Last year Lenny had an annual earned income of 58,475 he also had passive income of 1,255 and capital gains of 2,350 what was lennys total gross income for the year

Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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The sale of the four different sizes is an illustration of the Goodness of Fit Tests

The expected counts for each size box are 0.8, 3.6, 36.6 and 4.05 respectively

The null hypothesis is always represented by the equality sign i.e. 0 change or no change.

While the alternate hypothesis is always represented by an inequality.

So, the null and the alternate hypotheses are:

This calculated as:

E(x) = np

So, we have:

Small = 8 * 10% = 0.8

Medium = 24 * 15% = 3.6

Large = 61 * 60% = 36.6

Jumbo = 27 * 15% = 4.05

Hence, the expected counts for each size box are 0.8, 3.6, 36.6 and 4.05 respectively

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Step-by-step explanation:

The floor of a round hut has a diameter of 4 yards. What is the floor's area?

Answer:

12.56637 or 4 pi hope this helps

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

Answer:

Lauren needs to get 95  on her next math test so that the mean and median remain the same

Step-by-step explanation:

92+93+ 94+ 95+96+97+98  = 665

665/2 =95

mean=95

median=95

x=  score could Lauren get on her next math

(665+ x)/8 =95

multiply both sides by 8 to eliminate fraction

665 +x = 760

x=95

So now the median is the same

(95+95)/2=95

      shorcut:

with 7 scores 95 is the median(in the middle)

with 8 scores ,we need a number that added to 95 and divided by 2 is still 95  That number is 95

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The given expression can be rewritten as 2 × 5 × 5 × 5 × 5 and is equal to 1250. The correct option is (B).

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 2 × 5⁴.

It can be simplified using the rule of indices as follows,

The expression 5⁴ can be written as 4 times 5 as below,

5⁴ = 5 × 5 × 5 × 5.

Then, the expression can be evaluated as

⇒ 2 × 5 × 5 × 5 × 5

⇒ 1250

Hence, the expression can be simplified to obtain 1250.

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Answer:

Step-by-step explanation:

use SOH CAH TOA to remember sin cos and tan functions

Sin = oppostive/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent

22. cos(x) = b/c
24. sin(x) = 2/2sqrt(17) = 1/sqrt(17)
26. tan(x) = 2/8 = 1/4

28. cos(y) = 2/2sqrt(17) = 1/sqrt(17)
30. sin(30)
in a 30 60 90 triangle, the side opposite 30 is 1, the side opposite 60 is sqrt(3), the side opposite 90 is 2.
sin(30) = opposite/hypotenuse = 1/2/1 = 1/2
32.
in a 45 45 90 triangle, the side opposite 45 is 1, the side opposite 45 is 1, the side opposite 90 is sqrt2.

sin = opposite/hypotenuse = 1/sqrt(2)
34. cos(30) = sqrt(3)/2

36. tan(31) = AC/9 --> AC = 9tan(31) = 5.408

Answer:

22.  \(\dfrac{b}{c}\)

24.  \(\dfrac{\sqrt{17} }{17}\)

26.  \(\dfrac14\)

28.  \(\dfrac{\sqrt{17} }{17}\)

30.  \(\dfrac12\)

32.  \(\dfrac{\sqrt{2} }{2}\)

34.  \(\dfrac{\sqrt{3} }{2}\)

36. AC = 5.41 (nearest hundredth)

Step-by-step explanation:

Using trig ratios:

\(sin(\theta)=\dfrac{O}{H}\\\\\\cos(\theta)=\dfrac{A}{H}\\\\\\tan(\theta)=\dfrac{O}{A}\)

where \(\theta\) is the angle, O is the side opposite the angle, A is the side adjacent the angle, H is the hypotenuse of a right angle

22. \(cos(x)=\dfrac{b}{c}\)

24.  \(sin(x)=\dfrac{2}{2\sqrt{17} }=\dfrac{\sqrt{17} }{17}\)

