How do you find the radius when the circumference is given?

Answer:

x+50+80=180

x=180-130

x=50

Answer:

x=50

Step-by-step explanation:

(sry for the bad writing, i cant write well on a computer)

-Todo<3

Answer:

\( \longrightarrow \tt3x + 2 - ( x - 3)\)

\( \longrightarrow \tt \: 3x + 2 - x + 3\)

\( \longrightarrow \tt 3x - x + 2 + 3\)

\( \longrightarrow \boxed{ \tt 2x + 5 }\)

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The parallax problem is a phenomenon that arises when measuring the distance to a celestial object by observing its apparent shift in position relative to background objects due to the motion of the observer.

The parallax effect is based on the principle of triangulation. By observing an object from two different positions, such as opposite sides of Earth's orbit around the Sun, astronomers can measure the change in its apparent position. The greater the shift observed, the closer the object is to Earth.

However, the parallax problem introduces challenges in accurate measurement. Firstly, the shift in position is extremely small, especially for objects that are very far away. The angular shift can be as small as a fraction of an arcsecond, requiring precise instruments and careful measurements.

Secondly, atmospheric conditions, instrumental limitations, and other factors can introduce errors in the measurements. These errors need to be accounted for and minimized to obtain accurate distance calculations.

To overcome these challenges, astronomers employ advanced techniques and technologies. High-precision telescopes, adaptive optics, and sophisticated data analysis methods are used to improve measurement accuracy. Statistical analysis and error propagation techniques help estimate uncertainties associated with parallax measurements.

Despite the difficulties, the parallax method has been instrumental in determining the distances to many stars and has contributed to our understanding of the scale and structure of the universe. It provides a fundamental tool in astronomy and has paved the way for further investigations into the cosmos.

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Answer:

16

Step-by-step explanation:

3x + 4 = x + 12  [The straight line on the segments AB and BC indicate that they are the same length]

2x = 8  [Subtract x and 8 from both sides]

x = 4  [Divide both sides by two]

Length AB is equal to (3x + 4) as indicated by the diagram. Substituting x = 4, (3 * 4) + 4 = 16

Let's denote the area of the kitchen, playroom, and dining room as x, y, and z, respectively.

According to the given ratio, the areas of the three rooms are in the ratio 4:3:2. This can be expressed as:

x : y : z = 4 : 3 : 2

We can assign a common factor to the ratio to simplify the problem. Let's assume the common factor is k:

4k : 3k : 2k

Now, we know that the combined area of these three rooms is 144 square feet:

4k + 3k + 2k = 144

Simplifying the equation:

9k + 2k = 144

11k = 144

To solve for k, we divide both sides of the equation by 11:

k = 144 / 11

k ≈ 13.09

Now, we can find the area of each room by multiplying the corresponding ratio by the value of k:

Area of the kitchen = 4k ≈ 4 * 13.09 ≈ 52.36 square feet

Area of the playroom = 3k ≈ 3 * 13.09 ≈ 39.27 square feet

Area of the dining room = 2k ≈ 2 * 13.09 ≈ 26.18 square feet

Therefore, the area of each room is approximately:

Kitchen: 52.36 square feet

Playroom: 39.27 square feet

Dining room: 26.18 square feet

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Answer:

Step-by-step explanation:

Putting value of x in the equation

3(5) + 5

= 15 + 5

= 20

Answer:

B

Step-by-step explanation:

yeah it's B welcome lllllllll

Answer:

Step-by-step explanation:

Let's solve for a.

ax+3=6

Step 1: Add -3 to both sides.

ax+3+−3=6+−3

ax=3

Step 2: Divide both sides by x.

ax /x = 3 /x

a= 3 /x

Answer:

a= 3 /x

Answer:

ax = 3

Step-by-step explanation:

ax + 3 = 6

Subtract 3 from both sides of the equation

ax = 3

I hope this helps :)

Cube rolled = 50 times

1 or 2 came up = 19 times

In percentage, that is >>>

So, 1 or 2 occured 38% of the times where it should occur around 20% of the times.

