Circle a has a radius with the length of 5 units. Calculate the exact length of the apothem, line segment ah. In your final answer, include your calculations.

The cost of apples and bananas are $ 0.70 and $ 1.10 respectively if Patricia bought 4 apples and 9 bananas for $12.70 and Jose got 8 apples and 11 bananas for $17.70

Let the cost of one apple be a

the cost of one banana be b

In the case of Patricia,

12.70 = cost of 4 apples + cost of 9 bananas

Cost of 4 apples = 4a

Cost of 9 bananas = 9b

The equation we get is

4a + 9b = 12.70 ----(i)

In the case of Jose,

17.70 = cost of 8 apples + cost of 11 bananas

Cost of 8 apples = 8a

Cost of 11 bananas = 11b

The equation we get is

8a + 11b = 17.70 ----(ii)

Multiply (i) by 2

8a + 18b = 25.40 --- (iii)

Subtract (ii) and (iii)

7b = 7.70

b = $ 1.10

4a + 9 (1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = $ 0.70

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Answer:

it is -3 8 and 2

Step-by-step explanation:

Answer:

i think its  -3 8 and 2 (maybe)

Step-by-step explanation:

i asked my friend

The given expression √10 and √26  are irrational numbers.

The sum of √10 and √26 cannot be simplified because the two numbers are not like terms. However, we can estimate the value of the sum by using the fact that the square root of a number is between two consecutive perfect squares.

For √10, we know that 9 < 10 < 16, so √10 is between 3 and 4. For √26, we know that 25 < 26 < 36, so √26 is between 5 and 6. Therefore, we can estimate the sum of √10 and √26 to be between 8 and 10.

To get a more precise value, we can use a calculator to evaluate the sum of √10 and √26. Using a calculator, we find that the sum of √10 and √26 is approximately 7.051. Therefore, we can describe the sum of √10 and √26 as a decimal number that is approximately 7.051.

Alternatively, we can write the sum of √10 and √26 as a simplified radical expression. To do this, we need to combine the two radical terms into a single term using the distributive property of multiplication. We have:

√10 + √26 = √(10 × 1) + √(26 × 1) = √10 × √1 + √26 × √1 = √10 + √26

Therefore, we cannot simplify the sum of √10 and √26 any further, and we can describe it as the sum of two irrational numbers.

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The fractions of sixth graders that reached their goal after each day are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

In which the technical terms related to x and y are as follows:

The fraction can be represented by bars, in which:

As shown by the image at the end of the answer, the fractions are given as follows:

The image is given at the end of the answer.

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Answer:

A

Step-by-step explanation:

when growth of plant is zero means x=0 then y=2(0)+5 = 5

Answer:

Step-by-step explanation:

You can use the Heron's formula:

\(A=\sqrt{p(p-a)(p-b)(p-c)}\)

where

p - half of perimeter

a, b, c - lengths of sides

We have

\(a=12m;\ b=15m;\ c=9m\)

Calculate:

\(p=\dfrac{12+15+9}{2}=\dfrac{36}{2}=18\ (m)\\\\A=\sqrt{18(18-12)+(18-15)(18-9)}\\\\A=\sqrt{(18)(6)(3)(9)}\\\\A=\sqrt{2916}\\\\A=54\ (m^2)\)

Let's check that it is not a right triangle.

If the sum of the squares of the two shorter sides is equal to the square of the longest side, then this triangle is rectangular.

We have

\(9m < 12m<15m\)

Check:

\(9^2+12^2=81+144=225\\15^2=225\)

This is a right trianglr wherew 9m and 12m are legs and 15m is a hypotenuse.

The formula of an area of a right triangle is:

\(A=\dfrac{ab}{2}\)

a, b - legs

Substitute:

\(A=\dfrac{(9)(12)}{2}=\dfrac{108}{2}=54\ (m^2)\)

Answer: Table A

Step-by-step explanation: Table A is a function because none of the inputs have the same outputs in that table.

,  Hope this helps :)

Have a great day!!

