pleas help me with this one thank you

Answer:   The point in the interior of the circle that is equidistant from every point on the circle is called the center of the circle.

Step-by-step explanation:

The volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.

The equation of the circle can be given as,

\(x^2+y^2=r^2\)

Here, (r) is the radius of the circle.

Rewrite this equation as,

\(y^2=r^2-x^2\\y=\sqrt{r^2-x^2}\)

This will give you the half the length of the side. Thus, the length of the side of the square is,

\(s=2y=2\sqrt{r^2-x^2}\)

The area of the square it square of its side. Thus, the area of the square is,

\(A(x)=s^2\\A(x)=(2\sqrt{r^2-x^2})^2\\A(x)=4(r^2-x^2})\)

The volume of the solid can be got by integrating the area of the cross-section.

\(V=\int\limits {A(x)} \, dx\)

Here, A(x), provides the area of the square at the point x. Thus,

\(V=\int\limits {A(x)} \, dx\\V=\int\limits_{-r}^r {4(r^2-x^2)} \, dx\\V=[ {4(r^2x-\dfrac{x^3}{3})}]^r_{-r}\\V= {4(r^2(r)-\dfrac{(r)^3}{3})}- {4(r^2(-r)-\dfrac{(-r)^3}{3})}\\V=4[r^3-\dfrac{r^3}{3}}+ {r^3-\dfrac{r^3}{3}]\\V=\dfrac{16r^3}{3}\)

Thus, the volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.

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Answer:

y=3/4x-8

Step-by-step explanation:

"ba" = 11,

"ab" = 38,

38 - 11 = 27,

Sooooo... Now you have the value of "ba" and "ab."

Welcome!! <3

Answer:

n/3 - 4 = 10

Step-by-step explanation:

hope this helps

Answer:

11) 6

12) 3

Step-by-step explanation:

2 log 2 8

so 2(log2 8)

Base 2 so 2^x=8 so 3.

2*3 is 6.

log a a cubed

base a so a^ x = a^3

x=3

so 3.

Hope this helps ;D

Answer:

6 and 3

Step-by-step explanation:

Using the rules of logarithms

log\(x^{n}\) ⇔ n log x

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

\(log_{a}\) a = 1

(11)

let 2 \(log_{2}\)8 = n , then

\(log_{2}\) 8² = n

\(log_{2}\) 64 = n

\(log_{2}\) \(2^{6}\) = n

\(2^{6}\) = \(2^{n}\)

Since bases on both sides are equal, equate the exponents, that is

n = 6

(12)

\(log_{a}\) a³

= 3 \(log_{a}\) a

= 3 × 1

= 3

Step-by-step explanation:

m1=2=m1×m2=-1

2y=x+2 (÷all sides by 2)

The simplified fraction is -x²(x + y)/y for the given expression.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The fraction is given in the question, as follows;

{(x³ -xy²)/y}/{y/x - 1}

{x(x² -y²)/y}/{(y - x)/x}

{x(x - y)(x + y)/y}/{(y - x)/x}

Reciprocal the terms in the above fraction,

{x(x - y)(x + y)/y} × {x/(y - x)}

{x(x - y)(x + y)/y} × {-x/(x - y)}

Reduce the same term in the expression,

{x(x + y)/y} × {-x}

-x²(x + y)/y

This is the simplified fraction.

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Answer:

3a. 7.2

3b. 0.9

4a. 7.2

4b. 2.4

5a. 104

5b. 260

hope this helps, everything in bold is the correct answer,

have an awesome day, -TJ

Answer:

3.a. 36

b. 4.5

4.a. 7.2

b. 2.4

5.a. 104

b. 260

Step-by-step explanation:

100/20 = 5

18 x 5 = 90 (100%)

18 x 2 = 36

18/4 = 4.5

14.4/2 = 7.2

7.2/3 = 2.4

52 x 2 = 104 (100%)

(195/3) 4 = 65 x 4

65 x 4 = 260 (100%)

For the study conducted by the researchers,

From the question, we have the following highlights:

When a study used a control group and an experimental group, then such study is a matched-pairs design.

The appropriate t-interval for inference for a matched-pairs design is the  t-interval for a mean difference

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Check the picture below.

The area of the space devoted to paintings is: 600 ft²

The formula for the area of a triangle is expressed as:

A = ¹/₂ * b * h

where:

A is area

b is base

h is height

From the 7th grade painting, we see that each box of 1 unit represents 10 ft actually.

Thus, area of space devoted to paintings is:

Area = ¹/₂ * 40 * 30

= 600 ft²

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#x

Angle 1

Angle 2

Answer:

A)  x = 44

B)  m∠1 = 118°

    m∠2 = 62°

Step-by-step explanation:

Part A

Angles on a straight line sum to 180°

⇒ (2x + 30) + 62 = 180

⇒ 2x + 30 + 62 = 180

⇒ 2x + 92 = 180

⇒ 2x = 88

⇒ x = 44

Part B

Vertical Angle Theorem:  The opposite vertical angles of two straight intersecting lines are congruent.