26. \(tan(x)=\dfrac{2}{8}=\dfrac14\)

28. \(cos(y)=\dfrac{2}{2\sqrt{17} }=\dfrac{\sqrt{17} }{17}\dfrac{}{}\)

30. \(sin(30)=\dfrac12\)

32. \(sin(45)=\dfrac{\sqrt{2} }{2}\)

34. \(cos(30)=\dfrac{\sqrt{3} }{2}\)

36. \(tan(31)=\dfrac{AC}{9}\)

\(\implies AC=9tan(31)=5.41\) (nearest hundredth)

Answer:

B.

Step-by-step explanation:

\(\sqrt[4]{2x^2} * \sqrt[4]{2x^3}\)

= \(2^{1/4}x^{2/4} * 2^{1/4}x^{3/4}\)

= B. \(2^{2/4}x^{5/4}\).

Hope this helps!

Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For function f(x), the multiplication by -1 of the function is in the output, meaning that it was a reflection over the y-axis. For function g(x), the multiplication is in the input, the domain, hence the reflection was over the x-axis.

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The price of sunglasses is greater original price and 0.45 is tax amount.

A tax is a mandatory fee or financial charge that a government imposes on a person or a business in order to raise money for public projects like building the greatest infrastructure and services.

Taxes are required financial contributions imposed by a government body, whether local, regional, or federal, on people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.

Given:

Original price of sunglasses = $10.

Price according to cashier= $10.45

So, the price of sunglasses is greater original price.

and, the difference both price

= 10.45 - 10

= 0.45 is tax amount.

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Answer:

hey there

The answer is 7/10

this is true because we have two green marbles and five blue

2+5=7

Step-by-step explanation:

Answer:

20% or 2/10

Step-by-step explanation:

10 marbles in total. We want to find the probability of not picking a green marble. 10marbles-3red-5blue=2marbles left.

So the probability of picking a green marble is 2/10 or 20%

Answer:

The linear equation is the equation of straight line. where m is the slope of the line and c is the y-intercept. Thus, the y-intercept is expressed as (0, c). That is where the graph intercepts the y-axis (thus, the x value would be 0).

Step-by-step explanation:

There are 50 predicted rolls for 5 in 300 times of rolls.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Janet rolls a 6-sided number cube 300 times,

Probability = (Favourable Outcomes)/(Possible Outcomes)

Favourable Outcomes: 5 (1 total)

Possible Outcomes: 1,2,3,4,5,6 (6 total)

Probability of a 5 in any given roll of a die = 1/6

1/6x300 = 50 = 50 predicted roll with 5.

Hence, There are 50 predicted rolls for 5 in 300 times of rolls.

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The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

7.615773105864

Step-by-step explanation:

\(\text{let A and B be the points of coordinates} \ A\left( 3,-9\right) \text{and} \ B\left( 6,-2\right)\)

\(AB=\sqrt{\left( 6-3\right)^{2} +\left( -2-(-9)\right)^{2} }\)

     \(=\sqrt{\left( 3\right)^{2} +\left( 7\right)^{2} }\)

     \(=\sqrt{58} =7.615773105864\)

Answer: 85.7

Step-by-step explanation:

Answer:

a) 23

b) 0.4

c) 0.7

d) 0.08

e) 3.9

f) 1.6

g) 5.5

h) 12.4

Step-by-step explanation:

Answer:

If you want 915/7 simplified, it is 130.714285714.

Step-by-step explanation:

Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

<95141404393>

Answer:

below

Step-by-step explanation:

hope it is well understood?

The slope is 4 and y- intercept is 13

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

Given

Slope

y = 4x-3

dy/dx = 4

slope =  4

intercepts y = 4(4) 3

y = 16-3

y = 13

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Answer:

A. this is a vector, so you need a bar on top (ie not D)

Step-by-step explanation:

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

about 65%

I already answered this