The relationship between the actual air temperature x (in
degrees Fahrenheit) and the temperature y adjusted for wind
chill (in degrees Fahrenheit, given a 30 mph wind) is given by
the following formula:

y = -26 +1.3x

Estimate the actual temperature if the temperature adjusted
for wind chill is -35 degrees Fahrenheit.

The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The input and output variables for this problem are given as follows:

V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

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You will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.

Explain whole numbers

Whole numbers are a set of numbers that includes all natural numbers (positive integers) and zero. They are represented by the symbol "W" and do not include any fractions or decimals. Whole numbers are used in counting, measuring, and representing quantities of discrete objects or entities, and are a fundamental concept in mathematics.

According to the given information

First, let’s convert the length of the stone paver from inches to feet: 14 inches = 14/12 feet = 1.17 feet.

The perimeter of the patio is (12 + 14 + 12) feet = 38 feet. Since each stone paver is 1.17 feet long, you will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.

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Answer:

False

Step-by-step explanation:

3√2 sec(theta) + 7 = 1

3√2 sec(theta) = -6

sec(theta) = -2/√2

sec(theta) = -√2

theta = arcsec(-√2)

However, the range of secant function is [-∞, -1] U [1, ∞]. Since -√2 is not within this range, we cannot take the arcsecant of -√2. Therefore, there is no real value of theta that satisfies the equation, including 3π/4.

Therefore, the statement "The value 3π/4 is a solution for the equation 3√2 sec(theta) + 7 = 1" is False.

I hope it helps you

The total amount that Meihua pays for the 36 pencils is  9M - 36n

We know that a set of 4 pencils has a price M, then the price of each single pencil is:

P = M/4

And we also know that Meihua got a discount of n in each pencil, so the price that she pays for each pencil is:

P = M/4 - n

Now we know that she buys 36 of these, so the amount that she pays is given by the product:

amount  = 36*(M/4 - n)

amount = 9M - 36n

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The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.

A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.

A rectangular prism's volume V is determined by:

V = l × w × h

where l denotes the prism's length, w its width, and h its height. Here are the facts:

l = 2 3 ft

w = 1 1/2 ft

h = 1 1/4 ft

When we enter these values into the formula, we obtain:

V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)

= (7/3 ft) × (3/2 ft) × (5/4 ft)

= 35/8 ft³

Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.

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The sportsman has a final distance with respect to his home equal to 305 meters.

In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:

X = ∑ xₙ, for n = {1, 2, 3, ..., N}

Where the sportsman goes far away for his home for x > 0, in meters.

Now we proceed to determine the final distance:

X = + 350 m - 125 m + 80 m

X = + 305 m

The final distance of the sportsman with respect to his home is 305 meters.

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The inverse of the function y-∛x/3 -1 is:

To find the inverse of the given function, we need to express x in terms of y. We can start by swapping the positions of x and y in the original equation:

Now, we can solve for y in terms of x:

Therefore, Therefore, the inverse of the given function is f^-1(x) = 27(x-1)³. This means that if we substitute any value of x into the inverse function, we will get the corresponding value of y that makes the original function true. Similarly, if we substitute any value of y into the original function, we will get the corresponding value of x that makes the inverse function true.

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The percentage of Kira's free throws is 68%.

We have,

From the grid,

We can see that,

There are 25 boxes.

Now,

The number of shaded boxes = 17

Now,

The percentage of the shaded boxes.

= 17/25 x 100

= 17 x 4

= 68%

Thus,

The percentage of Kira's free throws is 68%.

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The complete question.

The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.

Find the percentage of Kira's free throws.

Johannes will need to pay $8.61 for 5 pounds of ground beef

Since Johannes needs 5 pounds of ground beef, and the available pounds are 1.5, 2, 3, and 3.75 pounds.

To reduce the cost, he need to select the package with the lowest cost per pound.