⇒ m∠1 = (2x + 30)

Substituting the found value of x:

⇒ m∠1 = 2(44) + 30

⇒ m∠1 = 88 + 30

⇒ m∠1 = 118°

Using the Vertical Angle Theorem:

⇒ m∠2 = 62°

Function 1

Let us calculate the equation of the line of function 1 picking any two points

The two points picked are (1 , 0) and (0 , -4)

The formula for the equation given two points is

Given:

Hence,

Therefore, the equation for the function is

Where, the coefficient of x is the slope and the constant variable is the y-intercept.

Hence,

Function 2

Let us calculate the equation of the line of function 2 picking any two points from the data in the table.

The two points picked are (-2 , 8) and (2 , -12)

Therefore,

Hence,

Where,

Function 3

The given equation is

Function 4

Given:

Hence,

a) The functions that have graphs with slopes less than 3 are Function 2, Function 3 and Function 4.

b) The function that has the graph with a y-intercept closest 0 is Function 3.

c) The function that has the graph with greatest y-intercept is Function 4.

A light rail system can be described as a smaller rail-based transportation system that is powered by electricity, providing efficient and sustainable urban transit options for passengers.

A light rail system refers to a smaller rail-based transportation system that operates within urban or suburban areas. It typically consists of light rail vehicles (LRVs) that run on tracks, similar to a traditional railway system. However, light rail systems are designed to serve shorter distances and provide more frequent stops compared to heavy rail systems.

One distinguishing characteristic of a light rail system is that it is powered by electricity. The LRVs usually run on overhead electrical wires or through an electrified third rail system. This electric power source allows for a more sustainable and environmentally-friendly mode of transportation.

Light rail systems are often integrated into the existing urban infrastructure and provide convenient and efficient transportation options for commuters. They offer a balance between the capacity of traditional heavy rail systems and the flexibility of buses. Light rail vehicles can accommodate a significant number of passengers and operate on fixed routes, offering a reliable and comfortable mode of public transportation.

Overall, a light rail system can be described as a smaller rail-based transportation system that is powered by electricity, providing efficient and sustainable urban transit options for passengers.

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Answer:

9\(x^{2}\)-3x-12

9\(x^{2}\)+6x-7-9x-5

(Group liked terms)

9\(x^{2}\)+6x-9x-7-5

( subtract the numbers ) -7-5= -12

9\(x^{2}\)+6x-9x-12

( add similar elements ) 6x-9x=-3x

9\(x^{2}\)-3x-12

Step-by-step explanation:

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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The domain of the exponential function in this problem is given as follows:

0 ≤ n ≤ 5.

The exponential function in this problem is defined by the rule presented as follows:

g(n) = 10(1.02)^n.

In which the variables are listed as follows:

When the study was finished, the height of the flower was of 11.04 inches, hence the day at which the study was finished is obtained as follows:

10(1.02)^n = 11.04

(1.02)^n = 11.04/10

log[(1.02)^n] = log(11.04/10)

Applying the logarithm of power property, we have that:

nlog(1.02) = log(11.04/10)

n = log(11.04/10)/log(1.02)

n = 5.

The domain is the number of days for which the student was realized, hence:

0 ≤ n ≤ 5.

As the number of days cannot assume negative values.

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Answer:

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

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

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Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

Using a proportional relationship, it is found that:

a. The function is d = 21g.

b. Values less than 0 and greater than 20 are excluded from the domain.

c. The greatest distance that Armando can travel on the highway after the low fuel light comes on is of 52.5 miles.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Armando’s vehicle averages 21 miles per gallon on the highway, hence the distance that he can travel on g gallons is given by:

d = 21g.

The domain is the set that contains all possible input values, hence:

Hence:

Values less than 0 and greater than 20 are excluded from the domain.

The low fuel light comes in when the number of gallons remaining is:

g = 1/8 x 20 = 20/8 = 2.5 gallons.

The distance that he can travel is:

d = 21g = 21 x 2.5 = 52.5 miles.

The greatest distance that Armando can travel on the highway after the low fuel light comes on is of 52.5 miles.

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Using calculator, the value of  the angle 5 sin (20 +10°) -4 = 0​ where 0 <x<90 is 17.5 degrees

You should understand that the sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle

The given angle is 5 sin (20 +10°) -4 = 0

To find the angle, first open the bracket to have

5sin(30) - 4 = 0

Collecting like terms to have

5 sin 30 = 4

Dividing both sides by 5 we have

5 sin30/5 = 4/5

This means that sin30 = 0.8

⇒sin30 - 0.8 = 0

⇒ 0.5 -0.8 = 0

-0.3

Therefore sin⁻-0.3 = 17.5⁰

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the length of DO is 16/5 feet (approx) and the length of OG is 15.56 feet (approx).

How to solve the problem ?

Given that Triangle CAT is similar to Triangle DOG, we know that the corresponding sides of both triangles are proportional. The proportion of the corresponding sides is equal to 1/2.

