what is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?

Phelan now has 81.48 x 1.08 = 87.79 US dollars, which is 87.79 dollars of the original 250 dollars.

First, we need to find out how many euros Phelan has left after spending 150 euros on his trip.

We are taking the exchange rate of 1 euro = 1.08 USD

He started with 250 US dollars, which he exchanged for 250 / 1.08 = 231.48 euros.

After spending 150 euros, he has 231.48 - 150 = 81.48 euros left.

To convert the euros back to US dollars, we need to multiply the number of euros by the exchange rate (1 US dollar = 1.08 euros)

So, Phelan now has 81.48 x 1.08 = 87.79 US dollars, which is 87.79 dollars of the original 250 dollars.

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The expected value of y is (D.) 35.5.

The expected value of a discrete random variable is found by multiplying each value of the variable by its corresponding probability and then summing these products. In this case, the probability distribution of y is given in the table.

To find the expected value of y, we need to calculate the sum of the products of each value of y and its corresponding probability.

y * probability = y * P(y)

The expected value of y is E(y) = 100.10 + 200.25 + 300.05 + 400.30 + 500.20 + 600.10

= 2 + 5 + 1.5 + 12 + 10 + 6 = 37.

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A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need.

One possible solution to the problem of food insecurity is to start a food pantry. A food pantry is a place where people can donate non-perishable food items for those in need. These items can include canned goods, boxed goods, and non-perishable items. People can then come to the pantry and take what they need. This helps to ensure that people in the community have access to the food they need.

A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need. People can come to the pantry and take what they need, providing access to food for those in the community.

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Therefore, 0.4854 to 0.5546 is the 95% confidence range for the percentage of businesses that are anticipated to need greater employee payments for health insurance coverage in 2009.

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let's enter the formula.

Level of confidence = 1-0.95

Level of confidence = 0.05

The following step is to use this formula to get Z.

Zα/2

Let's enter the formula.

Z= 0.05/2

Z=0.025

Finding the Z score of Z=0.025 is the third stage.

Zα/2=1.96

Let's now use this approach to calculating the margin of error.

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Calculating the proportion of businesses anticipated to demand greater employee payments for health insurance coverage in 2009 with a 95% confidence interval

computation for the confidence interval's outer limits

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

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Answer:

9261

Step-by-step explanation:

[tex](-3-2(-12))^3=(-3+24)^3=21^3=441(21)=9261[/tex]

Answer: [tex]90^{\circ}[/tex]

Step-by-step explanation:

By the converse of the alternate interior angles theorem, we need [tex]\angle CBA \cong \angle BAD[/tex].

The x-coordinates of the left edges of the rectangles are 1,5/4,6/4,7/4.

The area of this region with a Riemann Sum is 0.7595.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

Given function is f(x) = 1/x on the interval [1,2] is shown.

The four rectangles of width 1/4 are present.

From the figure we can see that the x coordinate of the left edges of the rectangle are:

1,5/4,6/4,7/4

Now we plug these values in the function to find the height of rectangles.

For x=1 ,f(x) = 1

For x=5/4 ,f(x) = 4/5

For x=6/4 ,f(x) = 4/6

For x=7/4 ,f(x) = 4/7

Now, Area = length*width, and width of each rectangle is 1/4

Area of rectangle 1 = 1*1/4 = 1/4

Area of rectangle 2 = 4/5*1/4 = 1/5

Area of rectangle 3 = 4/6*1/4 = 1/6

Area of rectangle 4 = 4/7*1/4 = 1/7

Total Area is = 1/4+1/5+1/6+1/7  = 0.7595

This is an overestimation of ln(2).

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To create a model to represent (a+b), you could use a mathematical equation such as y = a + b.

Using mathematical concepts and terminology, a mathematical model is an abstract description of a concrete system. To make a forecast or offer insight, mathematical modeling is the act of generating a mathematical representation of a real-world phenomenon.

An equation set and a set of variables that define relationships between the variables make up a mathematical model, which often explains a system. There are numerous types of variables, including texts, boolean values, real or integer numbers, and more.

In this case, the equation y = a + b can be used. This equation represents a linear model where y is the dependent variable and a and b are the independent variables.

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Answer:

y^2 + 5y - 750 = 0

y(y + 5) = 750

750 - y(y - 5) = 0

Step-by-step explanation:

The value of x in the similar triangles is 40.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangles are similar.

That means,

the corresponding sides are in the proportion to each other.

That means,

(x + 8)/x = 12/10

10x + 80 = 12x

2x = 80

x = 40

Therefore, the value of x is 40.

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Step-by-step explanation:

what is the question ?

solve for x and y ?

multiply the second equation by 3 and add that result to the first equation. then solve for x. then pick any original equation and solve for y.

-2x - 3y = 8

15x + 3y = 18

-----------------------

13x 0 = 26

x = 26/13 = 2

5×2 + y = 6

10 + y = 6

y = -4

We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal. AB = 8cm ; BC = 6.5 cm.

We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal.

The formula for calculating the area of a circle is [pi r 2], which we should keep in mind. With respect to a rectangle, there is only one such circle.The Pythagorean theorem states that the diagonal of a rectangle with sides lengths a and b is equal to a2 + b2.

