Ezra had 46 green marbles. Then he bought 6 bags of blue marbles. There were 8 marbles in
each bag. How many marbles does Ezra have now?
marbles

Answer:

\(\dfrac{x\sqrt{4-x^2}}{4-x^2}\)

Step-by-step explanation:

Given:

\(\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)\)

\(\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}\)

Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}\)

Simplify the denominator:

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}\)

\(\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}\)

Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}\)

Simplify:

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}\)

Answer:

Hope this is correct

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

exact form : 2√3

decimal form : 3.46410161… or 3.46

hope this helps you!

Answer:

The value of the function is \(\sqrt{12}\). Rounded to the nearest hundredth, the answer is 3.46

Step-by-step explanation:

We are given the value of x, so we simply have to evaluate the function:

\(f(x)=\sqrt{x+4}\)

Substitute 8

\(f(8)=\sqrt{8+4}\)

Add in the radical

\(\sqrt{12}\)

The value of the function is sqrt(12).

Rounded to the nearest hundredth: \(3.46\)

Answer:91 years

Step-by-step explanation:

The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

Answer:

30,000

Step-by-step explanation:

3,000 x 10 = 30,000

Therefore, if 24 teaspoons of vegetable oil were used, we would need 16 teaspoons of vinegar to make the recipe correctly.

According to a salad recipe, each serving requires 6 teaspoons of vegetable oil and 9 teaspoons of vinegar. If 24 teaspoons of vegetable oil were used, we can determine the amount of vinegar needed for the recipe to be correct as follows:

First, we must determine the ratio of vinegar to oil in the recipe. To do this, we divide the amount of vinegar needed per serving (9 teaspoons) by the amount of oil needed per serving (6 teaspoons):

9 ÷ 6 = 1.5

This means that for every 1.5 teaspoons of oil used, we need 1 teaspoon of vinegar. Next, we use this ratio to determine the amount of vinegar needed when 24 teaspoons of oil are used:

1.5 ÷ 1 = 1.5

(teaspoons of oil per 1 teaspoon of vinegar)

24 ÷ 1.5 = 16

(teaspoons of vinegar needed)

For such more question on vegetable oil

https://brainly.com/question/5412318

#SPJ8

It means the class has been removed from your schedule and replaced with another class.

\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll use this one}}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(5)+\log_2(6.4)\implies \log_2( ~~(5)(6.4) ~~ )\implies \log_2(32) \\\\\\ \log_2(2^5)\implies \text{\LARGE 5}\)

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

b=10

Step-by-step explanation:

I think the other part would be √-300   √3   but that's the best i could do

Answer:

5l²mn + lm²n - 2lmn².

Step-by-step explanation:

3l²mn - lm²n + 2lm²n + lmn² + -3lmn² +2l²mn

Bringing like terms together:

= 3l²mn +2l²mn  - lm²n + 2lm²n + lmn² - 3lmn²

= 5l²mn + lm²n - 2lmn².

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

Learn more about percentage on:

brainly.com/question/843074

#SPJ1

Answer

Option B is correct.

Volume = 252 cm³

Explanation

The volume of the pyramid is given as

Volume = ⅓ (LWH)

L = Length = 9 cm

W = Width = 6 cm

H = Height = 14 cm

Volume = ⅓ (LWH)

Volume = ⅓ [(9) (6) (14)]

Volume = 252 cm³

Hope this Helps!!!

The equation of the line of best fit is \(y = -\frac{5}{6}x + \frac{82}{3}\) and

We start by drawing an approximated line of best fit (see attachment)

From the attached graph, we have the following points:

(x, y) = (4, 24) and (28, 4)

The equation of the line of best fit is then calculated as:

\(y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1\)

This gives

\(y = \frac{4 -24}{28 -4} * (x - 4) + 24\)

Evaluate the difference

\(y = -\frac{20}{24} * (x - 4) + 24\)

Simplify

\(y = -\frac{5}{6} * (x - 4) + 24\)

Expand

\(y = -\frac{5}{6}x + \frac{10}{3} + 24\)

Evaluate the sum

\(y = -\frac{5}{6}x + \frac{10 + 24*3}{3}\)

\(y = -\frac{5}{6}x + \frac{82}{3}\)

Hence, the equation of the line of best fit is \(y = -\frac{5}{6}x + \frac{82}{3}\)

The time spent on TV is given as:

x = 15

So, we have:

\(y = -\frac 56 * 15 + \frac{82}3\)

Evaluate the product

\(y = -\frac{75}6 + \frac{82}3\)

Evaluate the sum

\(y = \frac{-75+164}6\)

This gives

\(y = \frac{89}6\)

Simplify

y = 15

Hence, the amount of time spent during homework is 15 hours for a student that spent 15 hours on TV

Read more about regression equations at:

https://brainly.com/question/17844286

#SPJ1

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

I believe that the answers are:

a= 65 degrees

b= 80 degrees

Step-by-step explanation:

Purple 80 and b should be the same so 80 degrees

180 - 80 is 100 which is A so a equals 100-35 whis is 65.