Looking at the answer choice, third option (C) is right.

Answer:

the factor is 2 because 7x2 is 14 and 3x2 is 6

Answer:

4(7+6)

2(7+7) x 2(6+6)

Step-by-step explanation:

I didn't know if you mean 28+24 or 28 x 24 so i put both

Writing it as a product of two factors and using the distributive property gives us 2(7 + 7) × 2(6 + 6)

To start with, we find the meaning of GCF. GCF stands for Greatest Common Factor. This means that the highest factor that is present in both numbers. If we are also going to write it as a part of distributive property, then we have.

2(7 + 7) × 2(6 + 6)

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We want to imagine where the shading should be, and with that determine which point is a solution for both inequalities. We will see that the solution is the point (7, -8)

In this case, the inqualities are:

You can see that in both cases, y is smaller than the line, thus, for both inequalities, we must shade the part that is below the lines.

With that in mind, the region of solution will be the region that is below both lines at the same time, and that region will be the "triangle" that you can see at the middle below the horizontal axis.

Now that we know the region of solutions, we only need to see which point belongs there, from the given options the only that belongs to that region is the point (7, -8), which means that this point is a solution for both inequalities.

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Tyler can buy at most 8 songs.

We have given that,Tyler solved an inequality to determine the number of songs he can buy with a $20 credit at his favorite music website.

inequality, In mathematics, a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

A number line going from 5 to 13.

A solid circle is at 8.

Therefore,from the given we can say that,

he cannot buy no more than 8 songs.

Therefore,Tyler can buy at most 8 songs.

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Answer:

? wdym

Step-by-step explanation:

well points i guess i also need one more brainliest if you can give

Answer:

The first one answer is 4 because 8x2=16 divide by 4 will equal 4.

The second one answer is 10 because 10 x 4=40 and divided by 4 will equal 4.

The third one answer is 6/6 which will equal 1 because it is an whole number.

The approximate percent increase between carbon dioxide levels 150,000 years ago and carbon dioxide levels today is about 50%.

Carbon dioxide (\(CO2\)) levels fluctuate naturally over long periods of time due to various factors. Comparing the approximate \(CO2\) levels from 150,000 years ago to today, there has been a significant increase of about 50%. During the pre-industrial era, \(CO2\) levels were relatively stable at around 280 parts per million (ppm).

However, with the advent of industrialization and the burning of fossil fuels, human activities have contributed to the release of large amounts of \(CO2\) into the atmosphere. Currently,\(CO2\) levels have risen to over 400 ppm. To calculate the approximate percent increase, we can use the formula: ((New Value - Old Value) / Old Value) * 100. Applying this formula, the percent increase in \(CO2\) levels from 150,000 years ago to today would be approximately 50%.

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Answer:

The equation for relationship between the thickness and the number of weeks is f(x)=3.8 -0.2*x

Step-by-step explanation:

Ice thickness decreases at a rate of 0.2 meters per week. This can then be represented by the expression

f(x) = k - 0.2*x

where k is the thickness of the ice before the melting starts and x is the number of weeks.

After 7 weeks, the ice is only 2.4 meters thick. This means that x has a value of 7, while f (7) = 2.4. Replacing in the previous expression:

2.4=k -0.2*7

and solving you get:

2.4=k- 1.4

2.4 + 1.4= k

3.8= k

Then, the equation for relationship between the thickness and the number of weeks is f(x)=3.8 -0.2*x

a. Null hypothesis is a statement that suggests no significant difference or relationship exists between two variables or populations. It is the starting point of hypothesis testing, and the aim is to prove it wrong.
b. Alternative hypothesis is a statement that suggests there is a significant difference or relationship between two variables or populations. It is the opposite of the null hypothesis and is supported if there is enough evidence to reject the null hypothesis.
c. Critical values are the values that divide the rejection region from the acceptance region in hypothesis testing. They are determined based on the chosen alpha level and the degrees of freedom.
d. Rejection region is the area in the distribution where the null hypothesis is rejected. It is determined by comparing the test statistic with the critical values.
e. Test statistic is a calculated value that measures the difference between the observed sample data and the expected values under the null hypothesis. It is used to determine whether the null hypothesis should be rejected.
f. Alpha level is the significance level set by the researcher, which determines the probability of rejecting the null hypothesis when it is true. It is typically set at 0.05 or 0.01, indicating a 5% or 1% chance of rejecting the null hypothesis when it is true. The alpha level is used to determine the critical values and the rejection region.

