the least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. what is the sum of the digits of n?

Answer:

Step-by-step explanation:

To verify the solution, we can convert the given midterms to binary and check which ones satisfy the given POS equation.

4 : 0100, 15 : 1111, 17 : 0001 0001, 412 : 1100 1100, 11 : 1011, 13 : 1101, 25 : 0110 0101, 120 : 0111 1000, 21 : 0001 0101, 23 : 0001 0111, 28 : 0001 1100, 29 : 0001 1101, 31 : 0001 1111

Now, we can see that the given POS equation satisfies all the given midterms in binary form. Therefore, the given solution is correct.

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Answer:

In the centre of a triangle

Step-by-step explanation:

The number of 38 inches boards to be cut from the eight 2x4 boards that are each 10 ft long is 25 boards.

The length is the measurement of the distance from one point to another.

The length is used to identify the size of an object or the distance from one point to the other.

Number of 2x4 boards = 8

Length of each board = 10 feet

Total length of the 2x4 boards = 80 feet (10 x 8)

The total length of the 2x4 boards in inches = 960 inches (80 x 12)

Expected inches of each board = 38 inches

The number of 38 inches boards to be cut from the boards = 25 boards (906/38).

Thus, the number of 38 inches boards to be cut from is 25 boards.

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Answer:

b

Step-by-step explanation:

a is not correct because the domain includes negative numbers as well

c is not correct because the domain includes positive numbers as well

and

d is not correct because the range for this function includes ordered pairs from the quadrants I and III (not I and IV)

hope this helps :)

Answer: 28/3

Step-by-step explanation:

Triangle ACB is similar to Triangle AED because of AA.

Therefore AB/BC = AD/DE

x/7 = (x+8)/13

We can cross-multiply.

13x = 7(x+8)

We can distribute the 7.

13x = 7x + 56

6x = 56

x = 28/3

Answer: y-5=2(x-1)

Step-by-step explanation: you simply use the point given and turn the also given equation into a point slope form.

The function r(x) is an example of a Pade approximation to f(x). it is not always possible to find such an approximation r(x). However,

It is not always possible to find an approximation r(x). However, the function r(x) is an example of a Pade approximation to f(x).

What is Pade approximation A Pade approximation is a technique for approximating a function using a ratio of two polynomials. This approximation is used to approximate functions that may be difficult to compute or solve exactly.

Pade approximations are often used in numerical analysis, scientific computing, and engineering to obtain accurate solutions to problems that are too complicated or expensive to solve exactly.How to find an approximation r(x) To find an approximation r(x), we need to find a ratio of two polynomials that approximates f(x).

The Pade approximation r(x) is given by the ratio of two polynomials: P(x) and Q(x). The P(x) and Q(x) are usually chosen to be of the same degree to minimize the error between the approximation and the exact value of f(x).Therefore, it is not always possible to find such an approximation r(x). However, the function r(x) is an example of a Pade approximation to f(x).

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Edward has 12 coins of the quarter and 8 coins of nickel with him

Total number of coins = 20

The total amount of money = $3.40

Let x represent the number of quarters and y represent the number of nickels

Formulating the equations we get:

x + y = 20-------(1)

0.25x + 0.05y = 3.40

Simplifying by removing the decimals and solving

25x + 5y = 340------(2)

Multiplying equation (1) by 5 and subtracting with equation (2) we get the following:

5x + 5y = 100

25x + 5y = 340

= 20x = 240

x = 12

So, y = 8

So, the number of quarters is 12 and the number of nickels is 8

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Answer: There were 99 more skateboarders than skaters at the park on Saturday.

Step-by-step explanation:

Let there were 8x skaters and 3x skateboarders on Friday.

There were 168 skaters on Friday.

So, \(8x=168\)

\(\Rightarrow\ x=\dfrac{168}{8}=21\)

3x = 3 (21)=63

Total skaters and skateboarders on Friday = 168+63 =  231

Also, the  ratio of the number of skaters to the number of skateboarders was 2:5

Let there were 2x skaters and 5x skateboarders on Saturday.

Then,

\(2x+5x= 231\\\\\Rightarrow\ 7x = 231\\\\\Rightarrow\ x=\dfrac{231}{7}\)

\(\Rightarrow\ x=33\)

Number of skaters = 2(33) = 66

Number of skateboarders = 5(33) = 165

Difference = 165-66= 99

Hence, there were 99 more skateboarders than skaters at the park on Saturday.

Answer:

$100

Step-by-step explanation:

From the question, we are given the following

Rental price of the truck

percentage off coupon = 50%

Required

Sale tax of the truck rental

Sale tax of the truck rental = 50% of the truck price

Sale tax of the truck rental = 50% of $200

Sale tax of the truck rental = 50/100 * 200

Sale tax of the truck rental = 0.5 * 200

Sale tax of the truck rental = $100

Hence the sale tax of the truck rental is $100

Therefore, the equation of the line tangent to the graph of f(x) = x^4 + 2x^2 at the point where f'(x) = 1 is:y = -3x + 13/16 or y = 3x + 1/16.