Given that a consumer with u(x,y)=x^3 y^2 pays

px=3,

py =4. Utility is maximized when

y=2We have to determine the consumer's income.

Let I be the income of the consumer. Then the consumer's budget constraint can be represented aspx x+py y=I, where px=3 and

py=4. Hence we have3x+4y

=I ................

(1)From the utility function, the consumer's marginal rate of substitution is given byMRS = (∂u/∂x)/(∂u/∂y)

= 2x^2/3y^2Setting this equal to the price ratio py/px

= 4/3, we get2x^2/3y^2

= 4/3or x^2/y^2

= 2Substituting y

=2 (since utility is maximized when y

=2), we getx^2/4

= 2or x^2

= 8Hence, x

= ±2√2.

Substituting this in equation (1), we get3(±2√2)+4(2) = Ior I

= 14 ± 6√2Since I is the income, it cannot be negative. Hence the income is given byI

= 14 + 6√2.

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The estimated proportion for this case is

n = [ p( 1 - p)] ÷ ( ME/Z)²

The number of students that should be sampled is n = 6146 when the margin of error is 20%.

An interval of assurance is "a set of values that, with a particular level of certainty, includes the population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage ".

The range of values in a confidence interval that lies below and above the sample statistic is known as the margin of error.

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

The population proportion has the following distribution:

p ∼ N( p, √[p(1-p)/n ] )

We must consider the fact that we are determining the interval for a proportion in order to determine the crucial value, hence in this situation, the z distribution must be used. Since our interval has a 95% confidence level, = 1 - 0.95 = 0.05 and α/2 = 0.95 would indicate our significance level. The crucial value would then be determined by:

Z(α/2) = - 1.96, Z(1 - α/2) = 1.96

The margin of error for the proportion interval is given by this formula:  

ME = Z(α/2) × √[p(1-p)/n ]                                                      ----------------(1)

The estimated proportion for this case is p = 0.2

And on this case, we have that ME = ± 0.1 and we are interested in order to find the value of n, if we solve n from equation (1) we got:  

n = [ p( 1 - p)] ÷ ( ME/Z)²                                                         ----------------(2)

And replacing equation (2) the values from the part we got:

n = 0.2( 1 - 0.2 ) / ( 0.01/1.96)²

n =  0.16/0.00002603082

n = 6146.56

n ≈ 6146

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The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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Answer:

Coordinates are

(1,-5)

(-6,1)

The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

\(x^{2} =y^2+z^2\)

Let's substitute the values into the formula and solve for the hypothenuse

\(x^{2} =3^2+4^2\)

\(x^{2}\) = 9 + 16

\(x^{2}\) = 25

\(x=\sqrt{25}\)

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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Step-by-step explanation:

Let the coordinates of the left endpoint of the line segment be (x1, y1) and the coordinates of the right endpoint be (x2, y2). Let the point dividing the line segment be (x, y). Then the distance between the left endpoint and (x, y) is mx/(m+n) and the distance between (x, y) and the right endpoint is nx/(m+n).

Using the distance formula, we have:

\(distance \: between \: (x1, y1) \: and \: (x, y) = \sqrt{((x - x1)^2 + (y - y1)^2)} = \frac{mx}{(m+n)} \)

\(distance \: between \: (x, y) \: and \: (x2, y2) = \sqrt{((x2 - x)^2 + (y2 - y)^2)} = \frac{nx}{(m+n)} \)

Squaring both equations, we get:

\((x - x1)^2 + (y - y1)^2 = \frac{mx}{(m+n)^2}\)

\((x2 - x)^2 + (y2 - y)^2 = \frac{nx}{(m+n)^2}\)

Expanding the squares, we get:

\(x^2 - 2x1x + x1^2 + y^2 - 2y1y + y1^2 = \frac{mx}{(m+n)^2} \)

\(x^2 - 2x2x + x2^2 + y^2 - 2y2y + y2^2 = \frac{nx}{(m+n)^2}\)

Rearranging and simplifying, we get:

\(x = \frac{(mx2 + nx1)}{(m+n)} \: and \: y = \frac{(my2 + ny1)}{(m+n)}\)

