A man went to a post office to buy some stamps. If he bought x, 50 cents stamps and y, 25 cents stamps, the total cost would have been $3.50. If, however, he bought twice as many 50 cents stamps and half as many 25 cents stamps, then the total cost would have been $4.75. Evaluate x and y.​

Answer:

5.41

Step-by-step explanation:

The derivative of the function f(x) is:

f'(x) = (sinx +  2cosx)/(2√x)  

Differentiation involves finding the derivative of a function. The derivative of a function represents the rate of change of the function with respect to its input variable.

For any function of the form f(x) = u(x)·v(x). The derivative is given by:

f'(x) = u'(x)·v(x) + v'(x)·u(x)

f(x) = (√x)·sinx can be written as f(x) = [tex]x^{\frac{1}{2} }[/tex] . sin x

Thus, if f(x) = (√x)·sinx, the derivative will be:

f'(x) = (1/2)[tex]x^{-\frac{1}{2} }[/tex]sinx + [tex]x^{\frac{1}{2} }[/tex]cosx

f'(x) = sinx/(2√x) + cosx/(√x)  

f'(x) = (sinx +  2cosx)/(2√x)  

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Answer:~471.24 m

Step-by-step explanation:

1). The formula is V=πr²[tex]\frac{h}{3}[/tex]

2). Substitute: V= π5²[tex]\frac{18}{3}[/tex]

Which will give you 471.2389 but rounded approximately 471.24.

Answer:

t=18

Step-by-step explanation:

3=54/t

times both sides by t

3t=54

then divided by 3 on both sides to get t by itself

t=54/3

to simplify this it's

t=18

Answer: 18/49

Step-by-step explanation:

P(Yellow) = 9/14

= 9/14 • 9-1/14

=9/14 • 8/14

= 72/196 or 18/49

Check the picture below.

so we can look at this, this way, let's find P which is 1/5 of the way from A to B, and also find R which is 3/5 of the way from A to B.

[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{1}{5}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{7}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 5 ~~,~~ -10 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{2}~~+~~\frac{1}{5}(5)~~,~~\stackrel{y_1}{6}~~+~~\frac{1}{5}(-10) \right)\implies \stackrel{\textit{\LARGE P} }{(3~~,~~4)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{3}{5}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{7}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 5 ~~,~~ -10 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{2}~~+~~\frac{3}{5}(5)~~,~~\stackrel{y_1}{6}~~+~~\frac{3}{5}(-10) \right)\implies \stackrel{ \textit{\LARGE R} }{(5~~,~~0)}[/tex]

Answer: 4/20; 10/20

Step-by-step explanation:

There are 20 marbles in total and 4 are blue;

Numerator: 4

Then the total is at the bottom!

Denominator:20

Same as for red marbles.

Have a lovely day!!

The probability you randomly pick one marble that is not red is 7/10.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

Red = 6 marbles

Blue = 4 marbles

Yellow = 10 marbles

Total marbles= 6 +4 + 10 = 20

So, the probability of getting NO red

= (20 - 6) / 20

= 14 / 20

= 7/ 10

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The surface area of the rectangle is 14 square millimeters (mm²).

Given that

Dimension = 7mm  by 2mm

The surface area of a rectangle is calculated by multiplying its length by its width.

Therefore, the surface area of a rectangle with a length of 7mm and a width of 2mm

So, we have

Surface area = length x width

Surface area = 7mm x 2mm

Surface area = 14mm²

Therefore, the surface area of the rectangle is 14 square millimeters (mm²).

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Answer  17.67

Step-by-step explanation:

x = ticket price

y = number of spectators (in thousands)

[tex]\frac{y-23000}{x-10} = \frac{26-23}{7-10} = -1[/tex]

R = revenue (in thousands)

R = xy = x * (23-3(x-10))

          = x * (23-3x+30)

R' = 53-3x

R'' = - 3

R'=0 (-) x = 53/3 = 17.67 (local maximum)

The length οn the map that represents 1 meter in real is 2/3 centimetres.

When twο numbers are cοmpared, the ratiο between them shοws hοw οften the first number cοntains the secοnd. As an illustratiοn, the ratiο οf οranges tο lemοns in a dish οf fruit is 8:6 if there are 8 οranges and 6 lemοns present.

