to find the Width of stationery section.

So, let us put the two values to find the third value.

\(\Rightarrow 48 = 12 \times Width\\\Rightarrow Width = \dfrac{48}{12}\\\Rightarrow \bold{Width = 4\ ft}\)

So, the answer is:

Stationery section will be 4 feet wide.

Given that 3 unit factor growth is 1.65

Then 1 unit growth factor = (1.65)^1/3 = 1.181

2 unit growth factor of F  = 1.396

And 1/2 unit growth factor = (1.65)^0.5/3 = (1.65)^0.53/3 = (1.65)^1/6

                                              = 1.0875

or 1/2 unit growth of factor f = 1.0875

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The original price of the book is $39

Mark up is 7.5% . This means there is an increase in price

7.5% increase is 100 + 7.5

= 100 + 7.5

107.5%

To calculate the discount dollar

The mark up price is

107.5/100 x $39

= 1.075 x 39

= $ 41.925

The discount dollar amount = Marked up price - Original price

= $41.925 - $39

= $2.925

The discount dollar amount is $2.925

The selling price is $41.925

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer:

8 in 26 i think.

Step-by-step explanation:

im pretty sure if it is supposed to be less than five then you need to add the number of digits and those are the odds. pretty sure.

5%

Did the quiz and got it right, explanation given:

Determine the size of the sample space. Look for how many of those outcomes result in the dice adding up to either a 4, 3, or 2. Then use the addition rule to get the probability.

Answer:

The general equation for a line (written in the slope-intersect form) is:

y = f(x) = a*x + b

Such that the line is already written in function notation.

Where a is the slope, and b is the y-intersect.

If a line passes through a point (x₁, y₁) and (x₂, y₂), the slope can be written as:

y = (y₂ - y₁)/(x₂ - x₁)

We know that the line in the graph passes through the points:

(-2, -1) and (2, 0)

Then the slope of the line will be:

a = (0 - (-1))/(2 - (-2)) = 1/4

Then the function for the line will be something like:

y = f(x) = (1/4)*x + b

Now we want to find the value of b.

Because we know that this function passes through the point (2, 0), this means that:

f(2) = 0 = (1/4)*2 + b

We can solve that for b:

0 = 2/4 + b

-2/4 = b

Then the function for the line is:

y = f(x) = (1/4)*x - 2/4

1. What is an equation of the line in point-slope form?

y+1=[1/3][x+2]

2.How can the point-slope form be written in function notation?

f[x]=[1/3]x-[1/3]

Therefore, the equation of the tangent to the curve at the point (0, 0) is y = -x.

To find the equation of the tangent to the curve at the point corresponding to the parameter t = -1, we need to find the slope of the tangent and the coordinates of the point.

Given:

x = t^3 + 1

y = t^4 + t

Substituting t = -1 into the equations, we get:

x = (-1)^3 + 1 = 0

y = (-1)^4 + (-1) = 0

So, the point corresponding to t = -1 is (0, 0).

To find the slope of the tangent, we take the derivative of y with respect to x:

dy/dx = (dy/dt)/(dx/dt) = (4t^3 + 1)/(3t^2)

Substituting t = -1 into the derivative, we get:

dy/dx = (4(-1)^3 + 1)/(3(-1)^2) = -3/3 = -1

The slope of the tangent at the point (0, 0) is -1.

Using the point-slope form of the equation of a line, we can write the equation of the tangent:

y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Substituting the values, we have:

y - 0 = -1(x - 0)

Simplifying, we get:

y = -x

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Answer:$25.80

Step-by-step explanation:

6.45/5 = 1.29

1.29 x 20 =25.80

Step-by-step explanation:

Hey there!

The points through which the line passed are; (-3,-7) and (12,3).

Note: Use double point formula.

\((y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)\)

Keep all values.

\((y + 7) = \frac{3 + 7}{12 + 3} (x + 3)\)

Simplify it.

\((y + 7) = \frac{10}{15} (x + 3)\)

\((y + 7) = \frac{2}{3} (x + 3)\)

\(y + 7 = \frac{2}{3} x + 3 \times \frac{2}{3} \)

\(y = \frac{2}{3} x + 2 - 7\)

\(y = \frac{2}{3} x - 5\)

Therefore, the required equation is; y = 2/3x - 5.

Hope it helps...

Step-by-step explanation:

.5 / 1.5    is  1/3       (1/3)^2  = 1/9

Answer: 0.09

Step-by-step explanation:

0.5 ÷ 1.5 = 0.3 0.3squared = 0.09

Answer:

I'll give you some clues in the solution. Please read them so you can do the rest faster.

Solution:

First thing you do is write the vertex. The vertex is basically the last number in the absolute value bars and the number outside of them (to the right of the bars). The vertex is the opposite of the last number in the absolute value brackets and if there is no number to the right, assume it is 0.

We start at (2,0).

The domain is 99% of the time all real numbers. Write that for domain.

The range is the y value where things start to increase (the y value of the vertex). The range is 0.

The type of function is absolute value function btw

The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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Answer:

Volume = 261.8 cm³

Surface area = 254.2 cm²

Step-by-step explanation:

To calculate the volume of the cone, we have to use the following formula:

\(\boxed{V = \frac{1}{3} \pi r^2 h}\),

where:

V ⇒ volume

r ⇒ radius = 5 cm

h ⇒ height = 10 cm

Using the above formula and the provided measures, we get:

V = \(\frac{1}{3}\) × π × (5)² × 10

    = \(\frac{1}{3}\) × π × 25 × 10

      = 261.8 cm³

In order to calculate the surface area of the cone, we have to use the following formula:

\(\boxed{SA = \pi r^2 + \pi r l}\)

where:

SA ⇒ surface area

r ⇒ radius = 5 cm

l ⇒ slant length = \(\sqrt{r^2+h^2}\) = \(\sqrt{5^2+10^2}\) = 5√5 cm

Using the formula,

SA = π × (5)² + π × 5 × 5√5

     = π × 25 + π × 25√5

     = 254.2 cm²

\( \tt{}(8 \times 104)(4.5 \times 10 - 1)\)

\(\tt{}(832)(45 - 1)\)

\(\tt{}(832)(44)\)

\(\tt{}832 \times 44\)

\(\tt{}36608\)