The radius is simply a2+b22 since the diagonal has a diameter.Keep this response on hand.

BC = x- 1.5

x * (x-1.5) = 52

x^2 - 1.5x - 52 = 0

Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25

We are searching only positive value

(1.5 + 14.5)/2 = 16 / 2 = 8 cm

AB = 8 cm

BC = 8 - 1.5 = 6.5 cm

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Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

What is the combination?

In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.

If none of the numbers can be repeated, Joaquin can choose from a total of 22 numbers (0 through 21), and he needs to select three of them for his locker combination. This is a classic example of a combination problem, as the order in which he chooses the numbers does not matter. The number of ways to choose three numbers from a set of 22 without repetition is given by the formula for combinations:

C(22,3) = 22! / (3!(22-3)!) = 222120/(321) = 2310

So, Joaquin can choose from 2310 different locker combinations if none of the numbers can be repeated.

The name "combination lock" is appropriate because it refers to the process of combining numbers in a specific order to open the lock. In this case, the order of the numbers selected does not matter.

If Joaquin could repeat a number, but not use the same number twice in a row, the number of mathematical combinations are possible is given by the formula for permutations:

A(22,3) = 222120 = 9, 612

Hence, Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

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Answer:

5,040 minutes

Step-by-step explanation:

[tex]\frac{3.5 days}{1}[/tex] x [tex]\frac{24 hours}{1 day}[/tex] x [tex]\frac{60min}{1hour}[/tex]  

[tex]\frac{3.5days x 24 hours x 60 minutes}{1day x 1 hour}[/tex]  Cross cancels the words days and hours

[tex]\frac{3.5 x 24 x60min}{1x1}[/tex]

[tex]\frac{5040minutes}{1}[/tex] = 5040 minutes

The like radical to [tex]3\sqrt[4]{5x}[/tex] is given as follows:

[tex]7\sqrt[4]{5x}[/tex]

Like radicals are two radical expressions that have the same indices and radicand.

The concepts of the index and of the radicand of a radical are given as follows:

In the context of this problem, the radical expression is presented as follows:

[tex]3\sqrt[4]{5x}[/tex]

Hence the index and the radicand are given as follows:

Applying the concept of like radicals, any expression in this format is a like radical to 4 √ 5x.

n(4 √ 5x).

That is, any multiple of the term.

This means that the correct option is given by the first option, with n = 4.

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Answer:

it is you just find the total of the 29 mgs

The per cent of change for the volume of water inside the aquarium is 93.5.

An aquarium carries 8.6 cubic feet of water.

The aquarium is loaded up further to hold 9.2 cubic feet of water.

We have to find the per cent of change for the volume of water inside the aquarium.

A ratio or value that may be stated as a fraction of 100 is a percentage. If we calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The per cent of change for the volume of water inside the aquarium = Water holds by aquarium/Further filled water × 100

The per cent of change for the volume of water inside the aquarium = (8.6/9.2) × 100

The per cent of change for the volume of water inside the aquarium = 93.5%.

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There is no solution that satisfy the equation (1,1,1) x u = (7, -4, -3).

The term "vector" in mathematics and physics is used informally to refer to some values that cannot be stated by a single integer (a scalar) or to certain members of vector spaces. Though the components of an algebra are frequently not referred to as vectors, any algebra over a field is a vector space. They are sometimes referred to as vectors, mostly for historical reasons.

A real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, duration, or distance. Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number.

There is no value, not even 0, that would satisfy the equation, which is referred to as "no solution."

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The cost of a 3.4 mile ride when a taxi charges a base fee of $3.00 and $0.15 for every mile of the ride is $3.51.

Therefore the answer is $3.51

The cost of a 3.4 mile ride can be calculated by multiplying the distance of the ride by the cost per mile and adding the base fee. Here base fee is the fixed charge and $0.15 is the variable charge that depend on distance covered.

To calculate the cost of the ride:

= (3.4 miles * $0.15 per mile) + $3.00 base fee

= $0.51 + $3.00

= $3.51

So, a 3.4 mile ride would cost $3.51.

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Answer:

The tablecloth overhang is the amount of tablecloth that hangs over the edges of the table.

The area of the square table is 1.3m * 1.3m = 1.69m^2.

The area of the round tablecloth is pi * (diameter/2)^2 = pi * (2/2)^2 = pi * 1^2 = pi * 1 = pi m^2.

The overhang is the difference between the area of the round tablecloth and the square table.

Overhang = pi m^2 - 1.69m^2 = pi - 1.69

To find the percentage of the tablecloth that overhangs the table, we can divide the overhang by the area of the tablecloth and multiply by 100.

Overhang % = (pi - 1.69) / pi * 100 = (pi - 1.69) / pi * 100 = (3.14 - 1.69) / 3.14 * 100 = 1.45 / 3.14 * 100 = 46.14%.

So, the percentage of the tablecloth that overhangs the table is 46.14%.

It is solved using the concept of z-table. Correct option is: (E)

The difference from the mean is expressed as a z-score in standard deviation units. It is not clear either one agree or disagree with the null hypothesis. The likelihood that a point as severe as their statistic would be seen that under null hypothesis is known as the p-value.