Therefore, the point that divides the line segment into two parts so that the ratio of the lengths is m: n and the point is closer to the left endpoint is:

\((x, y) = \frac{(mx2 + nx1)}{(m+n)}, \frac{(my2 + ny1)}{(m+n)}\)

Answer:

Rs. 300

Step-by-step explanation:

The bicycle marked price = Rs. 2000

The amount the customer bought the bike given that there was some discount allowed by the shopkeeper including VAT = Rs. 1921

The VAT applied = 13%

The amount given as the discount = Required

The VAT is applied to the selling price

Let d represent the discount amount, we have;

The selling price = 2000 - d

The amount paid as VAT = (2,000 - d) × 13% = (2,000 - d) × 0.13

The amount the customer bought it including VAT = The selling price + The amount paid as VAT

The amount the customer bought it including VAT = Rs. 1921

∴ 1921 = 2000 - d + (2,000 - d) × 0.13 = 2,260 - 1.13·d

1.13·d = 2,260 - 1,921 = 339

d = 339/1.13 = 300

The amount given as discount, d = Rs. 300

(a) The mean number of hits a baseball player with a career batting average of .300 should get in 75 at-bats is approximately 22.5 hits.

(b) The standard deviation cannot be determined solely based on the batting average; additional information is required.

(a) The mean number of hits can be calculated by multiplying the batting average (.300) by the number of at-bats (75):

Mean number of hits = Batting average × Number of at-bats = 0.300 × 75 = 22.5 hits.

(b) The standard deviation cannot be determined solely based on the batting average because it only provides information about the average success rate per at-bat. The standard deviation requires additional information, such as the variance or distribution of hits among the at-bats.

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d. estimate effectiveness of the promotion , the effectiveness of the promotion, which includes analyzing customer response, sales figures, and other metrics.

The Chief Marketing Officer is responsible for managing the company's marketing strategies. After ABC's recent coupon promotion, the Chief Marketing Officer's role would be to estimate the effectiveness of the promotion, which includes analyzing customer response, sales figures, and other metrics.

The Chief Marketing Officer is responsible for managing the company's marketing strategies.

d. estimate effectiveness of the promotion , the effectiveness of the promotion, which includes analyzing customer response, sales figures, and other metrics.

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The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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For the g(x) functions provided, here are their key features:

g(x) = (x + 2)(x − 1)(x − 2)

End behavior: As x approaches negative or positive infinity, g(x) approaches positive infinity.

Y-intercept: g(0) = -4

Zeros: x = -2, 1, 2

Ray and Kelsey could both be accurate, all depending on the stated third-degree polynomial function.

It is conceivable for a third-degree polynomial to present up to three zeros, thus corroborating Kelsey's point that the function can have up to three intersection points with the x-axis maximum. Moreover, it can even occur that this function possesses a repeatable zero, causing a fourth interception.

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Answer:

I am fairly certain is y=8x

Step-by-step explanation:

The only definitive points are (0,0) and (10,80)

So using the slope formula rise/run i got 8

Let's evaluate each of the prefix expressions:

A) *2/8 4 3

To evaluate this expression, we start from the right and work our way to the left.

The division operation (/) is applied first: 4 divided by 3 is equal to 1.33 (approximately).

Next, we perform the multiplication operation (*): 1.33 multiplied by 2 is equal to 2.67 (approximately).

Therefore, the value of the expression is approximately 2.67.

B) 1- 33 425

Again, we start from the right and move to the left.

The subtraction operation (-) is applied first: 425 minus 33 is equal to 392.

Finally, we subtract 1 from 392: 392 minus 1 is equal to 391.

The value of the expression is 391.

C) + 132 123/6-4 2

Let's break down the expression step by step:

1. 123 divided by 6 is equal to 20.5.

2. Next, we have: 132 + 20.5 - 4 2.

To evaluate the addition and subtraction, we perform the operations from left to right:

3. 132 plus 20.5 is equal to 152.5.

