25+25= so first u want to add 5+5so that equals 10 so u put the one on the top of 2 then u add2+2+1 so that equals 5 so ur answer would be 50

The probability that a customer does not win an appetizer is given as follows:

p = 0.8 = 80%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of marbles is given as follows:

1 + 4 + 7 + 3 = 15 marbles.

An appetizer is won with a green marble, and 3 of the marbles are green, while 12 are not, hence the probability that a customer does not win an appetizer is given as follows:

p = 12/15

p = 0.8 = 80%.

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Jen needs \( \frac{3}{4} \) a pound of sunflower seeds to plant in her garden. Since there are 16 ounces in a pound, we can convert \( \frac{3}{4} \) of a pound into ounces by multiplying it by 16.

\( \frac{3}{4} \cdot 16 = 12 \)

Therefore, Jen will need to buy 12 ounces of sunflower seeds to plant her garden.

In summary, to find the number of ounces Jen needs to buy, we first converted \( \frac{3}{4} \) of a pound into ounces by multiplying it by 16. The result is 12 ounces, which is the amount of sunflower seeds she needs to purchase

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The unit rate of the beef if it cost $14.40 for 4.5 pounds of beef is $3.2 per pound

The unit rate is the cost of each unit of an item at a particular time.

Cost of 4.5 pounds of beef = $14.40

Unit rate of beef = Total cost / Total pounds

= $14.40 / 4.5

= $3.2 per pound

Check:

Cost of 4.5 pounds of beef = unit cost of beef × pounds of beef

= $3.2 × 4.5

= $14.4

In conclusion, the unit rate of beef is given as $3.2 per pound.

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The critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3 and (1, -1) is the only extremum or relative maximum of the function.

To find the relative maximum and minimum values of the function f(x, y) = (\(x^3\))/3 + 2xy +\(y^2\) - 3x + 1, we need to analyze its critical points and classify them using the second partial derivative test.

To find the critical points, we need to compute the partial derivatives of f with respect to x and y and set them equal to zero:

∂f/∂x = \(x^2\) + 2y - 3 = 0

∂f/∂y = 2x + 2y = 0

Solving these equations simultaneously, we find x = 1 and y = -1.

Thus, the critical point is (1, -1).

Next, we need to compute the second partial derivatives and evaluate them at the critical point:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 2

Now, we can use the second partial derivative test to classify the critical point.

The discriminant D = (∂²f/∂x²) × (∂²f/∂y²) - \(\left(\frac{{\partial^2 f}}{{\partial x \partial y}}\right)^2\) = (2)(2) - \((2)^2\) = 0.

Since D = 0, the test is inconclusive.

To determine the nature of the critical point, we can examine the function near the critical point.

Evaluating f at the critical point (1, -1), we find f(1, -1) = \((1^3)\)/3 + 2(1)(-1) + \((-1)^2\) - 3(1) + 1 = -1/3.

Hence, the critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3.

There are no other critical points to consider, so we can conclude that (1, -1) is the only extremum of the function.

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Prem purchased a plot for ₹1.1 lakh and its price increased at an annual rate of 5%.Ram's flat had a higher value than Prem's plot, Prem paid Ram the difference, which was ₹0.118 lakh or ₹11,800. Ram's flat is more valuable than Prem's plot of land

After two years, the value of Ram's flat would be ₹1.1 lakh + (10% of ₹1.1 lakh × 2 years) = ₹1.43 lakh.

Similarly, the value of Prem's plot of land would be ₹1.1 lakh + (5% of ₹1.1 lakh × 2 years) = ₹1.21 lakh.

Therefore, the difference in value between Ram's flat and Prem's plot of land is ₹1.43 lakh - ₹1.21 lakh = ₹22,000.

Ram would have to pay ₹22,000 to Prem as Ram's flat is more valuable than Prem's plot of land.

