Emma is buying e number of tomato plants, and Frank is buying f number of tomato plants. Each plant costs $7. Emma is
using a coupon that will give them $25 off the total cost of all their plants.
Which expression represents the total cost of all the plants with the coupon?

Answer:

\(\huge\boxed{\sf x = 10}\)

Step-by-step explanation:

Hypotenuse = x

Base = 4

Perpendicular = \(\sqrt{84}\)

Using Pythagoras Theorem:

\(\sf H^2 = P^2 + B^2\\\\ x^2 = (\sqrt{84} )^2 + (4)^2\\\\x^2 = 84 + 16\\\\x^2 = 100\\\\Taking \ sq \ root \ on \ both \ sides\\\\x = 10\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

Shifted to the right by 9 units, and down by 7 units

Step-by-step explanation:

y=x is the origin.

(x-9) shows that the graph has moved 9 units to the right, as what is inside the parentheses indicates the opposite direction

(you can be able to review why this is from online resources or you can ask your teacher)

the -7 shows that the graph moves 7 units down the graph, it's outside the parentheses, so it follows the same direction

let's sum up:

for this situation,

- what is inside the parentheses is the x

- what is outside the parentheses is the y

- the x-values direction shifts opposite from the sign (+/-)

- the y-values direction shifts like the sign (+/-)

So,

the vertex has been shifted to the right by 9 units, and down by 7 units compared to y=x.

Answer:

$11

Step-by-step explanation:

Since the boots are 30% off, he will pay only 70% of the original price of the boots.

70% of $70 = 0.7 × $70 = $49

He has $60.

$60 - $49 = $11

Answer: $11

One lily is $9

One shrub is $11

Step-by-step explanation:

Let the lillies be x

Let the shrub be y

2x + 6y= 84.........i

6x + 6y = 120..........ii

Lets make x the subject formula in eq(I)

2x= 84- 6y

x = 42 - 3y........iii

Put the value of x into eq (ii)

6(42-3y) + 6y = 120

252 - 18y + 6y= 120

252 - 12y= 120

12y= 252-120

12y= 132

Y= 11

Put the value of Y into eq (I)

2x + 6(11)= 84

2x + 66= 84

2x= 18

X= 9

Therefore,the cost of one day lily is $9 and the cost of one shrub is $11.

The distance between two locations on the same line of latitude can be calculated by summing the total distance between the points in degrees and multiplying it by the statute miles per degree for the shared line of latitude.

To calculate the distance in miles between two locations on the same line of latitude, we first need to find the total distance between the points in degrees. In the case of location A, which is 60°N, 30°W, and location B, which is 60°N, 50°E, the total distance between the two points is 80 degrees (50°E - 30°W).

Next, we need to multiply the sum of the degrees by the statute miles per degree for the shared line of latitude. Since the line of latitude is 60°N, we need to determine the statute miles per degree at that latitude.

The Earth's circumference at the equator is approximately 24,901 miles, and since a circle is divided into 360 degrees, the distance per degree at the equator is approximately 69.17 miles (24,901 miles / 360 degrees).

Multiplying the total distance in degrees (80 degrees) by the statute miles per degree (69.17 miles), we find that the distance between the two locations is approximately 5,533.6 miles.

Similarly, for location C, which is 30°S, 60°W, and location D, which is 30°S, 90°E, the total distance between the points is 150 degrees (90°E - 60°W). Since the line of latitude is 30°S, we use the same statute miles per degree value (69.17 miles).

Multiplying the total distance in degrees (150 degrees) by the statute miles per degree (69.17 miles), we find that the distance between the two locations is approximately 10,375.5 miles.

Therefore, the distance between locations A and B is approximately 5,533.6 miles, and the distance between locations C and D is approximately 10,375.5 miles, when calculated using the given method.

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The doc string should be the next indented line after the def statement.

According to the statement

we have to find that the for creating a doc string for the given function at which place should be the doc string.

So, For this purpose, we know that the

The doc string is used in the python which is the part of programming.

So, The Python is a computer programming language often used to build websites and software, automate tasks, and conduct data analysis.

