Cassie’s age is 3 less than twice Kara’s age. The sum of their ages is 42.

Create an equation to find Kara’s age, n.

n+ ( _ n- _ ) = _

Intellectually gifted people score in the top 1 - 2percent on a standard IQ test.

From the question, we have the following parameters that can be used in our computation:

IQ of intellectual gifted people

The general rule is that

People with intellectuals are usually ranked high and the range is usually small

Next, we test the options

A. 10

The top 10% has a high range

B. 5-10

The top 10% omits people in top 5%

C. 5

The top 5% has a high range

D. 1-2

This has a small range and it is the highest

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The given differential equation, y'' - 2y' + y = x^2e^(-x), is a second-order linear homogeneous differential equation with variable coefficients.

In the differential equation, the term y'' represents the second derivative of y with respect to x, y' represents the first derivative of y with respect to x, y represents the function y(x), and x^2e^(-x) is a non-homogeneous term on the right-hand side of the equation.

To classify the differential equation, we can examine the coefficients of the derivatives. Since the coefficient of y'' is 1 (non-zero), and the coefficients of y' and y are -2 and 1 (non-zero), respectively, the equation is a non-constant coefficient homogeneous differential equation.

In summary, the given differential equation, y'' - 2y' + y = x^2e^(-x), is a second-order linear non-constant coefficient homogeneous differential equation with a non-homogeneous term on the right-hand side.


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The exact length of curve C, which is the intersection of the given parabolic cylinder and the given surface, from the origin to the given point is 13.14 units.

To find the length of curve C, we can use the arc length formula for curves given by the integral:

L = ∫[a,b] \(\sqrt{(dx/dt)^2 }\)+ \((dy/dt)^2\) + \((dz/dt)^2\) dt

where (x(t), y(t), z(t)) represents the parametric equations of the curve C.

The given curve is the intersection of the parabolic cylinder \(x^2\) = 2y and the surface 3z = xy. By solving these equations simultaneously, we can find the parametric equations for C:

x(t) = t

y(t) =\(t^2\)/2

z(t) =\(t^3\)/6

To find the length of C from the origin to the point (4, 8), we need to determine the limits of integration. Since x(t) ranges from 0 to 4 and y(t) ranges from 0 to 8, we integrate from t = 0 to t = 4:

L = ∫[0,4] \(\sqrt{(1 + t^2 + (t^3/6)^2) dt}\)

Evaluating this integral gives the exact length of C:

L ≈ 13.14 units

Therefore, the exact length of curve C from the origin to the point (4, 8) is approximately 13.14 units.

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Answer:

SA=231.5 in^2

Step-by-step explanation:

2(1/2[5x4.3])+3(5x14)

2(1/2x21.5)+3x70

2(10.75)+3x70

21.5+3x70

21.5+210

231.5

Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

the answer is D

300/6 = x/10

once solved, it will be proportional

Yes, such a function exists. One example of such a function is the function \(f(x) = -x^3\).

Let's analyze the properties of this function:

\(f(x) > 0\): For any positive or negative value of x, when plugged into the function \(f(x) = -x^3\), the result will always be a negative number. Hence, \(f(x) > 0\).

f'(x) < 0: Taking the derivative of f(x) with respect to x, we get \(f'(x) = -3x^2\). The derivative is negative for all non-zero values of x, indicating that the function is decreasing for all x.

f''(x) > 0: Taking the second derivative of f(x) with respect to x, we get f''(x) = -6x. The second derivative is positive for all non-zero values of x, indicating that the function is concave up.

Therefore, the function \(f(x) = -x^3\) satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.

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Answer:

First group like terms

-10(-1f-9)-7f

multiply through

10f+90-7f

10f-7f=3f

90+3f

Answer:

A. 14x⁴ - 18x³ + 43x² + 24x - 15

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define expression

(7x + 5)(2x³ - 4x² + 9x - 3)

Step 2: Expand

Answer:

A. x-y=192 and 9/64x+3/32y=42

Step-by-step explanation:

i got it right dw

Answer:

Step-by-step explanation:

hjyr  kiknbvcctt t

Answer:

One

Step-by-step explanation:

Find the value of B

Applying the law of sines

\(\frac{a}{sin(A)}\) = \(\frac{b}{sin(B)}\)

substitute the given values

\(\frac{23}{sin(61)}\) = \(\frac{24}{sin(B)}\)

sin (B) = \(\frac{24}{23}\)Sin(61)

step 2

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

61 + 65.87 + C = 180

C = 53.13

step 3

Find the value of c

Applying the law of sines

\(\frac{a}{sin(A)}\) = \(\frac{c}{sin(C)}\)

substitute the given values

\(\frac{23}{sin(61)}\) = \(\frac{c}{sin(53.13)}\)

c = \(\frac{23}{sin(61)}\)SIN (53.13)

C=21.04 units

so

there can only be one value for each measurement, therefore there can only be one triangle

Answer:

The answer is 2 triangles

Step-by-step explanation:

I took the test.

So, the basketball player needs to shoot the ball with a velocity of u so that the maximum height attained by the ball is 10.0625 feet.

Given, A basketball player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of the ball can be modeled by the quadratic function,

h(x) = -0.005x² + 0.45x + 6

Here, the ball has released at an angle of 45 degrees, then the vertical velocity (v) and horizontal velocity (u) can be given as:

v = usinθ = ucosθ = gt...

As the projectile motion is a 2-D motion]where t is the time, g is the acceleration due to gravity.

As the maximum height is attained at the mid of the total time taken, thus the time taken to attain the maximum height (H) can be given as:

H = u sin(θ)/g

So, H = u/g [Here, sin(θ) = 1/root2]

Also, The total time (T) of flight can be given as:

T = 2u sinθ/g

We can calculate the value of T using the formula above.

T = 2u sinθ/g

= 2u(1/root2)/g

= u/g√2

Now, Let's put the value of T in the quadratic equation of the path of the ball,h(x)

= -0.005x² + 0.45x + 6h(x)

= -0.005(x² - 90x) + 6h(x)

= -0.005(x²- 90x + 2025 - 2025) + 6h(x)

= -0.005((x - 45)²- 1012.5) + 6h(x)

= -0.005(x - 45)² + 10.0625

As the vertex of the parabola represents the maximum height, thus the maximum height (H) can be given as, H

= 10.0625 feet

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Answer:

                          Cat owner           Dog owner           Total

Wet food                    9                         13                    22

Dry food                    10                        14                     24

Total                          19                        27                     46

Step-by-step explanation:

It is given that 9 cat owners and 13 dog owners chose "Wet food". 10 cat owners and 14 dog owners chose "Dry food".

Cat owners-Wet food = 9

Dog owners-Wet food =13

Cat owners-Dry food = 10

Dog owners-Dry food =14

We need to construct a two-way frequency table for the data.

Take owners in the first row and type of food in first column and construct a two-way frequency as shown below:

                          Cat owner           Dog owner           Total

Wet food                    9                         13                    22

Dry food                    10                        14                     24

Total                          19                        27                     46

Answer:

500*2%=10

500+10=510

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

14 ÷ 56 × 100

The formula that can be used to describe the sequence is:\(a(n) = (-1)^(n+1) * 3^(n) * 4.\)

The given sequence is -81, 108, -144, 192.

The formula that can be used to describe the sequence is:  \(a(n) = (-1)^(n+1) * 3^(n) * 4\), where n is the nth term in the sequence.

This formula is a geometric sequence formula that can be used to describe the given sequence.

The formula represents the nth term of the sequence as a function of the position of the term in the sequence.

Here, n represents the position of the term in the sequence

.For the given sequence, the first term is -81, which corresponds to the first position in the sequence (n = 1).

The second term is 108, which corresponds to the second position in the sequence (n = 2).

The third term is -144, which corresponds to the third position in the sequence (n = 3).

The fourth term is 192, which corresponds to the fourth position in the sequence (n = 4).

Therefore, the formula that can be used to describe the sequence is: \(a(n) = (-1)^(n+1) * 3^(n) * 4.\)

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Answer:

88

Step-by-step explanation:

Every triangle has a measure of 180, so if we know two of the angles we can find the last one easily. To find angle 1, we first must find angle 2. 2 must be equal to 42 because it is vertical to the other angle that is equal to 42 degrees. Then to find angle 1 do the operation 180-(50+42). This equals 88, which is the measure of angle 1.

Answer:

x = 30

Step-by-step explanation:

Using the converse of the Side Opposite 30° Theorem, we find that ∠X is 30°.

Hope this helps :)

The predicted percentage of adolescents having a cell phone in 2022 for state 13 if the percentage in 2012 was 25.3 is given as follows:

49.85.

From the image given at the end of the answer, we are given a table of the percentages from 2012 and from 2022, thus a linear regression equation is built from this table.

The points on the table are given as follows:

(11.9, 25.9), (15.3, 27.1), (16.8, 27.4), (19, 28.9), (21.1, 31.7), (21.3, 41.1), (21.4, 40), (21.5, 42), (22.1, 50.9), (24.6, 43.7), (28.7, 52.6), (30.8, 72.3).

Inserting these points into a linear regression calculator, the line of best fit is given as follows:

y = 2.335x - 9.23.

In which:

Hence the predicted percentage for 2022 is given as follows:

y = 2.335(25.3) - 9.23 = 49.85.

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

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Answer:

I think C. is correct

Step-by-step explanation:

Just trust me, I'm smart ;)

Answer:

they both are the same number

Step-by-step explanation:

Answer:

24/64

Step-by-step explanation:

To find the map's scale, use the formula below:

In this exercise,

map distane = 9 inches

distance on the ground = 3 miles.

So, the map scale is:

Dividing both numerator and denominator by 3:

The map scale is: 3 inches : 1 mile.

Answer:

Sum of angles of a triangle is 180, so x + y + w = 180

Straight angle is 180 , so y + z = 180

From the first 2 conditions :

=>x + y +w = y + z

=> x + w = z  

Option 1, 2, 5

The equations which are true are given by,

Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.

From angle sum property of triangle says that the sum of all interrior angles of a triangle is 180.

Here all interrior angles of triangle are x,y,w

So, x+y+w = 180

Hence first option is correct.

Again the exterrior angle of a triangle is equal to the sum of the opposite two interrior angles.

here exterrior angle is z and opposite two interrior of z are x,w

So, w+x = z

Hence last option is correct.

Again y+z = y+w+x

so second option is also true.

Hence correct options or equations are given by:

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