Answer:

a=65°, b=100°

Step-by-step explanation:

Hope the answers help! I got confused at first, but take a last look at line BE. Angle EAF is vertically opposite to this line. This means that angle BAF equals 80°. b=100°. a is just 180-80-35, so a=65°.

In order to calculate the carton's height, let's first convert from liters to cm³.

1 liter is equal to 1000 cm³.

Now, let's use the volume formula of a rectangular prism to calculate the height:

So the height is 20 cm.

a. The total interest paid on the 25-year mortgage is $110411.

b. The total interest paid on the 30-year mortgage is $135644.

What is the meaning of APR?

Annual percentage rate (APR) is the term used to describe the annual interest produced by a sum that is levied against borrowers or distributed to investors. APR is a percentage that expresses the actual yearly cost of borrowing money over the course of a loan or the income from an investment. This does not account for compounding and includes any fees or additional costs related to the transaction. Consumers can compare lenders, credit cards, or investment products using the APR as a benchmark figure.

Given that, the amount that is borrowed is $220,000.

If you borrow it for 25 years, you will pay $1,101.37 monthly.

The amount that you need to pay is (1,101.37×12×25) = 330411.

The total interest is =  (330411 - 220,000) = $110411.

If you borrow it for 30 years, you will pay $987.90 monthly.

The amount that you need to pay is (987.90×12×30) = 355644.

The total interest is =  (355644 - 220,000) = $135644

To learn more about the rate of interest, click on the below link:

https://brainly.com/question/26465648

#SPJ1

The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.

However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.

This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.

As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.

It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.

Know more about  disease   here:

https://brainly.com/question/27441596

#SPJ11

Answer:

Do you mean an MP3 player?

Step-by-step explanation:

The term "∈-minimal element" typically refers to an element within a set that satisfies a specific condition related to set membership.

More specifically, an element x is considered an "∈-minimal element" if there is no other element y in the same set such that y ∈ x, where "∈" represents set membership. In other words, x is the smallest element within the group in terms of the membership relation.

This concept is often used in the context of partially ordered sets or posts, where elements are related to each other by a partial order relation. An "∈-minimal element" is the smallest element within the group based on the given partial order relation defined on the set.

Learn more about the axiom of regularity here:

https://brainly.com/question/32269173

#SPJ1

The volume of the cuboctahedron is approximately \(32768 cm^3 - 512 * sqrt(3) cm^3.\)

By using the clue provided, we may determine the volume of the original cube and then deduct the volume of the cut corners.

All of the edges of the original cube measure 32 cm. As a result, its volume can be determined as follows:

\(Volume of cube = (Edge length)^3 = (32 cm)^3 = 32^3 cm^3 = 32768 cm^3\)

Let's now determine the volume of the corners that were eliminated. Each corner has a similar equilateral triangle with sides that are 16 cm long.

The volume of one equilateral triangle can be calculated using the formula:

Volume of equilateral triangle =\((sqrt(3) / 4) * (Side length)^2\)

Plugging in the values, we have:

Volume of one corner \(= (sqrt(3) / 4) * (16 cm)^2\)

Since there are 8 corners that are removed, we multiply the volume of one corner by 8 to get the total volume of the removed corners:

Total volume of corners = \(8 * [(sqrt(3) / 4) * (16 cm)^2]\)

Simplifying the expression:

Total volume of corners = \(8 * (sqrt(3) / 4) * (16 cm)^2\)

=\(2 * sqrt(3) * (16 cm)^2\)

Now, we can subtract the volume of the corners from the volume of the original cube to find the volume of the cuboctahedron:

Volume of cuboctahedron = Volume of cube - Total volume of corners

\(= 32768 cm^3 - 2 * sqrt(3) * (16 cm)^2\)

Calculating the expression:

Volume of cuboctahedron ≈ \(32768 cm^3 - 2 * sqrt(3) * (16 cm)^2\)

≈ \(32768 cm^3 - 2 * sqrt(3) * 256 cm^2\)

≈ \(32768 cm^3 - 512 * sqrt(3) cm^3\)

Therefore, the volume of the cuboctahedron is approximately\(32768 cm^3 - 512 * sqrt(3) cm^3.\)

Learn more about equilateral triangle here : brainly.com/question/7251133

#SPJ1

Answer:

(a) 0.1325

(b) 0.4045

(c) 0.463

Step-by-step explanation:

Let X denote the number of defective transistors.

The proportion of defective transistors is, p = 4/11 = 0.364.

All the transistors are independent of the others.

The random variable X follows a binomial distribution.

(a)

Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:

\(P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325\)

(b)

Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:

\(P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045\)

(c)

Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:

\(P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463\)

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

For more such questions on Number, click on:

https://brainly.com/question/30752681

#SPJ8

Answer:

not 100% confident but I think this is at least close

Step-by-step explanation:

solve for one variable

1. x-5y=2

x=2+5y

plug this in to another equations and simplify

2. (2+5y)-y=16

2+4y=16

4y=14

y=3.5

this can be plugged in to all other equations to find x

1. x-5(3.5)=2

x-17.5=2

x=19.5

2. x-(3.5)=16

x=19.5

3. 2x-(3.5)=5

2x=8.5

x=4.25

4. x-3(3.5)=4

x-10.5=4

x=14.5