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Probability is a measure of how likely an event is to occur. It is a value between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.

In this case, we're looking at the probability of certain outcomes related to the written driving test in Florida. The failure rate for this test is 60 percent, which means that the probability of failing the test is 0.6 and the probability of passing the test is 0.4.

a. To find the probability of all three test-takers failing the test, we can use the formula for the probability of independent events:

P(A and B and C) = P(A) x P(B) x P(C)

Where P(A), P(B), P(C) are the probability of each test-taker failing the test.

So in this case:

P(all three fail the test) = 0.6 x 0.6 x 0.6 = 0.216

The probability of all three test-takers failing the test is 0.216 or 21.6%.

b. To find the probability of none of the test-takers failing the test, we can use the formula for the probability of independent events:

P(A and B and C) = P(A) x P(B) x P(C)

Where P(A), P(B), P(C) are the probability of each test-taker passing the test.

So in this case:

P(none fail the test) = 0.4 x 0.4 x 0.4 = 0.064

The probability of none of the test-takers failing the test is 0.064 or 6.4%.

c. To find the probability of only one of the test-takers failing the test and two passing, we can use the combination formula:

(3 choose 1) x P(fail) x P(pass)^2 = 3 x (0.6 x 0.4^2) = 0.288

The probability of only one test-taker failing the test is 0.288 or 28.8%.

In summary, Probability is a measure of how likely an event is to occur, in this case we're looking at the probability of certain outcomes related to the written driving test in Florida, the failure rate for this test is 60 percent, which means that the probability of failing the test is 0.6.

To find the probability of all three test-takers failing the test we can use the formula P(A and B and C) = P(A) x P(B) x P(C) where P(A), P(B), P(C) are the probability of each test-taker failing the test.

To find the probability of none of the test-takers failing the test we can use the formula P(A and B and C) = P(A) x P(B) x P(C) where P(A), P(B), P(C) are the probability of each test-taker passing the test, and to find the probability of only one of the test-takers failing the test and two passing,

we can use the combination formula (3 choose 1) x P(fail) x P(pass)^2

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Answer:

11.9

Step-by-step explanation:

in maths, we are aware that in triangles we can use sine, cosine, and tangent.

using tangent, we have

tan 29⁰=6.6/x

and tan 29⁰=0.5543

0.5543=6.6/x

cross multiply

0.5543x=6.6

x= 6.6/0.5543

x= 11.9

The sales price of the item is $48.

The sale price of an item that costs 60% of its original price which is $80 is $48. The original price of the item is $80, and it costs 60% of the original price. The amount of money we'll be spending is calculated as follows: 60 per cent of $80 (60/100) × $80= $48 Therefore, the sales price is $48. The percentage discount for the item is calculated as follows:$80 - $48 = $32

$32 is the amount of money saved due to the discount, which is then divided by the original price, $32/$80 = 0.4 or 40%. Thus, there was a 40% discount on the original price.

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Answer:

d is the correct answer to your question

Answer:

9.2 units

Step-by-step explanation:

cause the last guy is right...

We can find several things for the given equation:

1. Magnitude of r(t):

| r(t) | = sqrt[ e^(-t)^2 + (8t^2)^2 + (3tan(t))^2 ]

2. Unit tangent vector T(t):

T(t) = r'(t) / | r'(t) |

where r'(t) = -e^(-t), 16t, 3sec^2(t)

3. Unit normal vector N(t):

N(t) = T'(t) / | T'(t) |

where T'(t) = -e^(-t), 16, 6sec^2(t)tan(t)

4. Unit binormal vector B(t):

B(t) = T(t) x N(t)

Note: "sec" stands for secant and "tan" stands for tangent.

