Nick has $7.00. Bagels cost $0.75 each, and a small container of cream cheese cost $1.29. How many bagels can Nick buy?

(i) c = 1/2 and the joint pdf is f(x, y) = (x+y)/2 over the unit square.

(ii) 1/16

(iii) 1/9

iv)  5/3

(v) E(X+Y) = 5/6.

we have,

i.

In order for f(x, y) to be a valid joint pdf, it must satisfy two conditions:

It must be non-negative for all (x,y)

The integral over the entire support must equal 1.

To satisfy the first condition, we need c(x+y) to be non-negative.

This is true as long as c is non-negative and x+y is non-negative over the support, which is the unit square [0,1]x[0,1]. Since x and y are both non-negative over the unit square, we need c to be non-negative as well.

To satisfy the second condition, we integrate f(x, y) over the unit square and set it equal to 1:

1 = ∫∫ f(x, y) dx dy

 = ∫∫ c(x+y) dx dy

 = c ∫∫ (x+y) dx dy

 = c [∫∫ x dx dy + ∫∫ y dx dy]

 = c [∫ 0^1 ∫ 0^1 x dx dy + ∫ 0^1 ∫ 0^1 y dx dy]

 = c [(1/2) + (1/2)]

 = c

ii.

P(X < 0.5, Y < 0.5) can be found by integrating the joint pdf over the region where X < 0.5 and Y < 0.5:

P(X < 0.5, Y < 0.5) = ∫ 0^0.5 ∫ 0^0.5 (x+y)/2 dy dx

                    = ∫ 0^0.5 [(xy/2) + (y^2/4)]_0^0.5 dx

                    = ∫ 0^0.5 [(x/4) + (1/16)] dx

                    = [(x^2/8) + (x/16)]_0^0.5

                    = (1/32) + (1/32)

                    = 1/16

iii.

P(Y<X) can be found by integrating the joint pdf over the region where

Y < X:

P(Y < X) = ∫ 0^1 ∫ 0^x (x+y)/2 dy dx

        = ∫ 0^1 [(xy/2) + (y^2/4)]_0^x dx

        = ∫ 0^1 [(x^3/6) + (x^3/12)] dx

        = (1/9)

iv.

P(X+Y) < 5 can be found by integrating the joint pdf over the region where X+Y < 5:

P(X+Y < 5) = ∫ 0^1 ∫ 0^(5-x) (x+y)/2 dy dx

          = ∫ 0^1 [(xy/2) + (y^2/4)]_0^(5-x) dx

          = ∫ 0^1 [(x(5-x)/2) + ((5-x)^2/8)] dx

          = 5/3

v.

The expected value of XY can be found by integrating the product xy times the joint pdf over the entire support:

E(XY) = ∫∫ xy f(x, y) dx dy

E(XY) = ∫∫ xy (x+y)/2 dx dy

= ∫∫ (x^2y + xy^2)/2 dx dy

= ∫ 0^1 ∫ 0^1 (x^2y + xy^2)/2 dx dy

= ∫ 0^1 [(x^3*y/3) + (xy^3/6)]_0^1 dy

= ∫ 0^1 [(y/3) + (y/6)] dy

= 1/4

The expected value of X+Y can be found by integrating the sum (x+y) times the joint pdf over the entire support:

E(X+Y) = ∫∫ (x+y) f(x, y) dx dy

      = ∫∫ (x+y) (x+y)/2 dx dy

      = ∫∫ [(x^2+2xy+y^2)/2] dx dy

      = ∫ 0^1 ∫ 0^1 [(x^2+2xy+y^2)/2] dx dy

      = ∫ 0^1 [(x^3/3) + (xy^2/2) + (y^3/3)]_0^1 dy

      = ∫ 0^1 [(1/3) + (y/2) + (y^2/3)] dy

      = 5/6

Thus,

(i) c = 1/2 and the joint pdf is f(x, y) = (x+y)/2 over the unit square.

(ii) 1/16

(iii) 1/9

iv)  5/3

(v) E(X+Y) = 5/6.

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The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Given ,IV solution of 110 mL at a drip rate of 5 gtt/min using a tubing factor of 10 gtt/ mL. The formula used to solve infusion time is: Infusion time = Volume ÷ Flow Rate Substitute the values in the formula given above.  Infusion time

= 110 ml ÷ 50 gtt/min Infusion time = 2.2 min/ml To convert minutes into hours, we divide by 60. 2.2 min/ml ÷ 60 min/h = 0.0367 h/ml To determine the total time for 110 ml, multiply 110 ml × 0.0367 h/ml

= 4.037 h Round the time to the nearest tenth of an hour, which is one decimal place. Thus, the infusion time is 4.0 hours. Therefore, the infusion time for the given problem is 4.0 hours (rounded to the nearest tenth of an hour).

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The significance level is the key indicator of whether or not a hypothesis can be supported. (option c)

In statistical analysis, there are several key indicators that are used to determine whether a hypothesis can be supported. One of these indicators is the significance level, which is denoted by the symbol alpha (α).

