a shipment of 14 televisions sets contains 4 defective sets. a hotel purchases 8 of these televisions sets. what is the probability that the hotel receives at least one of the defective sets?

Answer:

The answer is the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0), which is:

x^2 - \frac{y^2}{5} = 1

This equation describes the shape of the hyperbola and allows you to determine the location and size of the hyperbola on a coordinate plane.

Step-by-step explanation:

The standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0) is given by:

$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$

where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively. In this case, the distance between the vertices is 2, so the semi-major axis is 1 and the semi-minor axis is $\sqrt{5}$. Therefore, the equation of the hyperbola is:

$$\frac{x^2}{1^2} - \frac{y^2}{\sqrt{5}^2} = 1$$

which simplifies to:

x^2 - \frac{y^2}{5} = 1

Answer:

UT=11

Step-by-step explanation:

UV is twice the length of RS. Since UV=11 then RS=22. UT is also twice the length of RS. So if RS=22, then UT=[tex]\frac{1}{2} * 22[/tex]. UT=11

The 3 : 7 ratio into which the amount of money is shared by Moira and Non where Non gets $28 more than Moira, indicates;

a) The total amount of money they share is $70

b) The amount Moira gets is $21, while the amount Non gets is 3 : 7

A ratio is a quantitative expression that specifies the number of times a value is contained within another value.

The ratio by which Moira and Non share the money = 3 : 7

The amount Non gets = 28 + The amount Moira gets

Let x represent the amount Moira gets, therefore;

The amount Non gets = 28 + x

The specified ratio indicates;

[tex]\dfrac{x}{28 + x} = \dfrac{3}{7}[/tex]

7·x = 3 × (28 + x)

7·x = 84 + 3·x

7·x - 3·x = 84

4·x = 84

x = 84 ÷ 4 = 21

x = 21

The total amount of money = The amount Moira gets + The amount Non gets

Therefore; The total amount of money = x + 28 + x = 2·x + 28

2·x + 28 = 2 × 21 + 28 = 70

The total amount of money = $70

b) The amount of money Moira gets, x = $21

The amount of money Non gets = $28 + $21 = $49

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The soda still left in the bottle is given as 4 liters in 2-liter bottle.

As mentioned, Sergio poured 4/5 of the soda from a 2-liter bottle for his guests.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The soda left in the bottle will be the difference of the total quantity and the quality of the soda poured. So,
= 20 - 4/5 × 20
= 20 - 16
= 4

Thus, the soda still left in the bottle is given as 4 liters of a 2-liter bottle.

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Answer:

$31.99

Step-by-step explanation:

I have no idea what to put here

Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.

Scalene-Triangle-1

In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.

One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°

the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on

Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.

Examples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.

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Answer: Each point appears to give the same number of tickets

9 points give 54 tickets

Step-by-step explanation:

Each point appears to give the same number of tickets

To find the number of tickets, a point gives

divide the number of tickets by the number of points.

18/3 = 6

you get six tickets per point

find the number of points that give 54 tickets by dividing 54 by 6

54/6=9

9 points give 54 tickets

Answer:

Smaller number: 15           Larger number: 31

Step-by-step explanation:

Let's call the smaller number x

So, the larger number will be x+16 (it's 16 more)

Then, write an equation:
x (smaller number) + (x+16) (larger number) = 46 (sum)

x+x+16=46
2x+16=46
2x=30
x=15
So, the smaller number is 15
The larger number is x+16, so plug in x:
x+16 = 15+16 = 31
The smaller number is 15, and the larger number is 31

[tex]y = 15 \\ x = 31[/tex]

Step-by-step explanation:

[tex]y + 16 + y = 46 \\ 2y = 30 \\ y = 15 \\ \\ x = 15 + 16 \\ x = 31[/tex]

The answer is yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

A square root of a number is a value that, when multiplied by itself, gives the number.