The cost per pound for each package is:

Package 1: $5.58 / 1.5

              = $3.72 per pound

Package 2: $7.44 / 2

              = $3.72 per pound

Package 3: $1.16 / 3

              = $0.39 per pound

Package 4: $13.95 / 3.75

                = $3.72 per pound

Therefore, the package with the lowest cost per pound is Package 3 and package 2  which will give us 5 pounds

So he can do it as:

$1.16 + $7.44

= $8.6

Or

(1 package of 3 pounds x $0.39 per pound) + (1 package of 2 pounds x $3.72 per pound)

= $1.17 + $7.44

= $8.61

Therefore, Johannes will need to pay $8.61 for 5 pounds of ground beef.

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Answer:

We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:

15 = sqrt((-11 - 1)^2 + (y - 2)^2)

15 = sqrt(144 + (y - 2)^2)

15^2 = 144 + (y - 2)^2

225 = 144 + (y - 2)^2

81 = (y - 2)^2

y - 2 = ±9

y = 2 ± 9

So the possible coordinates of point A are (-11,11) and (-11,-7).

Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%

Step-by-step explanation:

The equation of a line that is perpendicular to the line y = –4x + 3 and passes through the point (8, 1) is y = 1/4(x) - 1

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Since the equation of this line is perpendicular to the line y = –4x + 3, the slope is given by;

Slope, m = -4

m₁ × m₂ = -1

-4 × m₂ = -1

m₂ = -1/-4

Slope, m₂ = 1/4

At data point (8, 1) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 1/4(x - 8)  

y = 1/4(x) - 1

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The equations that will make a linear function are

A linear equation, also referred to as a linear function in mathematics, is used to identify relationships between variables that can be plotted on a straight line.

This class of polynomial functions have a degree of 1, indicating that the highest power of the variable within the formula cannot exceed 1.

It takes on the standardized form:

y = mx + b

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Answer:

Step-by-step explanation:

1,2,3,4,6,8,12,16,24,48

hope i helped

Answer: To calculate the cost of the triangular lot, we need to first find the area of the triangle using the given dimensions. To do this, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is given by:

area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In this case, we have a = 188, b = 145, and c = 158. Substituting these values into the formula, we get:

s = (188 + 145 + 158)/2 = 245.5

area = √(245.5(245.5-188)(245.5-145)(245.5-158)) ≈ 12463.15 square feet

Now that we have the area of the lot, we can multiply it by the price per square foot to get the total cost:

cost = 12463.15 × $3 = $37,389.45

Therefore, the lot would cost approximately $37,389.45.

Step-by-step explanation:

Answer:

Okay, let's think through this step-by-step:

• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.

• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest

• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back

•Monthly payments = $3,797.50 / 12 months = $285.55

• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)

The choices do not match this:

A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.

B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.

C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.

D. $35.00 - This is also too low and does not make sense based on the loan details provided.

In summary, to find the interest in just the first payment, we calculate:

Interest over full loan ($297.50) / Number of payments (12) = $24.79

So the interest amount in just the first monthly payment is $24.79.

But the total interest paid over the life of the loan (1 year) is $297.50.

Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.

Let me know if you have any other questions!

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be  70% alcohol combination with 130 mL of the 55% alcohol mixture.

Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.

Here,

Let x represent the required amount (in mL) of the 70% alcohol mixture.

The total amount of alcohol in the final mixture would be equal to the desired 60% alcohol solution since it would be the sum of the alcohol in the 55% alcohol mixture and the alcohol in the 70% alcohol mixture.

=> 0.55 * 130 + 0.70 * x = 0.60 * (130 + x)

=> 71.5 + 0.70x = 78 + 0.60x

=> 0.10x = 6.5

=> x = 65

Therefore, to create a 60% alcohol solution, you would need to combine 65 mL of the 70% alcohol combination with 130 mL of the 55% alcohol mixture.

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Answer:

Step-by-step explanation:

Okay but seriously though, you would have to write the whole question down.

To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.

3/9 = 1/3, which is not a multiple of 1/9

4/9 cannot be simplified further and is therefore a multiple of 1/9

9/12 can be simplified to 3/4, which is not a multiple of 1/9

9/10 cannot be simplified further and is therefore a multiple of 1/9

2/9 cannot be simplified further and is therefore a multiple of 1/9

9/9 = 1, which is not a multiple of 1/9

Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.

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The area of the figure, given the vertices on the coordinate plane, is 14 square units.

