I need help on number 19 and 20

\(\\ \sf\longmapsto XY=\sqrt{x^2+y^2}\)

\(\\ \sf\longmapsto XY=\sqrt{a^2+2^2}\)

\(\\ \sf\longmapsto XY=\sqrt{a^2+4}\)

\(\\ \sf\longmapsto XY=2+a\)

Answer:

y = 5x - 8

Step-by-step explanation:

Here. we want to find the equation of the line

The general form is;

y = mx + b

where m is the slope and b is the y—intercept

To get the slope, we can pick any two points on the line

These are;

(2,2) and: (3,7)

we have the slope as follows;

m = (y2-y1)/)x2-x1) = (7-2)/3-2) = 5/1 =5

So we have;

y = 5x + b

To get b , use any point on the line and substitute its coordinates

using (3,7)

7 = 5(3) + b

7 = 15 + b

b = 7-15

b = -8

So the equation of the line is (

y = 5x - 8

The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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The division and simplification of √500 / √5 is equal to 10.

To divide and simplify √500 / √5, you can use the quotient rule of square roots. The quotient rule states that √a / √b is equal to √(a/b).

So, applying this rule to the given expression, √500 / √5 becomes √(500/5).

Simplifying the expression within the square root, 500/5 equals 100.

Therefore, √500 / √5 simplifies to √100.

Since the square root of 100 is 10, the simplified form of √500 / √5 is 10.

Hence, the division and simplification of √500 / √5 is equal to 10.

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160 students are identified to have measles in all at the end of the 6th day of the outbreak.

On the first day of a measles outbreak at a school, 5 students were identified to have the measles. Each day for the following two weeks, the number of new cases doubled from those identified with the disease the day prior. Here is the calculation below:

Number of cases of measles on the first day of outbreak = 5

Total number of cases of measles on day 2 = 5 x 2 = 10

Total number of cases of measles on day 3 = 10 x 2 = 20.

Total number of cases of measles on day 4 = 20 x 2 = 40

Total number of cases of measles on day 5 = 40 x 2 = 80

Total number of cases of measles on day 6 = 80 x 2 = 160

Therefore, 160 students are identified to have measles in all at the end of the 6th day of the outbreak.

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From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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Answer:

342.7 cubic cm

Step-by-step explanation:

see image

Calculate the volumes of the cylinder and the prism. Subtract.

see image.

Volume is the amount of three-dimensional space enclosed by a closed surface. The volume of the solid is 342.655 cm³.

The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity called volume.

The volume of the solid is the difference between the volume of the cylinder and the volume of the square prism.

\(\text{Volume of the solid} =\text{Volume of the cylinder}-\text{Volume of the square prism}\)

\(\text{Volume of the solid} =(\pi r^2 h)-(a^2 h)\)

We know that the radius of the cylinder is 4 cm while the length of the side of the square prism is 4 and the height of both is 10cm. therefore, substituting the values,

\(\text{Volume of the solid} =(\pi\times 4^2 \times 10)-(4^2 \times 10)\)

                               \(=4^2\times10 (\pi -1)\\\\= 342.655\RM\ cm^3\)

Hence, the volume of the solid is 342.655 cm³.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The ordered pair (1, 2) is a solution to the system of inequalities

x + y > 2 and

3x + 2y ≤ 6.

To find an ordered pair that is a solution to the system of inequalities:

Start with the first inequality:

x + y > 2.

Choose a value for x and y that satisfies this inequality. For example, let's choose

x = 1 and

y = 2.

Substituting these values into the inequality:

1 + 2 > 2, which is true.

Now, let's move to the second inequality:

3x + 2y ≤ 6.

Substitute the same values, x = 1 and

y = 2, into this inequality:

3(1) + 2(2) ≤ 6.

Simplifying, we have:

3 + 4 ≤ 6, which is true.

Therefore, the ordered pair (1, 2) is a solution to the given system of inequalities.

Hence the ordered pair (1, 2) is a solution to the system of inequalities

x + y > 2 and 3x + 2y ≤ 6.

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A) The new values for the mean and standard deviation, after adding 3 points to every score, would be a mean of 53 and a standard deviation of 10. B) The new values for the mean and standard deviation, after multiplying every score by 2, would be a mean of 100 and a standard deviation of 20.

A) Adding 3 points to every score in the population would result in a shift of the entire distribution. The new mean would be the original mean plus 3, so the new mean would be 50 + 3 = 53. The standard deviation would remain the same since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would still be 10.

B) Multiplying every score in the population by 2 would affect both the mean and the standard deviation. The new mean would be the original mean multiplied by 2, so the new mean would be 50 * 2 = 100. The new standard deviation would also be multiplied by 2 since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would be 10 * 2 = 20.

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Answer:

$5.05

Step-by-step explanation:

.85($5.60) + $1.79 - $1.50

$4.76 + $1.79 - $1.50 = $5.05

The observed odds ratio (the observed association between migraine headache and cell phone use) is OR = 1.23.

An investigator is studying the association between cell phone use and migraine headaches.

100 cases (migraine patients) and 100 controls (people who don't suffer from migraine), and asks each group how many hours they use their cell phones per day, on average.

To calculate odd ratio ( exposure is cell phone as to check cell phone use on migraine)

Odds of disease in exposed = 60/55= 1.09

Odd of disease in non exposed = 40/45 = 0.88

Thus the odds ratio will be = 1.09:0.88

=> Odds of disease in exposed / odds of disease in non exposed = 1.09/ 0.88 = 1.23

= OR = 1.23

Hence the answer is the observed odds ratio (the observed association between migraine headache and cell phone use) is OR = 1.23.