Given that, is it possible √a+√b = √a+b

Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

If either a or b equals zero, then the sums would be the same.

Since the square root of 0 is ±0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.

Hence, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

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The equation that correctly represents the problem is 3) y = x+ 3/8x

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

Given here, mio brought x grams and sol bought 3/8 times more than x hence, sol bought y = x  + 3/8x  

Hence, the correct option is 3) y=x+3/8x

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Let Q be the number of quarters and N be the number of nickels that Hugo has. We are given that Hugo has 4 * N quarters and that the total number of quarters and nickels is worth 840 cents. Since each quarter is worth 25 cents and each nickel is worth 5 cents, the total number of quarters is worth 25 * Q cents and the total number of nickels is worth 5 * N cents. Therefore, the total number of quarters and nickels is worth 25 * Q + 5 * N cents. Since the total number of quarters and nickels is worth 840 cents, we can set up the following equation to represent this information:

25 * Q + 5 * N = 840

We are also given that Hugo has 4 * N quarters, so we can set up the following equation to represent this information:

Q = 4 * N

We can solve this system of equations to find the number of quarters and nickels that Hugo has. Substituting the value of Q in the second equation into the first equation, we get the following:

25 * (4 * N) + 5 * N = 840

Distributing the 25 on the left side of the equation, we get the following:

100 * N + 5 * N = 840

Combining like terms, we get the following:

105 * N = 840

Dividing both sides of the equation by 105, we get the following:

N = 8

Substituting the value of N into the second equation, we get the following:

Q = 4 * 8

Solving for Q, we get the following:

Q = 32

Therefore, Hugo has 8 nickels and 32 quarters.

Answer:

32 quarters

8 nickels

Step-by-step explanation:

Information:

Define the variables:

If Hugo has 4 times as many quarters as nickels:

[tex]\implies x=4y[/tex]

If the combined value of quarters and nickels is 840 cents:

[tex]\implies 25x+5y=840[/tex]

Substitute the first equation into the second equation and solve for y:

[tex]\implies 25(4y)+5y=840[/tex]

[tex]\implies100y+5y=840[/tex]

[tex]\implies 105y=840[/tex]

[tex]\implies y=8[/tex]

Substitute the found value of y into the first equation and solve for x:

[tex]\implies x=4(8)[/tex]

[tex]\implies x=32[/tex]

Therefore, Hugo has:

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the perimeter of a triangle is 49 feet. The triangle's one side is seven feet shorter than its other. the length of each side , Second side: 16 feet, First side: 9 feet,Third side: 12 feet

To find the length of each side of the triangle, we need to start by looking at the perimeter, which is 49 feet.

Perimeter = 49 feet

Second side = 49 - 4 = 45 feet

First side = 45 - 7 = 38 feet

Third side = 45 + 4 = 49 feet

We know that the third side is 4 feet shorter than the second side, so we can subtract 4 feet from the perimeter to find the length of the second side, which is 16 feet. Then, we know that the first side is 7 feet shorter than the second side, so if we subtract 7 feet from the second side we can find the length of the first side, which is 9 feet. Finally, to find the length of the third side, we add 4 feet to the second side, which gives us 12 feet. Therefore, the length of each side of the triangle is 9 feet, 16 feet, and 12 feet.

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Answer:

x=2

y=0

Step-by-step explanation:

-x+2y= -2

   -2y. -2y

-x= -2-2y

/-1.  /-1 /-1

x=2+2y

3(2+2y)+2y=6

6+6y+2y=6

6+8y=6

-6.     -6

8y=0

/8 /8

y=0

3x+2(0)=6

3x=6

/3. /3

x=2

hopes this helps

Answer:

6x2 is multiplying 6 by 2 while 6² is said as '6 squared' meaning 6x6.