Let's denote the length of side DO as 'x'. Then the length of OG will be '2x' (since the ratio of corresponding sides is 1:2).

Using the given information, we can write the following ratios:

CA/DO = CT/OG = TA/DG = 1/2

Substituting the values given in the problem, we get:

8/x = 10/2x = 6/(DG)

Simplifying the ratios, we get:

x = 16/5

2x = 32/5

DG = 12

Now that we know the length of DG, we can use the Law of Cosines to find the length of OG.

Cos(58) = (12² + OG²- (32/5)²)/(212OG)

Simplifying the equation, we get:

OG = 15.56 feet (approx)

Therefore, the length of DO is 16/5 feet (approx) and the length of OG is 15.56 feet (approx).

Note: It's always a good idea to double-check your answer by verifying that the ratios of the corresponding sides are equal to 1/2. In this case, we can verify that:

CA/DO = 8/(16/5) = 5/2

CT/OG = 10/(15.56) = 0.643

TA/DG = 6/12 = 1/2

These ratios are approximately equal to 1/2, so our answer is reasonable.

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The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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\(\rule{300}{3}\)

\(\text{Hi!}\)

To find the cost per item (or in your case "rolls"), you will first have to divide the cost of the lunch rolls  \((2.50)\)  by the amount of lunch rolls there are \((5)\).

So in this case, it would look like

\( \textbf{$2.50/5} \)\(\text{$2.50 ÷ 5}\)\(\text{$2.50 / 5}\)\(\text{2.50}\) ÷ \(\text{5}\)

\(\text{=$0.50}\)= \(\text{\ 0.50}\)

\(\boxed{\$0.50{}}\)

\(\rule{300}{3}\)

The real interest rate, using the approximation formula, is 0.01 or 1%. This means that after considering the expected inflation rate, the purchasing power of the money grows at a rate of 1%.

The real interest rate can be calculated using the approximation formula: real interest rate = nominal interest rate - expected inflation rate.

We have:

Nominal interest rate (i) = 0.04

Expected inflation rate (+1) = 0.03

Using the formula, we can substitute the given values:

Real interest rate = 0.04 - 0.03

Calculating the difference:

Real interest rate = 0.01

Therefore, the real interest rate, using the approximation formula, is 0.01 or 1%.

The nominal interest rate represents the rate at which money grows in a bank account or investment without considering inflation. On the other hand, the real interest rate takes into account the effects of inflation, allowing us to understand the true purchasing power of the money.

To calculate the real interest rate, we subtract the expected inflation rate from the nominal interest rate. In this case, the nominal interest rate is 0.04 (4%), and the expected inflation rate is 0.03 (3%).

Substituting the values into the formula, we get:

Real interest rate = 0.04 - 0.03

Real interest rate = 0.01 or 1%

Therefore, the real interest rate, in this scenario, is 0.01 or 1%. This means that after accounting for inflation, the purchasing power of the money grows at a rate of 1%.

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The expression (x - 10) + (3x - 6) is equivalent to the expression 4x - 16.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x - 10) + (3x - 6)

Simplify the expression, then we have

⇒ (x - 10) + (3x - 6)

⇒ x - 10 + 3x - 6

⇒ 4x - 16

The expression (x - 10) + (3x - 6) is equivalent to the expression 4x - 16.

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1) dy/da = y(1 - y) , because y = 1 / (1 + e⁽⁻ᵅ⁾), so 1 - y = e⁽⁻ᵅ⁾ / (1 + e⁽⁻ᵅ⁾ )

2) the minimum of G(p) occurs at the points p = 0 and p = 1.

1) If y = sigmoid(a), then y = 1 / (1 + e⁽⁻ᵅ⁾).

To find dy/da, we need to take the derivative of y with respect to a.

dy/da = e⁽⁻ᵅ⁾ / (1 + e⁽⁻ᵅ⁾)²= y(1 - y)

This is because:

- The derivative of 1 / (1 + e⁽⁻ᵅ⁾) is e⁽⁻ᵅ⁾ / (1 + e⁽⁻ᵅ⁾)²

- y = 1 / (1 + e⁽⁻ᵅ⁾), so 1 - y = e⁽⁻ᵅ⁾ / (1 + e⁽⁻ᵅ⁾ )

- Therefore, dy/da = y(1 - y)

2) Gini's index, G(p), is used to measure inequality and is defined as G(p) = 1 - (p² + (1-p)²), where 0 <= p <= 1.

To maximize G(p), we need to find the point where its derivative with respect to p is zero:

dG(p)/dp = -2p - 2(1-p) = 0

Solving for p, we get p = 0.5

Thus, Gini's index is maximized at p = 0.5. For the minimum of G(p), we consider the endpoints, which are p = 0 and p = 1.

In both cases, G(p) = 1 - (1² + 0²) = 0.

So, the minimum of G(p) occurs at the points p = 0 and p = 1.

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Answer:

6.2x10^3

Step-by-step explanation:

I just used a scientific calculator