You are a medical assistant in a pediatrician’s office and one of your responsibilities is evaluating the growth of newborns and infants. Your first patient, a baby girl named Ivy Smith, was 21.5 inches long at 3 months old. At 8 months, you measure her at 24 inches long. For your medical records, all measurements must be given both in inches and in centimeters: 1 inch = 2.54 cm

I need to come up with an equation for this.

Answer:

\(Probability = \frac{1}{792}\)

Step-by-step explanation:

Given

\(Questions = 12\)

\(Selection = 5\)

Required

Probability of grading the selected 5 by Andrew

First, we need to determine the total number of selections.

This is calculated as: \(^{12}C_{5}\)

Solving further:

\(^{12}C_{5} = \frac{12!}{(12-5)!5!}\)

\(^{12}C_{5} = \frac{12!}{7!5!}\)

\(^{12}C_{5} = \frac{12*11*10*9*8*7!}{7!*5*4*3*2*1}\)

\(^{12}C_{5} = \frac{12*11*10*9*8}{5*4*3*2*1}\)

\(^{12}C_{5} = \frac{95040}{120}\)

\(^{12}C_{5} =792\)

There is only 1 for Andrew's question selection.

So, the required probability is:

\(Probability = \frac{1}{792}\)

The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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Answer:

Step-by-step explanation:

These equations are all written in slope-intercept form, so the question is relatively easy to answer. These rules apply.

1. y=-6x-2; y=-6x-2 --- infinitely many

2. y=0.5x+5; y=0.5x+1 --- zero

3. y=0.25x-2; y=5x-4 --- one

4. y=2x+3; y=4x-1 --- one

5. y=2x+1.5; y=2x+1.5 --- infinitely many

6. y=-x-3; y=-x+3 --- zero

_____

Slope-intercept form is ...

  y = mx +b

m is the slope

b is the y-intercept

Answer:

Step-by-step explanation: 1. y=-6x-2; y=-6x-2 --- infinitely many

2. y=0.5x+5; y=0.5x+1 --- zero

3. y=0.25x-2; y=5x-4 --- one

4. y=2x+3; y=4x-1 --- one

5. y=2x+1.5; y=2x+1.5 --- infinitely many

6. y=-x-3; y=-x+3 --- zero

Answer:

Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.

F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b

The slope of a line is positive with a value of 3/2 or 1.5.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

The slope of a line is used to describe the steepness and direction of the line.

Mathematically, the formula for the slope of a line is given as;

slope = Δy / Δx

where;

The slope equation is expanded as follows;

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

From the graph, the values of x and y is determined as;

( x₁, y₁ ) = ( - 2, 0 )

( x₂, y₂) = ( 0, 3 )

The slope of the line is calculated as follows;

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 - - 2)

m = 3 / 2

m = 1.5

Thus, the line has a positive slope.

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The complete question is below:

What is the slope of the line? type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

The type of graph that would be the most appropriate for Rick to use would be the line graph. That is option B.

A graph is defined as the representation of data on two lines that intercepted on an y and x axis which is used for easy interpretation of results obtained from a data set.

The different types of graph include the following;

The line graph is used for the representation of data taken for a short period of time that appears to have little to no difference.

The difference between the temperature of the different days analysed is limited therefore a line graph can be used.

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Answer:

\(\huge \boxed{{x\geq -3, \ x \neq 2}}\)

Step-by-step explanation:

The function is given,

\(\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}\)

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

\(x+8\neq 0\)

Subtract 8 from both parts.

\(x\neq -8\)

\(x-2\neq 0\)

Add 2 on both parts.

\(x\neq 2\)

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

\(x+3\geq 0\)

Subtract 3 from both parts.

\(x\geq -3\)

The domain of the function is \(x\geq -3\), \(x\neq 2\).

The domain of the given function will be x ≥ -3 and x ≠ 2.

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = \(\sqrt{\frac{x+3}{(x-8)(x-2)} }\)

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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Answer:

k=-63

Step-by-step explanation:

multiply both sides by -9

k=7*-9

k=-63

Answer:

-63

Step-by-step explanation:

by simplifying both sides of the equation, then isolating the variable.  k= -63

-9 x 7 = -63

Answer:

Um, the second one is 120 units..

Step-by-step explanation:

Answer:

The first one is 64 sq un

The second one is 120 sq un

Step-by-step explanation:

I do Rsm lol I cant figure out the third one

Answer:

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

ENGLISH

If you Multiply 9x100 you get 900 then you divide 15 divided by 900 is 60

SPANISH

Si multiplica 9x100 obtiene 900, entonces divide 15 dividido por 900 es 60

Hope this will help you

Answer:

24.5 points

8 points

Step-by-step explanation:

khan academy

Answer:

(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Step-by-step explanation:

i literally just learned this today so here we go:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:

(x - (-7))^2 + (y - (-4))^2 = r^2

(x + 7)^2 + (y + 4)^2 = r^2

We also know that the circle contains the point (-1, -8).

We can substitute these values for x and y, and solve for r:

(-1 + 7)^2 + (-8 + 4)^2 = r^2

36 + 16 = r^2

r^2 = 52

Substituting this value of r^2 into the equation for the circle, we get:

(x + 7)^2 + (y + 4)^2 = 52

Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

To find the vertex (h,k), we have to find h using the following formula

Where a = 1 and b = -10.

Then, we find k by evaluating the function when x = 5.

The axis of symmetry is given by the h coordinate of the vertex.