Ram purchased a flat for ₹1.1 lakh and its price increased at an annual rate of 10%. After two years, the flat's value would be:

1.1 lakh * (1 + 0.1)^2 = 1.1 lakh * 1.21 = ₹1.331 lakh

Prem purchased a plot for ₹1.1 lakh and its price increased at an annual rate of 5%. After two years, the plot's value would be:

1.1 lakh * (1 + 0.05)^2 = 1.1 lakh * 1.1025 = ₹1.213 lakh

After exchanging their properties, the difference in value is:

₹1.331 lakh (flat) - ₹1.213 lakh (plot) = ₹0.118 lakh

Since Ram's flat had a higher value than Prem's plot, Prem paid Ram the difference, which was ₹0.118 lakh or ₹11,800.

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2.5kg of sultana brand cost 4.80$

price of 1 kg sultana brand = 0.520$ per kg

1.5 kg of weetabix costs $2.95

price of 1 kg weetabix brand = 0.509$

The best buy is weetabix !

Answer:She will have:

N = 200 smaller lots

Step-by-step explanation: N = (total acres of land) / (smaller lots of land)

Substituting the values we have:

N = 10 / (1/20)

Rewriting we have:

N = 10 * 20

N = 200 lots

Answer:

Please check the explanation.

Step-by-step explanation:

Part a)

Given that the two parallel lines are crossed by a transversal line.

Given that

m∠2 = 2x + 54 and m∠6 = 6x - 11

Angle ∠2 and ∠6 are corresponding angles.

Corresponding angles are congruent.

Thus,

m∠2 = m∠6

2x + 54 = 6x - 11

flipe the equation

6x - 11 = 2x + 54

subtract 2x from both sides

6x - 2x - 11 = 2x - 2x + 54

4x - 11 = 54

adding 11 to both sides

4x - 11 + 11 = 54 + 11

4x = 65

dvide both sides by 4

4x/4 = 65/4

x = 16.2500    (round to 4 decimal places)

Part b)

We have already determined

x = 16.2500

Given

m∠2 = 2x + 54

substitute x = 16.2500 in the euation

        = 2(16.2500) + 54

        = 86.5°

As angle ∠2 and angle ∠1 lie on a straight line. Hence, the sum of their angles must be 180°.

i.e.

m∠1 + m∠2 = 180°

substituting m∠2 =  86.5° in the equation

m∠1 + 86.5°  = 180°

subtracting 86.5° from both sides

m∠1 + 86.5° - 86.5° = 180° - 86.5°

m∠1 = 93.5°

Therefore, the measure of angle m∠1 is:

Answer:

1008 calories

Step-by-step explanation:

one pound = 16 ounces

16 ÷ 8 = 2

504 × 2 =

1008

Based on the given information in Exhibit Cape May Realty, the question is asking to test the significance of the slope coefficient at a significance level of a = 0.10. The p-value is less than 0.10, which means that the null hypothesis can be rejected. This leads to the conclusion that the population slope coefficient is different from zero. Therefore, option C is the correct answer.

This means that there is a statistically significant relationship between square footage and property rental rate. As the slope coefficient is different from zero, it indicates that there is a positive or negative relationship between the two variables. However, it does not necessarily mean that there is a causal relationship. There could be other factors that influence the rental rate besides square footage.

In summary, the statistical analysis conducted on Exhibit Cape May Realty indicates that there is a significant relationship between square footage and property rental rate. Therefore, the population slope coefficient is different from zero. It is important to note that this only implies a correlation, not necessarily a causal relationship.

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The perimeter "P" is equal to the length of the base of one triangle multiplied by the "n" number of triangles in the figure plus two times the length of another side. The equation for the perimeter is P = 5n + 14.

We are given triangles. The triangles are arranged in a certain pattern. The length of the base of each triangle is equal to 5 units. The length of the other two sides is 7 units each. We conclude that all the triangles are isosceles. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P".