4. Subtracting 4 from 152.5 gives us 148.5.

5. Finally, we subtract 2 from 148.5, resulting in 146.5.

Therefore, the value of the expression is 146.5.

D) +3+3 13+333

Following the same procedure, we evaluate the expression step by step:

1. 3 plus 3 is equal to 6.

2. Next, we have: 6 + 13 + 333.

To evaluate the addition, we perform the operations from left to right:

3. 6 plus 13 is equal to 19.

4. Finally, we add 333 to 19, resulting in 352.

Therefore, the value of the expression is 352.

Q3. It seems that there is no specific question mentioned for Q3. If you have any additional question or clarification, please let me know and I'll be happy to assist you.

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2.25$. The call is priced at 15 cents per minute

Answer:

13

Step-by-step explanation:

just add them both and divide by 65

Answer:

Step-by-step explanation:

To find how many buses are needed, add the number of boys to the number of girls, then divide it to how many person can be accomodated in 1 bus.

\( \frac{407 + 438}{65} = \frac{845}{65} = \boxed{13}\)

The SI unit for arc length is the meter

Arc length is a measure of the length of a portion of a curve, which is a continuous and smooth path between two points. It is defined as the distance along the curve between two points, usually measured in a straight line.

The arc length formula is given by:

L = ∫ [a,b] √[1 + (dy/dx)²] dx

where L is the arc length, [a,b] is the interval on which the curve is defined, dy/dx is the derivative of the curve with respect to x, and the integral is taken over the interval [a,b].

The result of this formula is in meters, which is the standard unit of length in the SI system. This means that the arc length of a curve is measured in meters, regardless of the shape or size of the curve.

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Answer:

Step-by-step explanation:

T + 3 = 17 - 5

T + 3 = 12

T = 12 - 3

T = 9

Answer:

T = 9

Step-by-step explanation:

Lets evaluate

T + 3 = 17 - 5

T + 3 = 12

T = 12 - 3

T = 9

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

After a period of 3 years, the investment results in approximately $427.73. To find the amount that results from the given investment, we can use the compound interest formula:

A = \(P(1 + r/n)^(nt)\)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

Given:

P = $300

r = 12% or 0.12 (decimal form)

n = 4 (quarterly compounding)

t = 3 years

Substituting the values into the formula:

A =\(300(1 + 0.12/4)^(4*3)\)

A = \(300(1 + 0.03)^(12)\)

A = \(300(1.03)^12\)

Calculating the expression:

A ≈ 300(1.425761)

A ≈ $427.73

Therefore, after a period of 3 years, the investment results in approximately $427.73.

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The solution to the initial-value problem dy/dx - 4xy = sin(x^2), y(0) = 3 can be expressed as y = e^(2x^2)∫sin(x^2)e^(-2x^2) dx + 3e^(2x^2).

We begin by finding the integrating factor for the differential equation dy/dx - 4xy = sin(x^2). The integrating factor is given by e^(∫-4x dx) = e^(-2x^2). Multiplying both sides of the differential equation by this integrating factor, we get:

e^(-2x^2)dy/dx - 4xye^(-2x^2) = sin(x^2)e^(-2x^2)

Now we can recognize the left-hand side as the product rule of (ye^(-2x^2))' = e^(-2x^2)dy/dx - 4xye^(-2x^2). Using this fact, we can rewrite the differential equation as:

(ye^(-2x^2))' = sin(x^2)e^(-2x^2)

Integrating both sides with respect to x, we get:

ye^(-2x^2) = ∫sin(x^2)e^(-2x^2) dx + C

where C is the constant of integration. To solve for y, we multiply both sides by e^(2x^2) to get:

y = e^(2x^2)∫sin(x^2)e^(-2x^2) dx + Ce^(2x^2)

Therefore, the solution to the initial-value problem dy/dx - 4xy = sin(x^2), y(0) = 3 can be expressed as:

y = e^(2x^2)∫sin(x^2)e^(-2x^2) dx + 3e^(2x^2)

where the integral on the right-hand side can be evaluated using techniques such as integration by parts or substitution.

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