And the The doc string should be the next indented line after the def statement.

it means the place of the doc string is at the next indented line after the def statement.

So, The doc string should be the next indented line after the def statement.

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In this problem, we have a binomial probability distribution

so

n=3

p=0.50

q=0.50

Find out P(X=2)

9514 1404 393

Answer:

  y = 20·2^x

Step-by-step explanation:

Use the given points to write two equations, then solve for 'a' and 'b'.

  20 = a·b^0 = a

  5120 = a·b^8 = 20·b^8   ⇒   256 = b^8

  b = 256^(1/8) = 2

Your function is ...

  y = 20·2^x

Answer:

-21 ÷ b = 3, b =        b=-7

3c + 1 = 10, c =        c=1/7

Hope this helps!

Answer:

$1.73 per pint

Step-by-step explanation:

2 quarts is the equivalent of 4 pints. Therefore, in order to get the price per pint you must divide 6.92 by 4. This gives you $1.73 per pint.

A negative net exposure position in foreign currency means that a Financial Institution will experience a loss if the foreign currency appreciates.

A net exposure position in foreign currency refers to the overall amount of foreign currency assets and liabilities held by a Financial Institution. When a Financial Institution has a negative net exposure position, it means that it owes more in foreign currency liabilities than it holds in foreign currency assets. In this case, if the foreign currency appreciates (increases in value relative to the domestic currency), the Financial Institution will need to pay more in domestic currency to fulfill its foreign currency obligations. Consequently, the Financial Institution will incur a loss.

On the other hand, a positive net exposure position (option D) implies that the Financial Institution will make a gain if the foreign currency depreciates (decreases in value relative to the domestic currency) because it will receive more domestic currency when converting its foreign currency assets.

Option A is incorrect because a negative net exposure position implies a loss, not a gain if the foreign currency appreciates. Option B is incorrect because not all of the statements are true. Option E is unrelated to the question and therefore not applicable.

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The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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Answer:

Step-by-step explanation:

the nth term of a geometric sequence is

∙

x

a

n

=

a

r

n

−

1

where a is the first term and r the common ratio

r

=

a

2

a

1

=

a

3

a

2

=

...

...

=

a

n

a

n

−

1

here  

a

=

3

and  

r

=

9

3

=

27

9

=

3

⇒

a

10

=

3

×

3

9

=

3

10

=

59049

The transfer price set by the selling division should be equal to the selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally. Option D.

The transfer price refers to the price at which goods or services are transferred between divisions within the same organization. When the selling division sets the transfer price, it needs to consider various factors. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, is the most appropriate choice.

The selling price less the variable costs ensures that the selling division covers its direct costs associated with the transferred goods or services. This ensures that the division remains financially viable and does not incur losses. However, it is also important to consider the opportunity cost of making the transfer internally.

The foregone contribution to the organization represents the potential profit or contribution that the selling division could have made if it had sold the goods or services to external customers instead of transferring them internally. By including this foregone contribution in the transfer price, the selling division accounts for the potential value it could have added to the organization.

In conclusion, the transfer price set by the selling division should consider both the variable costs associated with the transfer and the foregone contribution to the organization. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, captures both of these factors and provides a comprehensive approach to setting the transfer price.

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To compute the given linear combination of the two vectors ū = 51 – 2i and ū = 71 - 6j, we need to multiply each vector by a scalar and then add them together.

The linear combination is given by:

7ū + 60i + و تا

Substituting the values of ū = 51 – 2i and ū = 71 - 6j:

(7(51 – 2i)) + (60i) + و تا

= (357 – 14i) + (60i) + و تا

= 357 + 46i + و تا

So the given linear combination of the two vectors is 357 + 46i + و تا.

Note: The symbol "و تا" seems to be Arabic or Persian, but it doesn't have a specific mathematical meaning in this context. It is treated as a constant term in the linear combination.

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Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

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Answer:

Write your question.

Step-by-step explanation:

We're waiting...

Answer:

whats the question?

Step-by-step explanation:

The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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The inequality can be simplified to:

-7 < x < 3

And the graph can be seen in the image at the end.