P(1) = 14 + 5(1)

P(2) = 14 + 5(2)

P(3) = 14 + 5(3)

We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.

P(n) = 14 + 5n

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Answer:

Step-by-step explanation:

14

Answer:

Step-by-step explanation:

5

Answer:

9. 4(3x+5)

10. 8a+7c+3

Step-by-step explanation: A square has 4 sides and since each side is that equation times that equation by 4, and for the second one combine like terms.

Answer:

slope is 0.6

Step-by-step explanation:

y1-y2     2-11

x1-x2     -5-10

equals

-9 over 15

simplify

3/5, decimal form is 0.6

hoped this helped

The first-order Taylor formula for f(x, y) at (0, 0) is:

f(x, y) ≈ f(0, 0) + ∂f/∂x(0, 0)x + ∂f/∂y(0, 0)y

The second-order Taylor formula for f(x, y) at (0, 0) is:

f(x, y) ≈ f(0, 0) + ∂f/∂x(0, 0)x + ∂f/∂y(0, 0)y + (1/2)∂²f/∂x²(0, 0)x² + ∂²f/∂x∂y(0, 0)xy + (1/2)∂²f/∂y²(0, 0)y²

The first-order Taylor formula is an approximation of a function using its first derivatives.

In this case, the function f(x, y) is approximated at the point (0, 0) using the first partial derivatives ∂f/∂x and ∂f/∂y evaluated at (0, 0).

The formula consists of the function value at (0, 0) plus the partial derivatives multiplied by the corresponding variables x and y.

The second-order Taylor formula extends the approximation to include second partial derivatives.

In addition to the terms in the first-order formula, it includes the second partial derivatives ∂²f/∂x², ∂²f/∂x∂y, and ∂²f/∂y².

These terms account for the curvature of the function and provide a more accurate approximation near the point (0, 0).

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The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

13 °C

Step-by-step explanation:

You just ask yourself how you got from -6 to +7. So in other words, what plus -6 gets you 7. I know that 13-6=7. the aswer is 13°C.

hope this helps!!

Answer:

The point on the bottom right quadrant which is the lowest. (Look at photo.)

Step-by-step explanation:

The first coordinate always coresponds to the x coordinate and the second to the y coordinate. So here the x coordinate is 1.5 and the y coordinate is -5. All you need to do is find both of these values on the axis and find where they intercept.

I circled the correct location in the attachment.

The following probabilities of the given question are ,

p(3 ≤X ≤5) = 0.18522 + 0.324135 + 0.302526

= 0.811881.

a) To find p(X = 2) when X~Bin(4,0.6)

When X~Bin(n,p),

the probability mass function of X is given by:

p(X) = \((nCx)p^x(1-p)^_(n-x)\)

Here, n=4,

x=2 and

p=0.6

So, the required probability is given by

p(X = 2)

= \((4C2)(0.6)^2(0.4)^(4-2)\)

= 0.3456b)

To find p(X > 2) when X~Bin(8,0.2)

Here, n=8 and p=0.2So, p(X > 2) = 1 - p(X ≤ 2)

Now, we need to find

p(X ≤ 2)p(X ≤ 2)

= p(X=0) + p(X=1) + p(X=2)

By using the formula of Binomial probability mass function, we get

p(X=0)

=\((8C0)(0.2)^0(0.8)^8\)

= 0.16777216p(X=1)

=\((8C1)(0.2)^1(0.8)^7\)

= 0.33554432p(X=2)

= \((8C2)(0.2)^2(0.8)^6\)

= 0.301989888

Hence,

p(X ≤ 2) = 0.16777216 + 0.33554432 + 0.301989888

= 0.805306368So, p(X > 2)

= 1 - p(X ≤ 2)

= 1 - 0.805306368 = 0.194693632c)

To find p(3 ≤X ≤5) when X ~ Bin(6, 0.7)

Here, n=6 and

p=0.7

So, p(3 ≤X ≤5)

= p(X=3) + p(X=4) + p(X=5)

By using the formula of Binomial probability mass function, we get

\(p(X=3) = (6C3)(0.7)^3(0.3)^3\)

= \(0.18522p(X=4)\)

= \((6C4)(0.7)^4(0.3)^2\)

= \(0.324135p(X=5)\)

= \((6C5)(0.7)^5(0.3)^1\)

= 0.302526.

