Penny is planning a trip to Egypt. She has mapped out the expected costs of some different components of her trip, and
has compiled them below, including whether the cost is in US
dollars ($) or Egyptian pounds (E).
Item
Cost
Currency
Plane ticket
3,241.77
£
Passport
65.00
$
Tour guide
494.25
£
International phone card
41.38
$
Hotel reservation
398.26
f
Car rental
644.48
£
If the exchange rate of the US dollar to Egyptian pound is 1:5.3841, how much has Penny currently budgeted for her trip,
in US dollars? Round all currencies to two decimal places.
a.
$895.25
b. $993.95
C.
$1,001.63
d
$1.468.01

Answer:

0.1733 = 17.33% probability the first stack was selected.

Step-by-step explanation:

To solve this question, it is needed to understand conditional probability, and the hypergeometric distribution.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Conditional probability:

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

Probability of all red cards for the first stack:

For this, we use the hypergeometric distribution, as the cards all chosen without replacement.

7 + 4 = 11 cards, which means that \(N = 11\).

7 red, which means that \(k = 7\)

3 are chosen, which means that \(n = 3\)

We want all red, so we find P(X = 3).

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 3) = h(3,11,3,7) = \frac{C_{7,3}*C_{4,0}}{C_{11,3}} = 0.2121\)

Conditional probability:

Event A: All red

Event B: From the first stack.

Probability of all red cards:

0.2121 of 50%(first stack)

1 of 50%(second stack). So

\(P(A) = 0.2121*0.5 + 1*0.5 = 0.60605\)

Probability of all red cards and from the first stack:

0.21 of 0.5. So

\(P(A \cap B) = 0.21*0.5 = 0.105\)

What is the probability the first stack was selected?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.105}{0.60605} = 0.1733\)

0.1733 = 17.33% probability the first stack was selected.

The angle  made by one of the tensions suspending particle P is 50⁰.

The angle θ made by one of the tensions is calculated by applying trig identities as follows;

the force opposite the angle = weight of the block = mg

W = 7.75 kg x 9.8 m/s²

W = 75.95 N

The angle θ made by one of the tensions is calculated as follows;

cos θ = (38 N ) / ( 59 N)

cos θ = 0.6441

θ = arc cos (0.6441)

θ = 50⁰

Thus, the angle θ made by one of the tensions is determined as 50 degrees.

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The missing part of the question is in the image attached.

Equation:

alcohol + alcohol = alcohol

0.40x + 0.85*10 = 0.65(x+10)

----

40x + 85*10 = 65x + 65*10

20*10 = 15x

-----

x = (2/3)20

---

x = 13 1/3 gallons (amt. of 40% solution needed)

Answer:

Interval notation (-5,3]

2 divided by 32 is 16 so im gonna say 16

16 is ur answer

The area of the shaded part of the given diagram would be = 176.74cm²

A semi circle is defined as the shape that is formed when a circle is divided into exactly two.

To determine the area of the shaded part the area of the two semi circles are determined through the following;

The formula of area of a circle = πr²/2

Radius = Diameter/2 = 15/2 = 7.5cm

The area = 3.142 ×7.5²/2

= 3.142×56.25/2 = 176.74/2 = 88.37cm²

There area of the two semicircles = 88.36875× 2 = 176.74cm²

The area of the main semi circle;

= πr²

where r = 15 cm

area = 3.142×15²/2

= 3.142 × 225/2

= 706.95/2 = 353.48 cm²

The area of the shaded part is the difference of the main semi circle from the two smaller semicircles. Thus;

353.48 - 176.74 = 176.74cm²

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The equation of a line that has a slope of 3 and passes through (8, 9) will be y = 3x - 15.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is 2. Then the equation is written as,

y = 3x + c

The equation is passing through (8, 9). Then the value of c will be

9 = 3(8) + c

9 = 24 + c

c = - 15

Then the equation will be given as,

y = 3x - 15

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Answer:

[-0.2  0.4]

[0.8   -0.6]

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

ANSWER

My answer is in the photo above

Mixed fraction:

3 2/5 = 17/5

4 4/5 = 24/5

Miles she ran:

17/5 + 24/5

= 41/5 miles or 8.2 miles

The calculation is not reasonable, because 0.45 is less tha 1/2 ( 0.50) and what he has for an answer is half the distance ( 250.17 is 1/2 of 500.34).

To find actual mileage, multiply by 0.45:

500.34 x 0.45 = 225.153 miles.

Round the answer as needed.

From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer:

sure just bring the question and it will be answered

Answer:

11.78

Step-by-step explanation:

Part A

The garden has an area of 400 ft².

• Length = 40 ft

• Width = 10 ft.

The new length will be 3 times the current length.

The new width will be 4 times the current length.

Part B

The area of the new garden will be 12 times the area of the current garden.

Part C

Bob wants his new garden to be 14 times the area of his current garden.