Another key indicator is the critical value, which is a value that is determined from a statistical distribution and is used to determine whether the observed data is statistically significant.

The test compares the observed frequencies of the categories to the expected frequencies, assuming that there is no association between the variables. The degrees of freedom refer to the number of categories minus one.

Therefore, to answer the original question, option (c)

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(1, -4)

You could just count the units

Answer:

\(a_n=19-4n\)

Step-by-step explanation:

If \(a_1=15\), then the second term is:

\(a_2=a_{2-1}-4\\a_2=a_1-4\\a_2=15-4\\a_2=11\)

This shows that our common difference is \(d=-4\), so we can write the explicit formula:

\(a_n=a_1+(n-1)d\\a_n=15+(n-1)(-4)\\a_n=15-4n+4\\a_n=19-4n\)

Answer:

4

Step-by-step explanation:

LJK is a special right triangle with angle measures of 90° 60° 30°

If the side length of hypotenuse is 8√2 the side length that sees 30° would be half of it so it's 4√2

LMJ is a special right triangle with angles 90° 45° 45° and if the side length of hypotenuse is 4√2 the the value of equal sides would be 4

Answer:

the answer would be 0.372

Answer:

its A hope this helps

Step-by-step explanation:

Answer:

 13 Vehicles Sold

Step-by-step explanation:

20% of 65 is equal to 13 :)

The decimal equivalent of 7 half’s is the number in decimal form

The exact decimal equivalent of 7 half’s is 3.5

A decimal number is a number represented by an integer and a fractional part

The number is given as:

7 halves

Express as product

7 * 1/2

Evaluate the product

3.5

Hence, the exact decimal equivalent of 7 half’s is 3.5

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Answer:

X=105

reason beng corresponding angle

Answer:

75

Step-by-step explanation:

The approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th is 61°. None of the provided answer choices match the correct answer.

To calculate the approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th, we can use the analemma.

The analemma is a figure-8 shaped curve that represents the position of the Sun in the sky at the same time each day over the course of a year. It accounts for the Earth's axial tilt and elliptical orbit around the Sun.

To find the approximate noon Sun angle, we need to consider the declination of the Sun on February 14th and the latitude of Long Island.

On February 14th, the Sun's declination is approximately -12°.

The Sun angle at noon can be calculated using the following formula:

Sun angle = 90° - (latitude - declination)

Substituting the values, we have:

Sun angle = 90° - (41° - (-12°))

Simplifying this equation, we get:

Sun angle = 90° - 41° + 12°

Sun angle = 61°

Therefore, the approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th is 61°.

None of the provided answer choices match the correct answer.

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The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.

To find the measure of angle ZCBD, we need to examine the given information.

From the figure, we know that angle CDE is 155°.

Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.

In a rectangle, the sum of the interior angles at a vertex is always 90°.

Therefore, angle CBD is 90°.

Hence, the measure of angle ZCBD is 90°.

Therefore, the correct option is J. 90.

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Step by step process:

Let's solve for x.

y−3=2(x+1)

Step 1: Flip the equation.

2x+2=y−3

Step 2: Add -2 to both sides.

2x+2+−2=y−3+−2

2x=y−5

Step 3: Divide both sides by 2.

2x/2=y−5/2

x=1/2y+(−5/2)

Answer: x=1/2y+(−5/2)

Let's solve for y.

y−3=2(x+1)

Step 1: Add 3 to both sides.

y−3+3=2x+2+3

y=2x+5

Answer:

y=2x+5

Answer:

D, 9^4 * 8^4

Step-by-step explanation:

The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.

I confirmed D is right on a calculator also.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

the 3rd option is the correct answer.

Therefore , the upper bound of the confidence interval is  - 8.82 .

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here,

n1 = 17 ; X1' = 78.4 ; s1² = 90.3

n2 = 13 ; X2' = 92 ; s2² = 107.8

Confidence interval :

(x1 - x2) ± Tcritical * \(\sqrt{[(sp^{2} /n1 + sp^{2}/n2)]}\)

Pooled variance = Sp²

=> Sp² = (df1*s1² + df2*s2²) / (n1 + n2 - 2)

df = n - 1

Sp² = (16*90.3 + 12*107.8) / 28

Sp² = 97.8

Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)

Tcritical = 1.313

(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]

Margin of Error = Tcritical *\(\sqrt{[(sp^{2} /n1 + sp^{2}/n2)]}\)

Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473

Upper boundary :

(78.4-92) + 4.7771473

-13.6 + 4.7771473

= -8.8228527

= - 8.82

Therefore , the upper bound of the confidence interval is  - 8.82 .