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Answer:

321

Step-by-step explanation:

Answer:

: x < 6

Step-by-step explanation:

Answer:

See explanation for answers

Step-by-step explanation:

Reason 1) Given from the problem statement(because it says that B is the midpoint of AC)

Reason 2) Because B is the midpoint of AC

Reason 3) Given frome the problem statement(because it says that AB/cong CD)

Reason 4) Because two lines congruent to each other have the same length

Reason 5(You didn't explain well)) BC=AB=CD, so BC=CD(Specific reason: Transitivity of equality)

And we're done!

Answer: y = -1/2x+7/2.

Step-by-step explanation:

Firstly, we need to understand the formula of point-slope form: y1-y2=m(r1-r2)

Where x and y is the coordinates and m is the slope respectively.

To find the slope:

y1-y2/r1-r2

In this case:

5-4/-3-(-1)=-1/2

We can then put the above slope and the point (-1,4) into the formula:

4-y = -1/2(-1-x)

-y = 1/2+1/2x-4

y = -1/2x+7/2

Alternatively:

y-4=-1/2(x-(-1))

y=-1/2x-1/2+4

y = -1/2x+7/2

Answer:

y - 5 = -1/2(x+3)

Step-by-step explanation

Slope = y2-y1/x2-x1

Slope = 4-5/-1-(-3) = -1/2

(x1,y1) = (-3,5)  

final answer : y - 5 = -1/2(x+3)

The total balance he will have in the accounts at the end of 2 years will be $870.88. The correct option is D.

In most cases, simple interest paid or received over a specific time period is a fixed percentage of the principal amount borrowed or lent. Borrowers must pay interest on interest as well as principal because compound interest accrues and is added to the accumulated interest from previous periods.

Given that Thomas deposited $450 into an account that pays 4.5% simple interest and deposited $350 into an account that pays 4.25% compounded annually.

The simple interest is calculated as,

SI = ( 450 x 4.5 x 2 )

SI = $40.5

Amount = 450 + 40.5

Amount = $490.5

The compound interest will be calculated as,

A = 350 ( 1 + 0.0425 )²

A = $380.38

The total balance in the account after 2 years will be,

Total balance = $490.5 + $ 380.38

Total balance = $870.88

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The half-range sine expansion of the function f(x) = 8x + 7 on the interval 0 < x < 3 is \(\[ f(x) = 19 + \sum_{n=1}^{\infty} \left[ \frac{48(-1)^{n+1}}{n^2 \pi^2} \sin\left(\frac{n \pi x}{3}\right) \right] \]\)

To find the half-range sine expansion of the function \(\( f(x) = 8x + 7 \)\) on the interval ( 0 < x < 3 ), we will use the half-range sine series formula:

\(\[ f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} [a_n \sin(\frac{n \pi x}{L})] \]\)

In this case, \( L = 3 - 0 = 3 \). Let's calculate the coefficients \(\( a_n \)\):

\(\[ a_0 = \frac{2}{L} \int_{0}^{L} f(x) \, dx \]\)

\(\[ = \frac{2}{3} \int_{0}^{3} (8x + 7) \, dx \]\)

\(\[ = \frac{2}{3} [4x^2 + 7x] \bigg|_{0}^{3} \]\)

\(\[ = \frac{2}{3} [(4 \cdot 3^2 + 7 \cdot 3) - (4 \cdot 0^2 + 7 \cdot 0)] \]\)