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For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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In conclusion: (a) The linear transformation f: M₂x₂ → R₃ given by f(a b; c d) = (b+d, a+b, d-a) is injective (one-to-one). (b) The linear transformation f is surjective (onto) if and only if every value of z can be expressed as the difference d - a for some real numbers d and a.

To determine whether the linear transformation f: M₂x₂ → R₃ is injective (one-to-one) and surjective (onto), we need to analyze its properties and conditions.

Let's define the linear transformation f as:

f(a b; c d) = (b+d, a+b, d-a)

(a) Injective (One-to-One):

A linear transformation f is injective if every distinct input vector in the domain corresponds to a distinct output vector in the codomain. In other words, if f(a₁ b₁; c₁ d₁) = f(a₂ b₂; c₂ d₂), then (a₁ b₁; c₁ d₁) = (a₂ b₂; c₂ d₂).

To test injectivity, we need to compare the outputs of f for two different input matrices and see if they are equal.

Let's assume two different input matrices: A₁ = (a₁ b₁; c₁ d₁) and A₂ = (a₂ b₂; c₂ d₂).

If f(A₁) = f(A₂), then we have:

(b₁+d₁, a₁+b₁, d₁-a₁) = (b₂+d₂, a₂+b₂, d₂-a₂)

Comparing the corresponding elements, we get the following system of equations:

b₁ + d₁ = b₂ + d₂ (1)

a₁ + b₁ = a₂ + b₂ (2)

d₁ - a₁ = d₂ - a₂ (3)

From equation (1), we can deduce that b₁ - b₂ = d₂ - d₁. Let's call this equation (4).

Similarly, equation (2) can be rewritten as a₁ - a₂ = b₂ - b₁. Let's call this equation (5).

Now, subtracting equation (3) from equation (4), we have:

(b₁ - b₂) - (d₁ - d₂) = (d₂ - d₁) - (a₂ - a₁)

(b₁ - b₂) - (d₁ - d₂) = (d₂ - d₁) - (b₂ - b₁)

Simplifying further, we get:

2(b₁ - b₂) = 2(d₂ - d₁)

b₁ - b₂ = d₂ - d₁

Using equation (5), we can substitute b₁ - b₂ = d₂ - d₁:

a₁ - a₂ = b₂ - b₁ = d₂ - d₁

This implies that a₁ = a₂, b₁ = b₂, and d₁ = d₂.

Therefore, we have shown that if f(A₁) = f(A₂), then A₁ = A₂. This confirms that f is an injective (one-to-one) linear transformation.

(b) Surjective (Onto):

A linear transformation f is surjective if every vector in the codomain has at least one corresponding input vector in the domain. In other words, for every vector (x, y, z) in the codomain R₃, there exists an input matrix A = (a b; c d) such that f(A) = (x, y, z).

To test surjectivity, we need to check if every vector (x, y, z) in R₃ can be expressed as f(A) for some matrix A = (a b; c d).

The codomain R₃ consists of 3-dimensional vectors, and the range of f is determined by the values of b, d, and the differences between b and d (b - d).

From the transformation equation f(a b; c d) = (b+d, a+b, d-a), we can observe that the third component z in R₃ is given by z = d - a. Therefore, any vector in R₃ can be expressed as f(A) if and only if z = d - a.

Since a and d are the diagonal elements of the input matrix A, we can conclude that for every vector (x, y, z) in R₃, there exists a matrix A = (a b; c d) such that f(A) = (x, y, z) if and only if z = d - a.

Therefore, f is surjective (onto) if and only if every value of z can be expressed as the difference d - a for some real numbers d and a.

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Joaquin will need 1 and two fifths cups to make his famous chocolate chip cookies for his friend's birthday party

To solve this problem we will use a rule of three with the problem information:

5 people-------- 1/4 cup of butter

28 people -------- x

Applying the rule of three we get:

x = ( 28 people * 1/4 cup of butter) / 5 people

x = 1,4 cup of butter

x = 1 + 2/5 cup of butter = 1 and two fifths cups

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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Answer:6

Step-by-step explanation:

Let the number be x.