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Answer:

Step-by-step explanation:

(2+x)(2-x)

2(2-x)+x(2-x)

4-2x+2x-x^2

4-x^2

Answer:

1256 meters

Step-by-step explanation:

The distance around the circle (circumference) can be found using the formula \(2\pi r\). r is the radius, which you're given. So 2 * pi * 10 is 62.8 if you use 3.14 as pi. Since the horse went around 20 times, we multiply the circumference by 20. 62.83 * 20 = 1256

The estimated revenue, in dollars, that the club will generate when the bags are priced at $13 each is 3) 1,040.

The revenue formula is the multiplication of the number of units sold and the price per unit.

To determine the total revenue, we must first ascertain the unit price and the quantity sold.

We know that market forces and the competitive environment determine the quantity sold or supplied.

The demand for tote bags at $11 = 100 units

Decrease in demand for every $1 price increase = 10 units

When the price is $13 each, the units to be sold = 80 (100 -10 x 2)

The total revenue at $13 each = $1,040 (80 x $13)

Total revenue at $12 each = $1,080 (90 x $12)

Total revenue at $11 each = $1,100 (100 x $11)

Thus, we can conclude that the club generates less revenue when it increases its price per tote bag from $11 to $13, justifying the interactions between supply, demand, and cost.

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Answer:

tan(57°) = 12/x

x tan(57°) = 12

x = 12/tan(57°) = 7.793

Answer:

x ≈ 7.8

Step-by-step explanation:

using the tangent ratio in the right triangle

tan57° = \(\frac{opposite}{adjacent}\) = \(\frac{12}{x}\) ( multiply both sides by x )

x × tan57° = 12 ( divide both sides by tan57° )

x = \(\frac{12}{tan57}\) ≈ 7.8 ( to the nearest tenth )

The required probability  which represents the a bill for veterinary services costs between $55 and $103 using normal distribution is approximately 0.7745, or 77.45%.

Let X be the cost of a standard veterinary service bill.

X follows a normal distribution with mean μ = $79

And standard deviation σ = $20.

The probability that X is between $55 and $103,

P(55 ≤ X ≤ 103)

To standardize X, we use the formula,

Z = (X - μ) / σ

Substituting the values for μ and σ, we get,

⇒Z = (X - 79) / 20

The probability of 55 ≤ X ≤ 103,

Calculate the corresponding z-scores for 55 and 103,

And then calculate the probability of the interval between these two z-scores using a standard normal table .

The z-score for 55 is,

Z = (55 - 79) / 20

  = -1.2

The z-score for 103 is,

Z = (103 - 79) / 20

  = 1.2

Using a standard normal table or calculator, the probability of the interval between these two z-scores is,

P(-1.2 ≤ Z ≤ 1.2) ≈ 0.7745

Therefore, the probability that a bill for veterinary services costs between $55 and $103 is approximately 0.7745, or 77.45%.

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With the help of standard deviation we can conclude our answer.

acc to our question-

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Answer:

B and D

Step-by-step explanation:

Letter B is 2 units below zero. Letter D is 2 units above zero.

Letter B and letter D are the same distance from distance from zero.

Therefore, opposite of letter B is letter D.

Thus, the letters that have their opposite labelled on the number line are B and D.

Answer:

D AND D

Step-by-step explanation:

Answer:

4/9 miles

Step-by-step explanation:

                 \(\sf Area = \dfrac{2}{3} \ square \ miles\\\)

               \(\sf length = 1\dfrac{1}{2}=\dfrac{3}{2} \ miles\)

\(\sf Width \ of \ rectangle = \dfrac{Area}{length}\)

                             \(\sf = \dfrac{2}{3} \div \ \dfrac{3}{2}\\\\ =\dfrac{2}{3}*\dfrac{2}{3}\\\\ =\dfrac{4}{9} \ miles\\\)

Use KCF method for faction division.

K- Keep the first fraction.

C - Change the division to multiplication.

F - Flip the second fraction.

Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

Answer:

Read this section of the text:

These raptors eat primarily flying insects, so they do most of their hunting on the wing.

What does primarily mean in this sentence?

Step-by-step explanation:

Answer:

Explanation:

−3x + 4y = −12

Add 3x to both sides

−3x + 4y + 3x = −12 + 3x

4y = 3x − 12

Divide both sides by 4

4y / 4 = 3x − 12 / 4

Simplify

Answer:

-3x+4y=-12

4y=-12+3x

y=3x/4-12/4

The value of x, y and z in the rhombus are -6, 9 and -2 respectively.

A rhombus is a quadrilateral with 4 sides equal to each other. Opposite sides are parallel in a rhombus.

Therefore, the value of x, y and z can be found as follows:

2y - 5 = 13

add 5 to both sides of the equation

2y = 13 + 5

2y = 18

divide both sides by 2

y = 18 / 2

y = 9

hence,

-2x + 1 = 13

-2x  = 13 - 1

-2x = 12

divide both sides by -2

x = 12 / -2

x = -6

Let's find z.

-2z + 9 = 13

-2z = 13 - 9

-2z = 4

divide both sides of the equation by -2

z = 4  /-2

z = -2

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