Given that Each 12 centimetre οn a map represents an actual length οf 18 οf a meter. Therefοre, the ratiο can be written as,

=>Length οn Map / Actual Length = (12) centimetres / (18) meters

=>Length οn Map / Actual Length = 2/3 centimetres per meters

Nοw, the length οn the map that represents 1 meter in real is,

=>Length οn Map / Actual Length = 2/3 centimetres per meters

=> Length οn Map / 1 meter = (2/3) centimetres / 1 meters

=>Length οn Map = 2/3 centimetres

Hence the length οn the map that represents 1 meter in real is  2/3 centimetres.

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The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

What is independent event ?

In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.

Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:

P(A and B) = P(A) x P(B)

If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.

According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.

We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.

If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.

This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.

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The measure of angle KLN in the given set of intersecting lines is 100°.

In geometry, intersecting lines are lines that cross or meet each other at a point. The point at which the lines intersect is called the point of intersection. Intersecting lines are a fundamental concept in geometry and are used to define many other geometric shapes and concepts. For example, the intersection of two lines can form an angle, and the measurement of this angle can provide information about the relative positions of the lines.

Here,

Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation:

M + 100 + (x-y) + m<KLN = 360

We also know that m<MOL = m<KLN, since they are opposite angles of a line. Therefore:

m<KLN = m<MOL

We can use the fact that the sum of angles in a triangle is 180 degreesto set up another equation:

m<MOL + m<MON + m<NOL = 180

Since m<MOL = m<KLN, we can substitute m<KLN for m<MOL:

m<KLN + m<MON + m<NOL = 180

Now we have two equations:

M + 100 + (x-y) + m<KLN = 360

m<KLN + m<MON + m<NOL = 180

We need to solve for m<KLN. Let's isolate m<KLN in the second equation:

m<KLN = 180 - m<MON - m<NOL

Now we can substitute this expression for m<KLN in the first equation:

M + 100 + (x-y) + (180 - m<MON - m<NOL) = 360

Simplifying, we get:

280 - m<MON - m<NOL + x - y = M

Rearranging, we get:

m<MON + m<NOL = 280 + x - y - M

100=x-y

y=2/7x

100=x-2x/7

x=700/5

x=140

y=2*140/7

y=40

x-y=100°

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Answer:

b= 65

Step-by-step explanation:

Answer:

65°

Step-by-step explanation:

because all angles in a triangle add up to 180°

180°-43°-72°=65°

so the remaining angle is 65°

The mean of ▁x is 6 and the standard deviation of ▁x is 0.48.

What is standard deviation ?

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from their mean (average) value. It tells us how much the individual data points differ from the mean. In other words, it measures the spread of the data around the mean.

A small standard deviation indicates that the data points are clustered closely around the mean, while a large standard deviation indicates that the data points are more spread out from the mean.

The formula for standard deviation is the square root of the sum of the squared differences between each data point and the mean, divided by the number of data points minus 1. It is denoted by the symbol σ for a population, and s for a sample.

The mean of the number of lightning strikes on a square kilometer of open ground in a year is 6, and the standard deviation is 2.4. Since we are interested in the mean of a sample of 25 square kilometers, the mean of the sample means, denoted by ▁x, can be found by:

Mean of ▁x = Mean of the population = 6

The standard deviation of the sample means, denoted by σ(▁x), can be found by dividing the population standard deviation by the square root of the sample size:

σ(▁x) = Population standard deviation / √Sample size

= 2.4 / √25

= 0.48

Therefore, the mean of ▁x is 6 and the standard deviation of ▁x is 0.48.

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\textit{elapsed time}\dotfill &8\\ \end{cases} \\\\\\ A = 9800(1 - 0.05)^{8} \implies A=9800(0.95)^8\implies A \approx 6501.52[/tex]

Answer: 6,502

Step-by-step explanation: 9,800(1-0.05)^8 = 6,502

Answer:

x = 1 and y = 2 so if in (x, y) form then (1, 2) and if in (y, x) form then (2, 1)

Step-by-step explanation:

We can solve the system of equations using substitution.  We can first isolate x in the second equation.  Then, we can plug in the resulting equation for x in the first equation to solve for y:

[tex]x-2y=-3\\x=2y-3\\\\3(2y-3)+5y=13\\6y-9+5y=13\\11y-9=13\\11y=22\\y=2[/tex]

Now, we can plug in 2 for y in either equation to find x:

[tex]x-2(2)=-3\\x-4=-3\\x=1[/tex]

Thus, the solution set is (1, 2) when in the (x, y) form, but it is (2, 1) when in the (y, x) form

Answer:c=y+25

Step-by-step explanation: since ∆ = 0​,

then, [tex]\frac{dy}{dx}[/tex] =2x+10;

2X+10=0;

2x=-10;

x=-5;

y=-25+c;

c=y+25

Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).