Now, 3x+6=24

3x=24-6

3x=18

x=18/3

x=6

Answer:

6

Step-by-step explanation:

We can work the problem backwards

Since something gives 24 that means it equals 24

= 24

Something increased by 6, so something added by 6

Something + 6 = 24

Making something = x

x + 6 = 24

If we subtract 6 from both sides

x = 18

Trice a number, so divide this number by 3

x = 6

Trice of 6 is 18... 18 increased by 6 gives 24

Answer:

-2

Step-by-step explanation:

Equation of slope intercept form

y = (slope × x) + y intercept

Answer:

D. y = 3·x² - 2·x + 11/12

Step-by-step explanation:

The coordinates of the focus of the parabola, f = (1/3, 2/3)

The directrix of the parabola, y = 1/2

The standard form of the equation of a parabola is (x - h)² = 4·p·(y - k)

The coordinates focus = (h, k + p)

The y-coordinates of the directrix, y = k - p

By comparison, we have;

h = 1/3...(1)

k + p = 2/3...(2)

k - p = 1/2...(3)

Adding equation (3) to equation (2) gives;

k + p + (k - p) = k + k + p - p = 2·k = 2/3 + 1/2 = 7/6

k = (7/6)/2 = 7/12

k = 7/12

From equation (2), we get;

p = 2/3 - k

∴ p = 2/3 - 7/12 = 1/12

p = 1/12

The equation of the parabola is therefore;

(x - 1/3)² = 4·(1/12)·(y - 7/12) = y/3 - 7/36

y = 3 × ((x - 1/3)² + 7/36) = 3 × ((x² - 2·x/3 + 1/9) + 7/36) = 3·x² - 2·x + 11/12

y = 3·x² - 2·x + 11/12.

We can factor this by grouping. We have to find two numbers that add up to -13 but multiply to 8 × 5.

The two numbers that work are -8 and -5. Expand -13n to -8n and -5n.

The trinomial in factored expression is \((8\text{n}-5)(\text{n}-1)\).

Trinomials are polynomials: expressions made up of a finite amount of constants (numbers) and variables (unknowns), linked together through multiplication, subtraction, and/or addition.

Specifically, trinomials are polynomials made up of three monomials (expressions of a single term).

To factorize the trinomial 8n² - 13n + 5, we need to find two binomials that multiply together to give us this trinomial.

First, we need to find the factors of 8n² and 5. The factors of 8n² are 8n and n (or 4n and 2n, or -2n and -4n, or -n and -8n). The factors of 5 are 5 and 1.

Now, we need to find two factors of 8n² and 5 that add up to -13n. The only pair of factors that work are -8n and -5n (since -8n x -5n = 40n², and -8n - 5n = -13n).

Therefore, we can write

\( \sf8n² - 13n + 5 \: \: as \: \: (8n - 5)(n - 1) \: in \: \: factored \: \: form.\)

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The question states that we have a supply function denoted as s(q) and a demand function denoted as d(q). We are required to complete parts (a) through (d) based on this information.

In this part, we are likely asked to find the equilibrium quantity q* where the supply and demand functions intersect. This occurs when s(q) equals d(q). By setting (q) equal to d(q) and solving for q, we can determine the equilibrium quantity q*. Part (b) may ask us to find the equilibrium price, denoted as p*, corresponding to the equilibrium quantity q* found in part. To do this, we substitute the equilibrium quantity q* into either the supply or demand function and solve for p.

Part (c) might require us to determine the consumer surplus at the equilibrium quantity q*. Consumer surplus represents the difference between the willingness of consumers to pay for a good or service and the actual price they pay. To calculate the consumer surplus, we integrate the demand function from zero to q* and subtract the area under the demand curve up to the equilibrium price.

In this part, we might be asked to find the producer surplus at the equilibrium quantity q*. The producer surplus measures the difference between the cost of production for a good or service and the price at which it is sold. To compute the producer surplus, we integrate the supply function from zero to q* and subtract the area under the supply curve up to the equilibrium price.

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