A z-table, sometimes referred to as the standard normal table, gives the area beneath the curve to the left of a z-score. This region indicates the likelihood that z-values will fall inside a particular area of the standard normal distribution.

Here, we have to calculate the confidence interval for determine the population interval.

Now, P₁ - P₂, this is the difference between the two population proportion.

thus, option (E) is the correct answer.

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The complete question is as follows:

On solving the provided question, we can say that Due to the size and revenue of this startup company, resources are somewhat limited.

In mathematics, "Size is an abstraction from the comparison and measurement of long and short items." Comparing or measuring objects allows us to determine their sizes. The amount's size will be decided by this. B. Mass or length with relation to measurement units. The total area of space occupied by a person or object; the size of someone or something. [Count] Box is 5 inches tall, 6 inches broad, and 12 inches long. The mistake was roughly the size of a dime. The size of twins is the same.

People make mistakes, but there is a potential that she can unintentionally destroy a personal file if she is removing something.

Due to the size and revenue of this startup company, resources are somewhat limited.

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Yes , a right triangle with the given sides 6 cm 10 cm and 8cm can be formed because the sides satisfies the Pythagoras Theorem .

According to Pythagoras Theorem , the square of the hypotnuse of triangle is equal to the square of the other two sides of triangle ;

The sides of the triangle are given as : 6cm ,10cm and 8cm ;

which means that ,

the hypotnuse is = 10 cm ;

According to Pythagoras Theorem ;

⇒ [tex]10^{2} =8^{2} +6^{2}[/tex] ;

⇒ [tex]100 = 64 + 36[/tex] ;

⇒ [tex]100= 100[/tex] ;

the side satisfies the condition to form  the right triangle .

Therefore , the given sides forms a Right Triangle .

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On solving the provided question we can say that so the value of triangle - y + Z = 1+ r = > 1 -r +

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

in triangle

by construction = y0 = r - 1

Pythagoras =  x² + y²

=> (1+r)² = x

=>  x = √(1+r)² - (1-r)²

Pythagoras  = x² + z² = 2²

=> z =√4-4r

so the value of triangle -

=> y + Z = 1+ r

=> 1 -r + 2√1 -r1 =  

=> r = -1 + √5/2

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The complete question is "In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown."

Answer:

22.6%.

Step-by-step explanation:

To calculate the percent error of a measurement, you can use the following formula:

Percent Error = (|measured value - actual value| / actual value) x 100%

Plugging in the values from the problem:

Percent Error = (|4.1 inches - 5.3 inches| / 5.3 inches) x 100% = (1.2 inches / 5.3 inches) x 100% = 0.226 x 100% = 22.6%

To the nearest tenth of a percent, the percent error is 22.6%.

Answer:

0.3

Step-by-step explanation:

Were you asking for 5% of 6? Because then you would just multiply 6 by 0.05 (because percents are always out of 100%, so converted to decimal it is out of 1) and then get 0.3

Answer: The percentage of 6 by 5 (i.e. 6:5) is 120

Step-by-step explanation:

Given: 6 by 5 i.e. 6/5

Solution: (value/ total value)* 100

hence, (6/5)*100

=1.2*100

=120.

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The average speed of the bus is 54.78 mph.

To find the average speed of the bus, we need to find the total distance traveled and the total time taken for the entire trip.

Distance traveled = 10 miles + 17 miles + 95 miles + 4 miles = 126 miles

To find the total time taken, we need to calculate the time taken for each segment of the trip and add them up.

Time taken for 10 miles at 25 mi/h = 10 miles / 25 mi/h = 0.4 hours

Time taken for 17 miles at 45 mi/h = 17 miles / 45 mi/h = 0.378 hours

Time taken for 95 miles at 80 mi/h = 95 miles / 80 mi/h = 1.1875 hours

Time taken for 4 miles at 12 mi/h = 4 miles / 12 mi/h = 0.333 hours

Total time taken = 0.4 hours + 0.378 hours + 1.1875 hours + 0.333 hours = 2.3 hours

Average speed = total distance / total time = 126 miles / 2.3 hours = 54.78 mph

So, the average speed of the bus is 54.78 mph.

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Answer:

yes a rational number

Step-by-step explanation:

a rational number has the form

[tex]\frac{a}{b}[/tex] with a and b integers

[tex]\frac{7}{11}[/tex] is in this form and is therefore a rational number

The right option is Option C: y = 5x + 1

The given line passes through the points (5,0) and (0,1).

The slope of the line is found by:

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

This implies that,

[tex]m = \frac{1-0}{0-5} \\m = \frac{-1}{5}[/tex]

The product of the slope of the two perpendicular lines should be negative one.

Thus,

[tex]m_{1} * m_{2} = -1[/tex]

This implies that,

[tex]\frac{-1}{5} * m_{2} = -1[/tex]

Giving us, m2 = 5

We can use the slope intercept formula,

y = mx + b

where b = 1 is the y-value of the y-intercept.

The equation thus becomes,

y = 5x + 1

Therefore, the right option is Option C: y = 5x + 1

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