The given function is f(x) = x^4 + 2x^2. We are to find the equation of the tangent line to this function at the point where f'(x) = 1. Let's first find the derivative of f(x) as follows:f(x) = x^4 + 2x^2f'(x) = 4x^3 + 4xAt the point where f'(x) = 1, we have:1 = 4x^3 + 4x4x^3 + 4x - 1 = 0Solving for x using the Rational Root Theorem gives:x = (-1/2) or x = (1/2) or x = (√5)/2 or x = -(√5)/2Substituting each of these values of x back into the original function gives the corresponding y-coordinates:f(-1/2) = (-1/16) + 1/2 = 7/16f(1/2) = (-1/16) + 1/2 = 7/16f(√5/2) ≈ 4.84f(-√5/2) ≈ 4.84Thus, there are two points where f'(x) = 1: (-1/2, 7/16) and (1/2, 7/16). We can now use the point-slope form of the equation of a line to find the tangent line at each of these points. For example, at the point (-1/2, 7/16), the slope of the tangent line is:f'(-1/2) = 4(-1/2)^3 + 4(-1/2) = -3Thus, the equation of the tangent line is:y - (7/16) = -3(x + 1/2)Simplifying:y = -3x + 13/16Similarly, at the point (1/2, 7/16), the slope of the tangent line is:f'(1/2) = 4(1/2)^3 + 4(1/2) = 3Thus, the equation of the tangent line is:y - (7/16) = 3(x - 1/2)Simplifying:y = 3x + 1/16

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An equation of the line tangent to the graph of,

\(f(x) = x^4 + 2x^2\)

The required equation is \(y = 3x - \frac{3}{16}\)

We know that if the line tangent to the graph of the function f(x) at the point (a,f(a)) exists, then it passes through the point (a,f(a)) and has the slope f'(a).

The slope of the function is f'(x) = 4x³ + 4x.

We want to find an equation of the line tangent to the graph of the function f(x) = x⁴ + 2x² at the point

where f'(x) = 1.

So, we have, f'(x) = 1 = 4x³ + 4x

Thus, solving this equation,

\(x(x^2+1) = \frac{1}{4}\)

\(x^3+x-\frac{1}{4} = 0\)

Thus, the roots of the polynomial,

\(x^3 + x - \frac{1}{4} = 0\)

are

\(x = \frac{1}{2},-1,-\frac{1}{2}\)

Now, we have to find the point of the function

\((\frac{1}{2}, f(\frac{1}{2}))\)

where the slope is 1.

We have,

\(f(x) = x^4 + 2x^2\)

\(f(\frac{1}{2}) = (\frac{1}{2})^4 + 2(\frac{1}{2})^2 = \frac{9}{16}\)

So, the point is ,

\((\frac{1}{2}, \frac{9}{16})\)

Therefore, an equation of the line tangent to the graph of

\(f(x) = x^4 + 2x^2\)

at the point

\((\frac{1}{2},\frac{9}{16})\)

where f'(x) = 1 is:

\(y - \frac{9}{16} = (4(\frac{1}{2})^3 + 4(\frac{1}{2}))(x - \frac{1}{2})\)

\(y - \frac{9}{16} = 3(x - \frac{1}{2})\)

Therefore,

is the required equation.

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Answer:

50%

Step-by-step explanation:

Para resolver este problema vamos a definir 4 variables:

V= número de varones bailando.

M= número de mujeres bailando.

V' = número de varones que no están bailando.

M' = número de mujeres que no están bailando.

Sabemos que hay 40 personas en la fiesta, por lo que podemos construir la siguiente ecuación:

V+M+V'+M'=40

Vamos a suponer que cada mujer que está bailando, está bailando varón respectivamente. (El problema no da más información, entonces podemos suponer esto.)

Entonces si hay 5 mujeres bailando, entonces también hay 5 hombres bailando, por lo que nuestra ecuación se reescribe de la siguiente manera:

5+5+V'+M'=40

y simplificamos:

10+V'+M'=40

V'+M'=40-10

V'+M'=30

Ahora bien, el problem nos dice que el número de varones que no bailan es el doble del número de mujeres que no bailan en un determinado momento. Entonces con esta información podemos construir la siguiente ecuación:

V'=2M'

Y podemos despejar el número de mujeres que no bailan, lo que nos da:

\(M'=\frac{V'}{2}\)

Entonces podemos sustituir esto dentro de nuestra ecuación para obtener:

\(\frac{V'}{2}+V'=30\)

y podemos entonces despejar V'

\(\frac{3V'}{2}=30\)

\(V'=\frac{2(30)}{3}\)

V'=20

Entonces hay 20 varones que no están bailando, por lo que la probabilidad de que el varón que se escoge al azar no esté bailando está dada por la siguiente fórmula:

\(P=\frac{V'}{total}\)

\(P=\frac{20}{40}=\frac{1}{2}\)

P=50%

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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well, she's 13 now, and when she'll be 21 that's 8 years later, so

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6439\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases}\)

\(A = 6439\left(1+\frac{0.04}{1}\right)^{1\cdot 8}\implies A=6439(1.04)^8 \implies \stackrel{ \textit{yeap, she will \checkmark} }{A \approx 8812.22}\)

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Answer: 3. Natural, whole, integer, rational, real

Answer:

Answer 3: Natural, whole, integer, rational, real

Step-by-step explanation:

The mass of the solid copper with a density of 9.86g/cm³ and dimensions of 5cm x 3cm x 10cm is 1.479kg.

To calculate the mass of the solid copper, we need to use the formula

mass = density x volume

First, let's calculate the volume of the solid copper

volume = width x height x depth = 5 cm x 3 cm x 10 cm = 150 cm³

Now, we can plug in the values we have

mass = density x volume = 9.86 g/cm³ x 150 cm³ = 1479 g

To convert grams to kilograms, we divide by 1000

mass in kg = 1479 g / 1000 = 1.479 kg

Therefore, the mass of the solid copper is 1.479 kg.

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The given question is incomplete, the complete question is:

The density of copper is 9.86g/cm[cubed] work out the mass of the solid in kg

width is 5cm

height is 3cm

depth is 10cm

The larger of the two consecutive even perfect squares is $15,536$.

Square is a four-sided shape that has four equal sides and four right angles. It is the most basic of all quadrilaterals and is a two-dimensional shape. A square has a line of symmetry that passes through the center and divides it into two equal halves. All four sides of a square are equal in length and all four angles are equal to 90 degrees.

To find this, we need to use the difference between the two squares and solve for the larger number. We know that the difference between the two squares is $268$, so we can write the following equation:

$15,536 - 268 = 15,268$

This equation tells us that the larger of the two squares is $15,536$.

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The larger of the two consecutive even perfect squares is 15,536.

Square is a four-sided shape that has four equal sides and four right angles. It is the most basic of all quadrilaterals and is a two-dimensional shape. A square has a line of symmetry that passes through the center and divides it into two equal halves. All four sides of a square are equal in length and all four angles are equal to 90 degrees.

To find this, we need to use the difference between the two squares and solve for the larger number. We know that the difference between the two squares is 268, so we can write the following equation:

So, 15,536 - 268 = 15,268

This equation tells us that the larger of the two squares is 15,536.

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The number of water specimen is 304.

What is standard deviation?

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

What is margin of error?

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.

Given,

margin of error = 0.5

Standard deviation = 5.4

To find the total water specimens.

Margin of Error = Z * ơ / √n

For two-sided confidence interva

p' = 1-α/2

α = 1- 0.90

= 0.1

p' = 1-0.1/2

p' = 0.95

The critical z value for cumulative probability of 0.95 is 1.64.

Margin of error = 1.64(5.4/\(\sqrt{n}\))

0.5 = 1.64(5.4/\(\sqrt{n}\))

n = 304

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Mercury is used to measure high temperatures and alcohol has a lower freezing point that mercury.

The freezing point of any substance, describe the transition of liquid into solid.

The freezing point of water is \(0\) °C or \(32\) °F.

At zero-degree water molecules are moving very slowly, and formation of solid begins i.e. Ice.

When salt or sugar is combined that is mixed with water or ice and it is evenly distributed, the freezing point is lowered.

Lowering of freezing point allows the street ice to melt at lower temperatures, it prevent the accumulation of dangerous, slippery ice.

Alcohol is used to measure the lower temperatures.

Mercury boils at \(357\) degree Celsius where as alcohol boils at \(78\) degree Celsius.

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Answer:

The expression (5m)³ can be expressed as 5into 5into 5·intom·xm·xm

Answer:

joy

Step-by-step explanation:

Answer:

Irene

Wendy

Seulgi

Joy

Yeri

Step-by-step explanation:

Answer:

the answer is 4

Step-by-step explanation:

Answer:

h ey ew   h  he    h dhv h   d   h h  h j  hd v   8 9  

Step-by-step explanation:

Answer:

165 Calories

Step-by-step explanation:

A gram of carbohydrate contains 4 calories. A gram of protein also contains 4 calories. A gram of fat, though, contains 9 calories

5x9=45 10x4=40 20x4=80 45+40+80= 165

Answer:

x=13

Q=30

P=126

R=24

Step-by-step explanation:

To find x put them all into an equation like this:

(4x-22)+(10x-4)+(x+11)=180 (we get 180 because all three angles of any triangle always equal 180)

calculate and you'll get x=13.

then to find each angle just put 13 in place of x

4(13)-22=30

10(13)-4=126

(13)+11=24

Answer:

12-3

9 is the range

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

9

Step-by-step explanation: