23. 33, with a standard deviation of 6. 13. Suppose that a person experienced their first marriage at age 23. If the area beyond the Z score associated with age 23 is 0. 24, what proportion of respondents experienced their first marriage

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

Step-by-step explanation:

3

x

2

+

4

x

+

19

−

f

(

x

)

=

0

Answer:

\(y = \frac{1}{3}x-4\)

Step-by-step explanation:

Step 1:  Solve for y in the first equation

\(3y - x = -12\)

\(3y - x + x = -12 + x\)

\(\frac{3y}{3} = \frac{x}{3} - \frac{12}{3}\)

\(y = \frac{1}{3}x - 4\)

Step 2:  Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1/3 which means that our slope is also going to be 1/3.  We also know that our line crosses the point (18, 2) which means that we can use the point slope form to determine our equation

Point Slope Form → \((y-y_1) = m(x - x_1)\)

Step 3:  Plug in the information and solve

\((y-2) = \frac{1}{3}(x - 18)\)

\(y - 2 = \frac{1}{3}x - 6\)

\(y - 2 + 2 = \frac{1}{3}x - 6 + 2\)

\(y = \frac{1}{3}x-4\)

Answer: \(y = \frac{1}{3}x-4\)

Answer:

The expression that fits into the box is x¹⁵⁸

Step-by-step explanation:

Let the empty box be y

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Here, we will apply the laws of indices.

The laws of indices gives the answer for the expressions

1) xᵏ × xˢ = xᵏ⁺ˢ

2) xᵏ ÷ xˢ = xᵏ⁻ˢ

3) (xᵏ)ˢ = xᵏ•ˢ

So,

(x¹²)⁵ = x⁶⁰

(x⁻²)⁹ = x⁻¹⁸

(x⁴⁰)⁵ = x²⁰⁰

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Becomes

x⁶⁰ × x⁻¹⁸ × y = x²⁰⁰

x⁶⁰⁻¹⁸ × y = x²⁰⁰

x⁴² × y = x²⁰⁰

y = x²⁰⁰ ÷ x⁴²

y = x²⁰⁰⁻⁴² = x¹⁵⁸

Hope this Helps!!!

Answer:

  3·ln(x) -ln(1+x)

Step-by-step explanation:

You want to "solve" the expression ln(x³/(1+x)).

The relevant rules of logarithms are ...

  ln(a^b) = b·ln(a)

  ln(a/b) = ln(a) -ln(b)

The given log expression can be expanded as ...

  \(\ln{\left(\dfrac{x^3}{1+x}\right)}=\ln(x^3)-\ln(1+x)=\boxed{3\ln(x)-\ln(1+x)}\)

Answer:

Step-by-step explanation:

Answer:

A^n = [4^n 4^n

0 1]

Step-by-step explanation:

To find the solution for the 2x2 matrix A:

[4 4

0 1] to the nth power = [ ]

We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:

A^1 = [4 4

0 1]

Now, let's solve for A^2 by multiplying A^1 by A:

A^2 = A x A^1

= [4 4 [4 4

0 1] 0 1]

= [16 16

0 1]

Next, let's solve for A^3:

A^3 = A x A^2

= [4 4 [16 16

0 1] 0 1]

= [64 64

0 1]

We can see a pattern emerging:

   A^1 = [4 4

   0 1]

   A^2 = [16 16

   0 1]

   A^3 = [64 64

   0 1]

We can generalize this pattern as follows:

A^n = [4^n 4^n

0 1]

Therefore, the solution for the 2x2 matrix A raised to the nth power is:

A^n = [4^n 4^n

0 1]

Answer:

the correct answer is B and E

Step-by-step explanation:

The system of inequalities represented by the graph is is y > 4 and y ≥ x

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

The graph

The graph has two lines

The blue line is a horizontal dotted line

This means that the line has a y value that exceeds the point where it crosses the y-axis i.e. y > 1

For the x-axis, we have:

A linear inequality with a closed line

The points on the line are (0, 0) and (2, 2)

When represented as an equation, we have

y = x

The upper part is shaded

So, we have

y ≥ x

Hence, the system is y > 4 and y ≥ x

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Answer:

hope its what u r searching for..

The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

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No. A prime number is a number whose only whole factors are 1 and itself.

The multiple of prime numbers can never be a prime number as they have a factor other than 1 and the number itself or we can say that they can be divided by a number other than 1 and the number itself.

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Answer:

8

Step-by-step explanation:

3+5 = 8

Answer:

F = 1/5

Step-by-step explanation:

Answer:

I don't know if your asking for the price for each ticket, but if you are, it's $41 each.

Step-by-step explanation:

5 x 3 = 15(price of the service charge)

138 - 15 = 123(price with out service tax)

123/3 = 41

Hope this was helpful

Answer:

3

Step-by-step explanation:

Part 1

\(a=\sqrt{12^2 + 21^2 -2(12)(21) \cos 35^{\circ}} \approx \boxed{13}\)

Part 2

\(\frac{\sin B}{b}=\frac{\sin A}{a}\\\\\sin B=\frac{b\sin A}{a}\\\\\sin B=\frac{12 \sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}}\\\\B=\sin^{-1} \left(\frac{12\sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}} \right)\\\\B \approx \boxed{32^{\circ}}\)

Part 3

\(\angle C=180^{\circ}-\angle A -\angle B=\boxed{113^{\circ}}\)

Answer: $3.10 per gallon

Step-by-step explanation: 9.30 divided by 3

Answer:

$3.10 is the answer

Step-by-step explanation:

To find Unit rate you do whole to part. So you divide the whole to the part. In this expression the whole is $9.30 and the part would be per gallon or $3 when you divide 9.30 by 3 it should give you 3.10 or 3.1 which is the same thing.

Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

Answer:

X ≥ 3   (D)

Step-by-step explanation:

I got it right on Khan Academy :)

Answer:

i think it's malik

Step-by-step explanation:

i took the test and passed

Answer:

Malik

Step-by-step explanation:

when you subtract three from both sides it says that -3 is greater than or equal to the absolute value of 6x. And an absolute value can never be less than or equal to a negative number smh Elise, Jake, and Xiao.

the equation of the line perpendicular to 5x - 4y = 10 and passing through the point (5,12) is y = -(4/5)x + 16.

How to determine?

To find the equation of the line perpendicular to the line 5x - 4y = 10 and passing through the point (5,12), we need to first find the slope of the given line.

Rewriting the equation of the given line in slope-intercept form (y = mx + b), we get:

5x - 4y = 10

-4y = -5x + 10

y = (5/4)x - 5/2

The slope of this line is (5/4), so the slope of any line perpendicular to it is the negative reciprocal of (5/4), which is -(4/5).

Now we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Plugging in the values we have, we get:

y - 12 = -(4/5)(x - 5)

Expanding and simplifying, we get:

y - 12 = -(4/5)x + 4

y = -(4/5)x + 16

Therefore, the equation of the line perpendicular to 5x - 4y = 10 and passing through the point (5,12) is y = -(4/5)x + 16.

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The number of tablets that the individual would take per dose would be = 0.5 tablet.

A drug is a substance that is usually prescribed by a physician which when taken has the ability to alter the physiological condition of an individual.

The order or prescribed dosage of the drug ABC = 175mg / dose

The vehicle measurement of the drug = 350mg/tab

If 1 tablet = 350 mg

X tablet = 175 mg

Make X tablet the subject of formula;

X tablet n= 175/350

X tablet = 0.5 tablet or 1/2 tablet.

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Answer:

Explanation:

Given:

To find:

the value of x using the quadratic formula

The quadratic formula is given as:

where a = -3, b = 4, c = 1

Answer:

savings account. After a year, the account balance will be $615. What is the interest rate?

Write the equation AND solve.

Step-by-step explanation:

savings account. After a year, the account balance will be $615. What is the interest rate?

Write the equation AND solve.

The height of the building is approximately 227 feet.

In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.

The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.

As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.

Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF

On substituting the values from the given data, we get:

AE/(EF + 5.5) = 7/5.5.... (1)

Similarly, we can write from the given data:

BD/DF = 162/5.5.... (2)

From equations (1) and (2), we can write:

AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)

On solving the above equation for AE, we get:

AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft

Therefore, the height of the building is approximately 227 feet.

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