The shoelace formula can be used to find the area. First, find the sum of the products :

= ( - 1 × 2 ) + ( -2 × - 3 ) + ( 4 × 2 ) + ( 4 × 4 ) + (1 × -2)

= 2 + 6 + 8 + 16 - 2

= 26

Then the products of the y coordinate and the x coordinates :

= ( -2 × - 2 ) + (2 × 4 ) + ( - 3 × 4 ) + ( 2 × 1) + ( 4 ×  -1 )

= - 2

We can then find the absolute value to be:

= | Sum 1 - Sum 2 | = | 26 - (- 2 ) | = | 26 + 2 | = 28

The area is then:

= 28 / 2

= 14 square units

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The volume of the gas at the height (i.e 6.5 Km) is 652 mL

The final volume of the gas can be obtained by using the Boyle's law equation as shown below:

[tex]P_1V_1 = P_2V_2[/tex]

[tex]1 \times 326 = 0.5 \times V_2[/tex]

[tex]326 = 0.5 \times V_2[/tex]

Divide both side by 0.5

[tex]V_2 = \dfrac{326}{0.5}[/tex]

[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]

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The pattern represents a straight line that passes through the origin with a slope of 1.

The form Ax + By + C = 0 is a two-variable linear equation, where A and B are the coefficients, C is a constant term, and x and y are the two variables, with each having a degree of 1.

The numerical pattern that represents the rule y = x + 0, starting with x = 0, is:

x y

0 0

1 1

2 2

3 3

4 4

... ...

This example shows that when x increments by 1, y additionally increments by 1. Since the rule for y is y = x + 0, we can see that adding 0 to x doesn't change its value, so y is just the same as x. As a result, x and y have a linear relationship with a slope of 1 and a y-intercept of 0.

To put it another way, the pattern is a straight line with a slope of one that runs through the origin.

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The function that has a range of all real numbers is given as follows:

f(x) = -x + 2.

Hence the range for each function in the context of this problem is given as follows:

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The ordered pair that represents the week before is given as follows:

A. (1,7).

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

The meaning of each coordinate in this problem is given as follows:

For the current week, the ordered pair is given as follows:

(5,3).

For the previous week, the total number of hours was the same, that is, 5 + 3 = 8, however with x = 1 and y = 8 - 1 = 7, as only one hour was spent on chores.

Thus option A is correct.

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The equation is expanding Pascal's triangle and the Binomial theorem

(x + 0.5)³ = x³/8 + 3x²/4 + 3x/2 + 1/8

(s + 4t)⁶ = s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶

(3a - 3b)⁴ = 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴

(3m - 2n)⁵  = 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵

(a-4)⁵ = a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024

The binomial theorem formula for any positive integer n.

(x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn x.

11) Using the Binomial Theorem, we have:

(x + 0.5)³ = C(3,0) x³(0.5)⁰ + C(3,1) x²(0.5)¹ + C(3,2) x¹(0.5)² + C(3,3) x⁰(0.5)³

= x³/2³ + 3x²/2² + 3x/2 + 1/2³

= x³/8 + 3x²/4 + 3x/2 + 1/8

12) Using Pascal's Triangle, we have:

(s + 4t)⁶ = C(6,0) s⁶(4t)⁰ + C(6,1) s⁵(4t)¹ + C(6,2) s⁴(4t)² + C(6,3) s³(4t)³ + C(6,4) s²(4t)⁴ + C(6,5) s(4t)⁵ + C(6,6) (4t)⁶

= s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶

13) Using Pascal's Triangle, we have:

(3a - 3b)⁴ = C(4,0) (3a)⁴(-3b)⁰ + C(4,1) (3a)³(-3b)¹ + C(4,2) (3a)²(-3b)² + C(4,3) (3a)(-3b)³ + C(4,4) (-3b)⁴

= 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴

14)Using Pascal's Triangle, we have:

(3m - 2n)⁵ = C(5,0) (3m)⁵(-2n)⁰ + C(5,1) (3m)⁴(-2n)¹ + C(5,2) (3m)³(-2n)² + C(5,3) (3m)²(-2n)³ + C(5,4) (3m)(-2n)⁴ + C(5,5) (-2n)⁵