Step-by-step explanation:

6x2 is basic multiplication of 6x2 while 6² means we should completed 6x6.

a) The amount of gold edging that they will need for each plate is of: 37.7 inches.

b) The amount of gold edging for a box of 24 plates is of: 904.8 inches.

c) The total cost for the box of 24 plates is given as follows: $29.41.

The gold edging is placed around the circumference of the circular plate, hence the circumference needs to be obtained.

The circumference of a circle of radius r is given by the multiplication of 2π and r, as follows:

C = 2πr.

The radius of the plate in this problem is given as follows:

r = 6 inches.

Hence the circumference of the plate in this problem is given as follows:

C = 2π x 6 = 12π inches = 37.7 inches.

For the box of 24 plates, the amount needed is given as follows:

24 x 37.7 = 904.8 inches.

It costs $3.25 per 100 inches of gold edging, hence the total cost for the 24 plates is obtained as follows:

904.8/100 x 3.25 = $29.41.

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The equation which shows that how many more t- shirts sal designed is x^{y} .....

If jay designed 4 t-shirts and sal designed 5 times as many t-shirts. So the equation which shows how more t- shirts sal designed is....

Firstly we make the data to simplify the peoblem:

Suppose:

T-shirts designed by jay =  x

T-shirts designed by sal = y

As t-shirts designed by jay are 4 so

x=4

and t-shirts designed by sal are 5 times as many t- shirts so

y= 5times = 4×4×4×4×4 = 1,024

So the equation which shows how many more t-shirts sal designed will be:

Required equation = x^{y}

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Answer:

The first step is 24 divided by 6 ..... (4)

The second step is 4 x 2 ...... (8)

Step-by-step explanation:

65(30-24 divided by 6 x 2)

65(30- 4 x 2)

65(30 - 8)

65(22)

1,430

Using the ratio provided and the value divided for Jaya and with simple arithmetic, The answer is 6300.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Comparing two integers that each stand for a component of a whole results in a proportion. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.

ratio = 3:4

for Jaya,

3x=2700

x=2700/3

x=900

total = 3x+4x

=3*900 + 4*900

=6300

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At the rate of 4 2/5 L of water is added into the reservoir per minute.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

As  It takes 5/11 minutes to fill the reservoir.

So, the rate at which Nizhoni adds water to the reservoir.

Rate=  Volume/ Time taken

Rate = 2 L/ (5/ 11)

        = 2 x 11/5

        = 22/5 L/ min

         = 4 2/5 L/ min.

Hence, at the rate of 4 2/5 L of water is added into the reservoir in one minute.

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Answer: 5

Step-by-step explanation: I answered this question.

Using the provided values for the depth and moving rate of the driver , We can use simple unitary method and the answer is 8.75 minute.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

The arithmetic operator is used to carry out mathematical operations on the provided operands, including addition, subtraction, multiplication, division, and modulus.

initial depth = 5 feet

shipwreck at 75 feet

depth to travel = 75-5 = 70 feet

rate = 8 feet/minute

time = 70/8

=8.75 minute.

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The slope of a line that is perpendicular to the line y = x - 5 is the negative reciprocal of the slope of y = x - 5. The slope of y = x - 5 is 1, so the slope of the line that passes through (4, 8) and is perpendicular to y = x - 5 is -1.

We can use the point-slope form of a line to write the equation of the line that passes through (4, 8) and has a slope of -1. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, (x1, y1) is (4, 8) and m is -1, so the equation of the line is y - 8 = -1(x - 4). Simplifying this equation, we get y - 8 = -x + 4. Adding 8 to both sides of the equation, we get y = -x + 12. This is the equation of the line that passes through (4, 8) and is perpendicular to y = x - 5.

The intervals that contain 11 states, are given as follows:

The bar graph presented by the image shown at the end of the answer shows the number of states present in each interval.

The features of the graph are given as follows:

Then the number of states for each interval are given as follows:

Hence the intervals 3 to 6 and 6 to 9 are the intervals that contain 11 states, being the correct answers to this problem.