Here we have the inequality:

|x + 2| + 1 > 6

To solve this, we need to isolate the variable x, so if we first subtract 1 we get:

|x + 2| +1 - 1 > 6 - 1

|x + 2| > 5

The absolute value part can be decomposed into two.

-5 < x + 2 < 5

Now we can subtract 2 in all the inequality, so we get:

-5 - 2 < x + 2 - 2 < 5 - 2

-7 < x < 3

The graph of this can be seen below

Answer: (7.5, 4.5)

Step-by-step explanation:

To find the midpoint, we can just find the average of the x values and the y values.

x=(10+5)/2=15/2=7.5

y=(5+4)/2=9/2=4.5

Answer:

¯\_(ツ)_/¯

Step-by-step explanation:

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

The surface area is increasing at the rate of (60 x + 150) cm² per second.

Let the side of the cube be x cm.

s = x cm

Surface area of the cube will be:

S = 6 x² cm²

Now, we are given that, the side of the cube is expanding 5 cm per second.

So, the side of the cube after 1 second will be:

s' = x + 5 cm

Surface area will be:

S' = 6 (x + 5)² cm²

S' = (6x² + 150 + 60 x) cm²

Change in the surface area is:

ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²

ΔS = (60 x + 150) cm²

Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.

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He made the mistake on line 1.

2x^2 - 8x + 5....move the 5 to the other side

2x^2 - 8x = -5....now divide by 2

x^2 - 4x = -5/2

x^2 - 4x + 4 = -5/2 + 4

(x - 2)^2 = -5/2 + 8/2

(x - 2)^2 = 3/2

x - 2 = (+-)sqrt 3/2

x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2

He made mistake on line 1.

Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27

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For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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The numerical expression using commutative property of multiplication that is equivalent to 2⁸ is 2² x 2² x 2² x 2² = 256.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Now the given exponent is,

2⁸

Now, 8 can be written as using associative property of addition,

8 = 2 + 2 + 2 + 2

Thus we can write,

2⁸ = 2^( 2 + 2 + 2 + 2 )

Using exponential property

x^(a + b) = x^a . x^b

Thus we get,

2⁸ = 2^2 . 2^2 . 2^2 . 2^2

Thus numerical expression for 2^8 = 2^2 . 2^2 . 2^2 . 2^2

Solving we get,

2^8 = 4 x 4 x 4 x 4 = 256

Thus, the numerical expression using exponential property of multiplication that is equivalent to 2⁸ is 2² x 2² x 2² x 2² = 256.

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Step-by-step explanation:

the distance between 2 points is the Hypotenuse of a right-angled triangle with the legs being the x coordinate difference and the y coordinate difference.

so, Pythagoras applies.

c² = a² + b²

distance² = (2 - -7)² + (11 - 9)² = 9² + 2² = 81 + 4 = 85

distance = sqrt(85) = 9.219544457... ≈ 9.2

The distance between the points A(2,11) and B(−7,9) is d = √85.

There are two points (a, b) and (c, d) then the distance between two points is

d= √(c -a)² + (d-b)²

We have the points A(2, 11) and B(-7, 9).

Using the Distance Formula

d = √(-7-2)² + (9-11)²

d= √(-9)² + (-2)²

d= √81 + 4

d = √85

Thus, the distance between points is √85 unit.

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Answer: (x−6)(x+1)

Step-by-step explanation:

Ask: Which two numbers add up to −5 and multiply to −6?

Answer: −6 and 1

Rewrite the expression using the above.

You will get (x−6)(x+1)

Answer：

x²-5x-6

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx-6 to find a and b, set up a system to be solved.

a+d=-5

a+d=-5ab=1(-6)=-6

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -6.

1,-6

1,-62,-3

Calculate the sum for each pair.

1−6=−5

1−6=−52-3=-1

The solution is the pair that gives sum -5.

a=-6

b=1

Rewrite x²5x-6 as

(x²-6x)+(x-6)

Factor out x in x²-6x.

x(x-6)+x-6

Factor out common term x−6 by using distributive property.

(x-6)(x+1)

DONE