Here,

To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.

L(e1) = (1+0, 0+0) = (1, 0)

L(e2) = (0+1, 1+0) = (1, 1)

L(e3) = (0+0, 1+0) = (0, 1)

So we can write:

L(x) = L(x1 e1 + x2 e2 + x3 e3)

= x1 L(e1) + x2 L(e2) + x3 L(e3)

Now we can assemble the coefficients of this linear combination into a matrix A:

A=  [tex]\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right][/tex]

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As a result, each row contains 2.5 chairs. The closest whole number must be rounded up because a chair cannot be split. Thus, each row contains three chairs.

What is length referred to as?

The British imperial or American customary schemes of measurement both use the inch as their standard unit of length (symbolized as in or ′′). It is equal to 136 yards or 112 feet.

Let x represent how many chairs are in each row. Two bits of knowledge are provided by the issue:

Hue can arrange 3 rows of a particular length with just 1 chair left behind, therefore her overall number of chairs is 3x + 1.

Hue can arrange seven rows that are identical in length using an additional 11 chairs, making her total chair count 7x + 11.

These two bits of knowledge can be used to create an equation:

3x + 1 = 7x + 11

After simplifying and locating x, we get:

4x = 10

x = 2.5

Thus, each row contains 2.5 chairs. A chair, however, cannot be divided, therefore we must round to the next whole number. There are three chairs for each row as a result.

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The total amount of classes attended is 5 classes.

A yoga studio offers memberships that cost $35 per month for unlimited classes.  The studio also accepts walk-ins, charging $7 per class.

Therefore, if someone attends enough classes in a month, the two options cost the same total. The total amount can be calculated as follows:

Let

x = number of classes attended in a month for the second option.

Hence,

7x = 35

divide both sides by 7

x = 35 / 7

x = 5

Therefore, the total amount of classes is 5 classes.

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Therefore, the rental cost for each movie is $2.75 and the rental cost for each video game is $5.75.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=). The left-hand side of the equation contains one expression and the right-hand side contains another expression. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

Let's call the cost of renting a movie "m" and the cost of renting a video game "v".

From the first month's rental, we know that:

7m + 9v = 71 (equation 1)

From the second month's rental, we know that:

5m + 3v = 31 (equation 2)

We now have two equations with two unknowns. We can solve for m and v using algebraic methods such as substitution or elimination.

Let's use elimination to solve for m and v:

Multiplying equation 2 by 3, we get:

15m + 9v = 93 (equation 3)

Subtracting equation 1 from equation 3, we get:

8m = 22

m = 2.75

Substituting m = 2.75 into equation 2, we get:

5(2.75) + 3v = 31

13.75 + 3v = 31

3v = 17.25

v = 5.75

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The required margin of error for Val is 9.8 pounds.

The margin of error is a statistic that describes how much random sampling error there is in survey results.

One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

Multiplying a key factor (for a specific confidence level) and the population standard deviation yields the calculation for the margin of error.

The square root of the sample's observational count is then used to divide the outcome.

So, the following equation provides the margin of error:

M = 1.96 s/√n

Now, calculate as follows:

M = 1.96 s/√n

M = 1.96 50/√100

M = 9.8

Therefore, the required margin of error for Val is 9.8 pounds.

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Correct question:

Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50) Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50) What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) / square root of N

the capacity of 1 cloud account is approximately 0.8421 terabytes, and the capacity of 1 hard drive is approximately 5.7895 terabytes.

Let's assume that the capacity of 1 cloud account is "C" terabytes and the capacity of 1 hard drive is "H" terabytes.