The y-intercept is found when x = 0.

The x-intercepts are found when y = 0.

To solve this expression, we have to look for two numbers which product is 9, and which addition is 10. Those numbers are 9 and 1.

Then, we use the zero product property to express both solutions

The minimum value is defined by the k coordinate of the vertex.

The domain of the function would be all real numbers because quadratic functions don't have any domain restrictions.

The range of the function is determined by the vertex, given that the parabola opens upwards, then the range is

Answer:

$90

Step-by-step explanation:

20 goes into 100 5 times

18 multiplied by 5 equals 90

Check:

90/5=20

Answer:

$50

Step-by-step explanation:

Answer:

{-12, 8}

Step-by-step explanation:

Let's solve your equation step-by-step.

|p+2|=10

Solve Absolute Value.

|p+2|=10

We know eitherp+2=10orp+2=−10

p+2=10(Possibility 1)

p+2−2=10−2(Subtract 2 from both sides)

p=8

p+2=−10(Possibility 2)

p+2−2=−10−2(Subtract 2 from both sides)

p=−12

Answer:

Step-by-step explanation:

sinθ < 0 means below the x axis

cotθ = cosθ/sinθ < 0

As sinθ  is already < 0 means cosθ has to be > 0 meaning right of the y axis.

Right of y and below x is the IV quadrant.

The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).

Trigonometric Identities are equality conditions that hold for all possible values of the variables in the equation and use trigonometry functions. There exists numerous unique trigonometric identities that relate a triangle's side length and angle.

here, we have,

Sine, cosine, and tangent are the fundamental three operations in trigonometry. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical notions exists built.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These exists identities that, geometrically speaking, involve certain functions of one or more angles.

we have,

sinθ < 0 means below the x axis

cotθ = cosθ/sinθ < 0

As sinθ  is already < 0 means cosθ has to be > 0 meaning right of the y axis.

Right of y and below x is the IV quadrant.

Hence, The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).

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The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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Answer:

$8.26

Step-by-step explanation:

$48.75= Total

$1.50= Coupon discount

5= Number of Sets bought by Mrs. James

*$48.75-($1.50*5)= $41.28*

41.28= Total after Coupon discount is removed

5= Number of Sets bought by Mrs. James

$41.28/5= $8.256

Round answer to show dollar value

Final Answer

$8.26

Answer:

angle a: 70°

angle d: 70°

angle dce: 35°

x: 15m

y: 14m

Step-by-step explanation:

all triangles add to 180° so 35 + 75 = 110 and 180-110 = 70

where the two triangles connect and cross, the angles will be the same so it will have the same angle measures as the first triangle which makes the triangles similar

knowing that they are similar triangles will help with figuring out the lengths of the sides.

since they are similar, their sides will be proportional, we just need to figure out the ratio

if we lay the triangles on top of each other, the two 75° angles match up and therefore the sides do too so we can make a fraction 12/18 = 10/x

now we can solve for x

multiply both sides by x

12x/18 = 10

now multiply both sides by 18

12x = 180

divide both sides by 12

x = 15

now we do the same for y

12/18 = y/21

12*21/18 = y

y = 14

hope this helps!

The simple interest on 1600 with a 6% interest rate for 2 years is $192.

The simple interest simply means the method that's used to calculate the interest that's charged on a loan or money given out.

In this situation, we want to calculate the simple interest on 1600 with a 6% interest rate for 2 years. This will be calculated thus:

Simple interest = Principal × Rate × Interest

Simple interest = $1600 × 6% × 2

Simple interest = $1600 × 0.06 × 2

Simple interest = $192

The interest is $192.

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Complete question

Calculate the simple interest on 1600 with a 6% interest rate for 2 years.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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We have the line in standard form:

We have to find the 2 intercepts.

The y-intercept correspond to the value of the line when x=0, so we can find the value of y that correspond to x=0 replacing x in the equation and solving for y:

Then, the ordered pair for the y-intercept is (0,-4).

In the case of the x-intercept the concept is equivalent but the coordinate that has a value of 0 is y. So we will replace y with 0 in the equation and solve for x:

Then, the ordered pair for the x-intercept is (-5,0).

We can graph the line and its intercepts as:

Answer:

X-intercept: (-5, 0)

Y-intercept: (0,-4)

Answer:

A' = (4, 4)

B' = (12, 4)

C' = (4, 10)

Step-by-step explanation:

Ok so you are given that the scale factor is 2. You will multiply 2 with the values given of point A, B, and C in order to find the value of point A', B', and C'.

A = (2, 2) ---> 2 × 2 = 4 and 2 × 2 = 4

A' = (4, 4)

B = (6, 2) ---> 6 × 2 = 12 and 2 × 2 = 4

B' = (12, 4)

C = (2, 5) ---> 2 × 2 = 4 and 5 × 2 = 10

C' = (4, 10)

Hope this helps and stay safe, happy, and healthy, thank you :) !!

Answer:

2/3 = x/48

3x = 2*48

x = 2*48/3

x = 32

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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Answe

G=1.5

Step-by-step explanation:

The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2

To solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:

8x²(x² - 4) = 0

Now we can use the difference of squares identity to factor the quadratic expression:

8x²(x + 2)(x - 2) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

8x² = 0 or x + 2 = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = -2 or x = 2

So the solution set for the equation is {0, -2, 2}.

To check the solution, we can substitute each value into the original equation and verify that it equals zero.

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