Make the length 2 times the current length and make the new width 7 times the current width.

Answer:

c

Step-by-step explanation:

Is is right?

System of Equations

Let

x = Number of sundaes sold

y = Number of banana splits sold

Sundaes are sold for $2 each and banana splits are sold for $3 each.

If we sell x sundaes, then we make $2x for selling sundaes.

If we sell y banana splits, then we make $3y for selling banana splits

The first condition states they made a total of $150, thus the first equation is:

2x + 3y = 150 [1]

It's also given the number of sundaes sold (x) is 5 more than the number of banana splits sold (y), thus the second equation is:

x = y + 5 [2]

Substituting [2] into [1]:

2(y + 5) + 3y = 150

Operating:

2y + 10 + 3y = 150

Simplifying:

5y + 10 = 150

Subtracting 10:

5y = 140

Dividing by 5:

y = 140/5

y = 28

Substituting in [2]

x = 28+ 5

x = 33

Answer: 33 sundaes and 28 banana splits were sold

By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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Answer:

60%

Step-by-step explanation:

let ,x% is birds of prey

total animals=110

birds of prey=66

then,

x%of 110=66

x/100×110=66

110x/100=66

1.1x=66

x=66/1.1

x=60%

I'm not sure if this is correct.

The area of a rectangle is given as:

Area = Length x width

The dimensions of the rectangle are 9 inches and 5 inches.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of a square = 49 in²

Area of a square = side²

This means the side of the square is 7 inches.

Now,

Let the same amount be x.

The area of the rectangle = 45 in²

The length of the rectangle = 7 + x

The width of the rectangle = 7 - x

The area of the rectangle = Length x Width

45 in² = (7 + x)(7 - x)

45 = 49 - 7x + 7x - x²

45 = 49 - x²

x² = 49 - 45

x² = 4

x = 2

Now,

The dimensions of the rectangle are:

Length = 7 + x = 7 + 2 = 9 inches

Width = 7 - x = 7 - 2 = 5 inches

Thus,

The dimensions of the rectangle are 9 inches and 5 inches.

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Answer:

Step-by-step explanation:

The area of the triangle is 97.07 units².

Given is a triangle we need to find the area,

So, let the triangle be ABC and the altitude be AD.

Using the trigonometric ratios,

Sin 52° = AB / AD

Sin 52° = 9 / AD

AD = 9 / Sin 52°

AD = 11.42

Now,

Tan 26° = DC / AD

Tan 26° = DC / 11.42

DC = 5.56

Also,

Cos 26° = AD / AC

Cos 26° = 11.42 / AC

AC = 12.7

BC = 11.42 + 5.56

BC ≈ 17

Now, the sides are BC = 17, AC = 12.7 and AB = 9,

The area of the triangle = 1/2 x BC x AD = 1/2 x 17 x 11.42

= 5.71 x 17

= 97.07

Hence the area of the triangle is 97.07 units².

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a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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The volume of the sphere is approximately 8181.510 cm³.

The volume of a sphere is the amount of space that is enclosed within the surface of a sphere.

It is a measure of the three-dimensional space that is contained within the sphere.

The volume of a sphere is used in a variety of fields, such as physics, engineering, and architecture, to calculate the space enclosed by a sphere or a spherical object, such as a planet or a ball.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Substituting r = 12.5 cm and π = 3.14, we get:

V = (4/3) × 3.14 × (12.5 cm)³

V ≈ 8181.51 cm³

The volume of the sphere is approximately 8181.510 cm³.

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The correct options are -

When something is bought on credit, an initial payment is made in the form of a down payment.

Given is that Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%.

We can calculate the amount she is putting in down payment as -

{x} = 20% of 125000

{x} = 20/100 x 125000

{x} = 20 x 1250

{x} = 25000

Therefore, the correct options are -

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Answer:

hey there is a snowman challenge for virtual

Step-by-step explanation:

join challenge at #snowmanchallenge

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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The value of 12x in the expression is 10

You multiply 5 = 6x  by 2 to get 12x

From the question, we have the following parameters that can be used in our computation:

2x + 5 = 8x

You subtract 2X from each side to get

5 = 6x

Then multiply both sides by 2

This gives

10 = 12x

So, we have

12x = 10

Why do you multiply both sides by 2

You multiply by 2 because the question requests for the value of 12x

Since, we have solved for 6x, the next step is to multiply 6x by 2 to get 12x

i.e. 6x * 2 = 12x

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Answer:

Step-by-step explanation:

Given data

distance of the route = 15miles

time taken on Monday= 1.75hours

speed= distance./time

speed= 15/1.75

speed= 8.57 miles per hour

her smart watch is correct

time taken on Thursday= 1.63hours

speed= distance./time

speed= 15/1.63

speed= 9.20 miles per hour

she was jogging at 9.20 miles per hour