We can then set up a system of two equations to represent the given information:

14C + H = 18 (equation 1)

4C + 3H = 22 (equation 2)

We can use either substitution or elimination method to solve for C and H. Let's use elimination method by multiplying equation 1 by 3 and equation 2 by -1:

42C + 3H = 54 (equation 1 multiplied by 3)

-4C - 3H = -22 (equation 2 multiplied by -1)

Adding the two equations together, we get:

38C = 32

Dividing both sides by 38, we get:

C = 0.8421...

Now we can substitute this value of C into either equation 1 or equation 2 to solve for H. Let's use equation 1:

14C + H = 18

14(0.8421...) + H = 18

H = 5.7895...

Therefore, the capacity of 1 cloud account is approximately 0.8421 terabytes, and the capacity of 1 hard drive is approximately 5.7895 terabytes.

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Accοrding tο the given infοrmatiοn, the value οf the lοan 10 years after it starts is [tex]\£15,640.16[/tex]

Cοmpοund interest is the interest earned οn bοth the principal amοunt and the accumulated interest frοm previοus periοds.

Tο find the rate οf interest per annum, we can use the fοrmula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A is the end value οf the lοan, P is the initial value οf the lοan, r is the interest rate per annum (as a decimal), n is the number οf times per year that the interest is cοmpοunded, and t is the time in years.

Using the table, we can see that after οne year, the lοan has increased tο £7920.00, which is an increase οf:

7920.00 - 7500.00 = 420.00

After twο years, the lοan has increased tο £8363.52, which is an increase οf:

8363.52 - 7500.00 = 863.52

Tο find the rate οf interest per annum, we can use the fοrmula:

[tex]r = (A/P)^{(1/t)-1[/tex], where A is the end value οf the lοan, P is the initial value οf the lοan, t is the time in years, and r is the interest rate per annum (as a decimal).

Using the values frοm the table, we get:

[tex]r = (8363.52/7500.00)^{(1/2)} - 1 = 0.06[/tex]

Sο the rate οf interest per annum is 6% (tο 1 decimal place).

Tο find the value οf the lοan after 10 years, we can use the fοrmula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where P is the initial value οf the lοan, r is the interest rate per annum (as a decimal), n is the number οf times per year that the interest is cοmpοunded, and t is the time in years.

Using the values we have, we get:

[tex]A = 7500(1 + 0.06/1)^{(1*10)} =\£15,640.16[/tex]

Sο the value οf the lοan 10 years after it starts is £15,640.16 (tο the nearest penny).

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Answer: 97445

Step-by-step explanation:

27.4% of x = 26,700

x = 26,700 divided by 27.4%

(convert 27.4% to decimal) x = 26,700 divided by 0.274

x = 97445 (note the answer is rounded because you cannot have .25 of a person)

Answer:

Step-by-step explanation:

(1)Suppose that 84% of a sample of 125 nurses working 7 AM to 3 PM shifts in city hospitals

express positive job satisfaction, while only 72% of a sample of 150 nurses on 11 PM to 7 AM

shifts express similar fulfillment. Establish a 90% confidence interval estimate for the difference

and interpret.

p1 – proportion of nurses working day shifts

p2 – proportion of nurses working night shifts

Conditions:

1. Random – assume samples are representative of the populations

2. Independence – it is safe to assume that the samples would be independent of each other

3. 10% Condition – 125 nurses is less than 10% of all nurses working a day shift. 150 nurses is

less than 10% of all nurses working a night shift.

4. Success/Failure -

1 1 2 2 n p n p

ˆ ˆ

    105 10 108 10

1 1 2 2 n q n q

ˆ ˆ

    20 10 42 10

All conditions have been met to use the Normal model for a 2 proportion z-interval.

CI:

1 2

1 1 2 2

1 2

1 2

105 108

ˆ ˆ 0.84 0.72

125 150

ˆ ˆ ˆ ˆ

( ) * ˆ ˆ

(0.84)(0.16) (0.72)(0.28) (0.84 0.72) 1.645

125 150

p p

p q p q

p p z

n n

   

  

  

CI: (0.0391, 0.2009)

We are 90% confident that the true proportion of nurses working a day shift who express positive

job satisfaction is between 3.9% to 20.1% higher than for nurses working a night shift.

Answer:

1

Step-by-step explanation:

it is one