\(\[ = \frac{2}{3} [36 + 21] \]\)

\(\[ = \frac{2}{3} \cdot 57 \]\)

\(\[ = 38 \]\)

\(\[ a_n = \frac{2}{L} \int_{0}^{L} f(x) \sin(\frac{n \pi x}{L}) \, dx \]\)

\(\[ = \frac{2}{3} \int_{0}^{3} (8x + 7) \sin(\frac{n \pi x}{3}) \, dx \]\)

Let's calculate \( a_n \) for \( n > 0 \):

\(\[ a_n = \frac{2}{3} \left[\int_{0}^{3} (8x \sin(\frac{n \pi x}{3}) \, dx + \int_{0}^{3} (7 \sin(\frac{n \pi x}{3}) \, dx \right] \]\)

The integral of \(\( 7 \sin(\frac{n \pi x}{3}) \)\) over the interval 0 to 3 will be zero since \(\( \sin(\frac{n \pi x}{3}) \)\) is an odd function and the interval is symmetric about the origin.

\(\[ a_n = \frac{2}{3} \int_{0}^{3} (8x \sin(\frac{n \pi x}{3}) \, dx \]\)

Now, we can proceed to calculate \(\( a_n \)\) using integration by parts:

\(\[ u = 8x, \, dv = \sin(\frac{n \pi x}{3}) \, dx \]\)

\(\[ du = 8 \, dx, \, v = -\frac{3}{n \pi} \cos(\frac{n \pi x}{3}) \]\)

Applying the integration by parts formula:

\(\[ a_n = \frac{2}{3} \left[ \left. -\frac{3}{n \pi} \cdot 8x \cos(\frac{n \pi x}{3}) \right|_0^3 + \frac{3}{n \pi} \int_0^3 8 \cos(\frac{n \pi x}{3}) \, dx \right] \]\)

\(\[ a_n = \frac{2}{3} \left[ -\frac{3}{n \pi} \cdot 8x \cos(\frac{n \pi x}{3}) \bigg|_0^3 + \frac{3}{n \pi} \cdot \frac{8}{n \pi} \sin(\frac{n \pi x}{3}) \bigg|_0^3 \right] \]\)

\(\[ a_n = \frac{2}{3} \left[ -\frac{3}{n \pi} \cdot 8 \cdot 3 \cos(n \pi) - 0 + \frac{3}{n \pi} \cdot \frac{8}{n \pi} (\sin(3n \pi) - 0) \right] \]\)

Since \(\( \cos(n \pi) = (-1)^n \)\) and \(\( \sin(3n \pi) = 0 \)\) for all integer values of n, we can simplify further:

\(\[ a_n = \frac{2}{3} \left[ -24 \cdot \frac{(-1)^n}{n \pi} + \frac{24}{n^2 \pi^2} \cdot 0 \right] \]\)

\(\[ a_n = -\frac{48}{n \pi} \cdot \frac{(-1)^n}{n \pi} \]\)

\(\[ a_n = \frac{48(-1)^{n+1}}{n^2 \pi^2} \]\)

Finally, we can write the half-range sine expansion of f(x) = 8x + 7  as:

\(\[ f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \left[ a_n \sin\left(\frac{n \pi x}{L}\right) \right] \]\)

Substituting the values of \( a_0 \) and \( a_n \):

\(\[ f(x) = \frac{38}{2} + \sum_{n=1}^{\infty} \left[ \frac{48(-1)^{n+1}}{n^2 \pi^2} \sin\left(\frac{n \pi x}{3}\right) \right] \]\)

\(\[ f(x) = 19 + \sum_{n=1}^{\infty} \left[ \frac{48(-1)^{n+1}}{n^2 \pi^2} \sin\left(\frac{n \pi x}{3}\right) \right] \]\)

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Answer:

Step-by-step explanation:

An example of a negative correlation is tv viewing and student test grades.

Another example is the video game playing and test grades