The bar graph is given by the image shown at the end of the answer.

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Answer:

y = -9x + 31

Step-by-step explanation:

We can find the slope of the second line using the formula

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the second line and m1 is the slope of the first.

Thus, since 1/9 is the slope of the first line, we have

[tex]m_{2}=-\frac{1}{(1/9)} \\m_{2}=-9[/tex]

Since the slope intercept form is y = mx + b, where b is the y-intercept, we need to it in the second line by plugging in (3, 4) for x and y and -9 for m:

[tex]4=-9(3)+b\\4=-27+b\\31=b[/tex]

The function to return the nth word of the sentence will be given as -

def get_word(sentence, n):

# Only proceed if n is positive

if n > 0 :

words = sentence.split()

# Only proceed if n is not more than the number of words

if n <= len(words) :

return words[n-1]

return("")

According to the data given in the question we can see that the method to obtain the string will be the split string method,

According to the split string method, we separate distinct parts of the strings based on the delimiter using signs such as comma(,), hyphen(-), whitespace), etc.

To extract the 4th word in the sentence, we will assume position 3 for the 4th word.

#The function to print lesson counting from 0,

print(get_word("This is a lesson about lists", 4))

print(get_word("This is a lesson about lists", -4))

#No printing as the first condition is not met

print(get_word("Now we are cooking!", 5))

#No printing occurs as it also does not meet the condition of the second statement.

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A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.

Explain about t-test?

The t-test is designed to compare the means of two populations based on the means of the two samples. (any sample from either population).

The most important observation is that the t-test computes the difference between two sample means.

If you have trouble understanding 'variance', you can use the word standard deviation from the previous text to get your points.

In other words, there is more than one difference between the groups, but we want one measure of Total Difference Between Groups. The t-test cannot do that.

So the procedure for groups of three or more is: Run ANOVA first. As a second step, if you have reason to believe that differences exist (based on this test), you can use the t-test to determine where those differences lie.

A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.

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Answer:

  -25/(12π) ft/min ≈ -0.663 ft/min

Step-by-step explanation:

You want the rate of change of height of the salt in a cone with height 5 ft and diameter 4 ft, filled 3 ft up from the vertex, and decreasing in volume at the rate of 3 cubic feet per minute.

The rate of change of height is the rate of change of volume, divided by the surface area.

The given cone dimensions tell you the radius is 2/5 of the height of the cone, so the radius of the surface when it is filled to a depth of 3 ft is ...

  r = (2/5)(3 ft) = 1.2 ft

The area of the surface is the area of a circle with this radius:

  A = πr² = π(1.2 ft)² = 1.44π ft²

Then the rate of change of height is ...

  h' = V'/A

  h' = (-3 ft³/min)/(1.44π ft²) = -25/(12π) ft/min ≈ -0.663 ft/min

Answer:

x=5

Step-by-step explanation:

To find the value of x, we need to first set up the proportion using the given information. Since the given values are in proportion, we can set up the proportion as follows:

x / 10 = (2x - 4) / 12

Next, we can cross-multiply to solve for the value of x:

12x = 10(2x - 4)

12x = 20x - 40

-8x = -40

x = 5

Thus, the value of x is 5. This means that the other values in the proportion are also 5, 10, 10, and 12, respectively.

Answer: -3r+4p+6 or 4p-3r+6

Step-by-step explanation:

Combine like terms

5r-8r=-3r

4p

6

-3r+4p+6

Answer:

–3r + 4p + 6

Step-by-step explanation:

5r + 4p – 8r + 6

= 5r – 8r + 4p + 6

= –3r + 4p + 6

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Answer:

[tex]12\pi[/tex]

Step-by-step explanation:

Circumference Formula: [tex]2\pi r[/tex]

Our radius is 6, plug that in.

[tex]2\pi 6[/tex]

12[tex]\pi[/tex]

Leave in terms of pi, so do not simplify further.