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From the present question, let's say that the missing angles are a, b, and c. We know that the sum of the other seven is equal to 1220°. By definition, the sum of the inner angles of any polygon is given by:

In the present case, n = 10. Which means:

From the information given, we are able to say that:

Here we found the first equation. The information about supplementary and complementary angles can be written as:

Now we have the following system of equations:

If we substitute the second equation in the first one, we are able to find the value for c. Performing this calculation, we find the following:

With this value, we are able to substitute the value of c in the third equation, and find the value of b, as follows:

Now, we can substitute the value of b in the second equation of the system, to find the value of a, as follows:

Now, from all the given information, we were able to find that, the three missing angles are:

Because the question did not name the angles, their name and order are not important, just the values.

The projection of u onto v is (3,9) and the vector component of u orthogonal to v is (6,-2).

To find the projection of u onto v, we use the formula:

proj_v(u) = (u.v/||v||²) × v

where u.v is the dot product of u and v, and ||v||² is the magnitude of v squared.

First, we calculate u.v:

u.v = (9)(1) + (7)(3) = 30

Next, we calculate ||v||²:

||v||² = (1)² + (3)² = 10

Now we can plug these values into the formula to get the projection of u onto v:

proj_v(u) = (30/10) × (1,3) = (3,9)

To find the vector component of u orthogonal to v, we use the formula:

comp_v(u) = u - proj_v(u)

We already calculated proj_v(u) to be (3,9), so we can subtract that from u:

comp_v(u) = (9,7) - (3,9) = (6,-2)

Therefore, the projection of u onto v is (3,9) and the vector component of u orthogonal to v is (6,-2).

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Answer:  -4.667/2.000 = -2.333

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :    y-(-7/3*x+5/2)=0

Simplify   \(\frac{5}{2}\)

Equation at the end of step : y -  ((0 -  (\(\frac{7}{3}\) • x)) +  \(\frac{5}{2}\))  = 0

The left denominator is : 3  The right denominator is : 2

Least Common Multiple:      6

 y - \(\frac{(15-14x)}{6}\)   = 0

y • 6 - \(\frac{(15-14x)}{6}\) \(\frac{6y + 14x - 15}{6}\)

\(\frac{ 6y + 14x - 15}{6}\)

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.500 and for x=2.000, the value of y is -2.167. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.167 - 2.500 = -4.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -4.667/2.000 = -2.333

 x-intercept = 15/14 = 1.07143

 y-intercept = 15/6 = 5/2 = 2.50000

Answer:

28

Step-by-step explanation:

The scale factor is 3.5 which is found out by doing 14 divided by 4. Once you know the scale factor you simply have to do 8 multiplied 3.5 which equals 28.

Answer:

24 cm

Step-by-step explanation:

(4+4) + (8+8)

Answer:

a= 77, b= 77, c= 103.

Step-by-step explanation:

a= 77 (vertically opposite)

b= a= 77 (corresponding angles)

c= 180-77

 = 103 (angles on a straight line)

Answer:

23 gallons per hour

Step-by-step explanation:

5 3/4 * 4 = 23

times the amount drank in 1/4 hours by 4 to get the amount drank in 1 hour

(1/4 * 4 = 1 hour (example))

Answer:

500

Step-by-step explanation:

it is a 3 digit number which means it is in the hundreds

Akira will lean the 5-meter ladder 4 m from the building to wash the a window.

information given in the question

hypotenuse = 5-meter ladder

opposite = 3 meters off the ground

adjacent =  how far away from the building = ?

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

5² = 3² + x²

25 = 9 + x²

25 - 9 = x²

x² = 16

x = √16

x = 4

Akira should place the ladder 4m from the building

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The cost of 11.5 sheets of stickers costs is $40.25.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, four sheets of stickers cost $14.

Now, the cost of 1 sheet of stickers is 14/4

= $3.5

The cost of \(11\frac{1}{2}\) =11.5 sheet of stickers is

11.5×3.5

= $40.25

Therefore, the cost of 11.5 sheets of stickers costs is $40.25.

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Answer:

10X^2-39x+14

(5x-2)(2x-7

Answer:

QPR SAS

Step-by-step explanation:

As you can see. Hope it can help

Answer:

-5 degrees fahrenheit

Given that the ordered pair makes the function and these pairs are

[ (2,5), (7,1), (5,9), (8,0), ( , ) ]

Since the function is the one that has the input having only one output.

Hence, the given options (3,4) is correct.

Therefore the ( 3, 4 ) is the pair.

Answer:

f(x)=x2+1g(x)=2xh(x)=x−1

Step-by-step explanation:

f takes the square of a number and adds 1

g doubles a number

h subtracts 1 from a number

Answer:

Step-by-step explanation:

Answer:

h(x)=20

Step-by-step explanation:

x=5

3(5)+5

15+5

20

Hope this helps!

Answer:20

Step-by-step explanation:

Hello!

So first you want to plug in 5 to all of the x

h(5) = 3(5) + 5

No you want to do 3(5)

3(5) = 15

h(5) = 15 + 5

Now you add 15 + 5

15 + 5 = 20

h(5) = 20

So your answer is 20

Answer:

48.

Step-by-step explanation:

12x4=48

Unit conversion converts one unit into another without changing its real value. The Four one-foot rulers laid end to end will have 48 inches.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm,

though the real measurement is still the same the units and numerical values have been changed.

We know that the 1 foot has 12 inches in it, therefore, when the Four one-foot rulers laid end to end will have 4 feet in total, and since one foot has 12 inches, thus,

\(\begin{aligned}\rm 4\ feet &= 4 \times 12\ inches\\&=48\rm\ inches\end{aligned}\)

Hence, the Four one-foot rulers laid end to end will have 48 inches.

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