What is the value of n ?

Answer:

B) 40 feet

Step-by-step explanation:

Essentially, there are two similar right triangles in the given problem.

base_L = Base [larger triangle] = 60 ft

base_S = Base [smaller triangle] = 6 ft

x = leg (larger triangle)

y = leg (smaller triangle) = 4 ft

Using the given proportion to solve for the value of x:

\(\frac{x}{base_{_L} } = \frac{y}{base_{_S} }\)

\(\frac{x}{60ft} = \frac{4 ft}{6 ft}\)

6x = 240

Divide both sides by 6:

6x/6 = 240/6

x = 40

From the given sequences following are the arithmetic sequences :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

As given in the question,

Arithmetic sequences are :-

1) yes, because the difference between the terms is same.

7 - 3 = 11-7 = 15 -11 = 4

5)yes, because the difference between the terms is same.

1/2 -1 = 0 -1/2 = -1/2 -0 = -1/2

7)yes, because the difference between the terms is same.

0 - 1 = -1 -0 = -2 -(-1) = -1

10)yes, because the difference between the terms is same.

7.5 - 9.5 = 5.5 - 7.5 = 3.5 -5.5 = -2

Difference between consecutive terms of these sequences are not equal . so these are not arithmetic sequences :-

2,3,4,6,8, 9

Arithmetic sequence

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 .. is arithmetic because the difference between consecutive terms is always two.

Therefore, the arithmetic sequences are :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

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Answer:

15,840 feet.

Step-by-step explanation:

We have been given that Maureen walked 3 miles. We are asked to convert the distance walked by Maureen in feet.

Since we know that 1 mile equals 5,280 feet, so to convert our given distance we will multiply 3 by 5,280.

Therefore, Maureen walked 15,840 feet.

1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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all work should be in the picture, lmk if theres anything confusing

The measure of the angle ADC is: 20°

The parameters are given as:

∠ABC = 40°

∠ADC = ?

We know from circle geometry that:

Angle subtended at the center is twice the angle subtended at the circumference.

Therefore:

∠ABC = 2 x ∠ADC

On substituting the value we get:

40° = 2 * ∠ADC

∠ADC = 20°

Therefore, the measure of the angle ADC is 20°

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Complete question is:

A circle is centered on point B. Points A, C and D lie on it's circumference.

If ABC measures 40 degrees, what does ADC measure?

Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

Answer:

1  13/20

Step-by-step explanation:

add 2 1/10 and 3 to get 5 1/10.  subtract, 6 3/4 minus 5 1/10. If you want to find the least common factors you get 6 15/20 and 5 2/20 to make it easier to subtract. Finally, you get 1 13/20.

Since each term can be written as the previous term divided by three, this is a geometric sequence.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

For this problem, we have that each term can be written as the previous term multiplied by one third or divided by three, hence the division of consecutive terms is always the same and this is a geometric sequence.

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The volume of the solid is 72π. of the x-axis, the volume of the solid is 72π of y axis, the volume of the solid is 192π of the line x=6 and the volume of the solid is 99π of the line x=9.

(a) Spinning the locale about the x-hub will make a strong with a round and hollow shape. The volume of the strong can be tracked down utilizing the equation:

\(V = ∫[a,b] πy^2 dx\)

where an and b are the x-directions of the marks of convergence of the bends y=x and y=0.

The convergence focuses are (0,0) and (6,6). In this way, the restrictions of coordination are 0 and 6.

V = \(V = ∫[a,b] πy^2 dx\)

=\(π(6^3)/3\)

= 72π

The volume of the strong is 72π.

(b) Spinning the locale about the y-hub will make a strong with a round and hollow shape. The volume of the strong can be tracked down utilizing the equation:

V = \(∫[a,b] πx^2 dy\)

where an and b are the y-directions of the marks of convergence of the bends y=x and y=0.

The convergence focuses are (0,0) and (6,6). In this way, the restrictions of coordination are 0 and 6.

V = \(∫[0,6] πy^2 dy\)

= \(π(6^3)/3\)

= 72π

The volume of the strong is 72π.

(c) Rotating the district about the line x=6 will make a strong with a washer shape. The volume of the strong can be tracked down utilizing the recipe:

V = \(∫[a,b] π(R^2 - r^2) dx\)

where an and b are the x-directions of the marks of convergence of the bends y=x and y=0, R is the separation from the line of upheaval to the external edge of the strong (y=x), and r is the separation from the line of transformation to the internal edge of the strong (y=0).

The convergence focuses are (0,0) and (6,6). R=6 and r=0, since the strong stretches out from the line of insurgency to the bend y=x.

V =\(∫[0,6] π(6^2 - x^2) dx\)

= \(π(6^3 - 2(6^3)/3)\)

= 32π(6)

The volume of the strong is 192π.

(d) Rotating the locale about the line x=9 will make a strong with a washer shape. The volume of the strong can be tracked down utilizing the recipe:

V =\(∫[a,b] π(R^2 - r^2) dx\)

where an and b are the x-directions of the marks of convergence of the bends y=x and y=0, R is the separation from the line of upheaval to the external edge of the strong (y=x), and r is the separation from the line of transformation to the internal edge of the strong (y=0).

The convergence focuses are (0,0) and (6,6). R=3, since the separation from the line x=9 to the bend y=x is 3 units. r=0, since the strong reaches out from the line of transformation to the bend y=x.

V = \(∫[0,6] π(3^2 - x^2) dx\)

= \(π(3^3 - 2(6^2)(3) + 6^3/3)\)

= 18π(6) - 27π

= 99π

The volume of the strong is 99π.

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Answer:

D is the answer

The correct option is  D)

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here the equation is y = 120 – 25x . Let the tank release water for x minutes and y be the volume of water after x minutes then the above equation satisfies the situation.

Hence the correct option is D

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A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9​-digit entry code if they know that no digits repeat?

Answer:

the probability of a person correctly guessing a 9​-digit entry code if they know that no digits repeat is 0.1

Step-by-step explanation:

We know that probability= number of required outcomes /number of all possible outcome.

From the given information;

the number of required outcome is guessing a 9-digit = 1  outcome

the number of all possible outcome = ¹⁰C₉ since there are 10 numbers and 9 number are to be selected.

Since there are only 9-digit that opens the lock;

the probability of a person correctly guessing a 9​-digit entry code is

\(P =\dfrac{1}{^{10}C_9}\)

\(P =\dfrac{1}{\dfrac{10!}{9!1!}}\)

\(P =\dfrac{1}{10}\)

P = 0.1

Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

Answer:

The answer is answer choice E.

Step-by-step explanation:

Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees

Answer:

1. Gather 45 tiles

2. Split them up into groups of 15. Your answer will be the amount of piles you  end up with. Hope this helps!

The conditions for the significance to be met are randomization condition, independence condition and sample size condition

To perform a significance test, we need to make sure that the following conditions are met:

1. Randomization condition: The cards must be randomly assigned to the different positions, and the order of presentation of the cards must be randomized.

This condition has been met as the friend plans to randomly assign the position of the correct picture on each trial.

2. Independence condition: The trials must be independent of each other.

This condition has been met as the outcome of each trial does not depend on the outcome of any previous trial.

3. Sample size condition: The sample size must be large enough so that the sampling distribution of the sample proportion is approximately normal.

This condition is met as the number of trials is large (60) and the expected number of successes (correct guesses) is at least 10 (0.25 x 60 = 15).

Therefore, the conditions for performing this significance test have been met.

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Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

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Complete question:

According to the computation, each ticket is $37.5 is t = ($175 - $25)/4.

An equation is a formula that uses the equals symbol (=) to denote the equality of two expressions. Multiple languages may have somewhat distinct meanings for the term equation and its cognates.  For instance, in English, an equation is any properly constructed formula that consists of two expressions joined by the equals sign, whereas in French, an equation is any well-formed formula that contains one or more

variables 5.

Given the overall cost of parking and four tickets for a baseball game = $175.00

cost of parking = $25

The price of 4 tickets = $175 - $25

let cost of each ticket is t

t =($175 - $25)/4

cost of each ticket is $37.5

Therefore, the formula for a ticket is

t = ($175 -$25)/4, cost of ticket is $37.5.

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Answer:

3x²-4x+12

Step-by-step explanation:

Answer:

\(=3x^2-4x+12\)

Step-by-step explanation:

So we have the expression:

\(x(2x+3)+(x-3)(x-4)\)

To simplify, distribute the left side and the right:

\(=x(2x)+x(3)+(x-3)(x)+(x-3)(-4)\)

Distribute:

\(=(2x^2+3x)+(x^2-3x)+(-4x+12)\)

Combine like terms:

\(=(2x^2+x^2)+(3x-3x-4x)+(12)\)

Simplify:

\(=3x^2-4x+12\)

Answer:

31 years

Step-by-step explanation:

A = P(interest rate)^number of years (n)

if the money is to quadruple, A = 4 X 22,000 = 88,000.

P = investment amount = 22,000.

interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.

n is number of years.

22,000 (1.045)^n = 88, 000

divide both sides by 22, 000:

(1.045)^n = 4

take logs for both sides:

log (1.045)^n = log 4

simplify using log laws (by bringing down the n):

n log (1.045) = log 4

divide both sides by log (1.045):

n = (log 4) / log (1.045)

= 31.49 (31 years to nearest year)

Answer:

Yes, (x - 3) is a factor of P(x) and 3 is a zero or root of P(x)

Step-by-step explanation:

Determine whether or not (x - 3) is a factor by using synthetic division with +3 as the divisor.  The coefficients of the polynomial p(x) are {2  -5  -4  0  9}.

Setting up synthetic division:

3   /   2    -5    -4    0    9

                6     3    -3   -9

    -------------------------------

          2     1     -1     -3    0

Since the remainder is zero (0), we know that 3 is a root of the polynomial P(x) and that (x - 3) is a factor of said polynomial.

Answer:

$137.80

Step-by-step explanation:

We can solve for \(\frac{1}{3}\) of Luis's money using this equation:

Subtracting that from the total cost:

275.59 is the leftover cost of the new gaming console that the siblings have to evenly split. To find out how much the sibling have to pay each, you can use this equation:

Therefore, to pay for the new gaming console, Benjamin and Audrey will need to each contribute $137.80 to evenly pay for the remaining cost.

Answer:

  a) 40

  b) 80

  c) 77

  d) 48

Step-by-step explanation:

To find the missing numerator, multiply the equation by the denominator of the fraction with the missing numerator.

a) (10/15)(60) = (x/60)(60)

  40 = x

__

b) (x/180)(180) = (4/9)(180)

  x = 80

__

c) (7/11)(121) = (x/121)(121)

  77 = x

__

d) (x/144)(144) = (2/6)(144)

  x = 48

Answer: -5057 if im wrong let me know

Answer:

-5057

Step-by-step explanation:

Simplify the expression:

-1083 + 3974

-1083 - 3974

-5057

Answer:

John paid $127 for football camp. He paid a $7 registration fee and $5 for each week he was enrolled in camp. What is w, the number of weeks John was enrolled in football camp?

Answer:

Given that a beetle has the pattern, 0.098 is the probability that it belongs to the rare subspecies

Step-by-step explanation:

Probability of having a pattern in rare subspecies \(= 0.98\\\)

Percentage of rare subspecies = 1 % = 0.01

Probability of a beetle with pattern belonging to rare subspecies is

\(=0.01 * 0.98 \\= 0.098\)