= 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵

15) Using Pascal's Triangle, we have:

(a-4)⁵ =  C(5,0) a⁵(-4)⁰ + C(5,1) a⁴(-4)¹ + C(5,2) a³(-4)² + C(5,3) a²(-4)³ + C(5,4) a(-4)⁴ + C(5,5) (-4)⁵

= a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024

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The equation is expanding Pascal's triangle and the Binomial theorem ,

[tex](x + 0.5)^3= x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]

[tex](s + 4t)^6 = s^6+ 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4+ 6s(4t)^5 + 4t^6[/tex]

[tex](3a - 3b)^4 = 81a^4 - 324a^3b + 486a^2b^2- 324ab^3 + 81b^4[/tex]

[tex](3m - 2n)^5 = 243m^5 - 810m^4n + 1080m^3n^2- 720m^2n^3 + 240mn^4- 32n^5[/tex]

[tex](a-4)^5= a^5 - 20a^4 + 160a^3 - 640a^2+ 1280a - 1024[/tex]

What is the binomial theorem formula?

The binomial theorem formula for any positive integer n.

[tex](x + y)^n = nC_0 x^n + nC_1x^{n-1} y+ nC_2 x^{n-2} y_2 + … + nC_{n-1} x y^{n-1} + nC_n x.[/tex]

11) Using the Binomial Theorem, we have:

[tex](x + 0.5)^3 = C(3,0) x^3(0.5)^0 + C(3,1) x^2(0.5)^1 + C(3,2) x^1(0.5)^2 + C(3,3) x^0(0.5)^3[/tex]

=[tex]x^3/2^3 + 3x^2/2^2 + 3x/2 + 1/2^3[/tex]

= [tex]x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]

12) Using Pascal's Triangle, we have:

[tex](s + 4t)^6 = C(6,0) s^6(4t)^0+ C(6,1) s^5(4t)^1+ C(6,2) s^4(4t)^2 + C(6,3) s^3(4t)^3 + C(6,4) s^2(4t)^4+ C(6,5) s(4t)^5 + C(6,6) (4t)^6[/tex]

= [tex]s^6 + 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4 + 6s(4t)^5 + 4t^6[/tex]

13) Using Pascal's Triangle, we have:

[tex](3a - 3b)^4 = C(4,0) (3a)^4(-3b)^0 + C(4,1) (3a)^3(-3b)^1 + C(4,2) (3a)^2(-3b)^2 + C(4,3) (3a)(-3b)^3 + C(4,4) (-3b)^4[/tex]

= [tex]81a^4 - 324a^3b + 486a^2b^2 - 324ab^3 + 81b^4[/tex]

14)Using Pascal's Triangle, we have:

[tex](3m - 2n)^5= C(5,0) (3m)^5(-2n)^0 + C(5,1) (3m)^4(-2n)^1 + C(5,2) (3m)^3(-2n)^2+ C(5,3) (3m)^2(-2n)^3 + C(5,4) (3m)(-2n)^4 + C(5,5) (-2n)^5[/tex]

= [tex]243m^5- 810m^4n + 1080m^3n^2 - 720m^2n^3 + 240mn^4 - 32n^5[/tex]

15) Using Pascal's Triangle, we have:

[tex](a-4)^5= C(5,0) a^5(-4)^0+ C(5,1) a^4(-4)^1 + C(5,2) a^3(-4)^2 + C(5,3) a^2(-4)^3 +C(5,4) a(-4)^4 + C(5,5) (-4)^5[/tex]

= [tex]a^5 - 20a^4 + 160a^3 - 640a^2 + 1280a - 1024[/tex]

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The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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Considering the definition of an equation and the way to solve it, the correct answer is option C: Riley need to work 13 weeks to save enough money to buy the new television.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of weeks Riley need to work, and knowing that:

the equation in this case is:

200.73 + 83.85x= 1290.78

Solving:

83.85x= 1290.78 - 200.73

83.85x= 1090.05

x= 1090.05 ÷ 83.85

x=13

Finally, Riley need to work 13 weeks.

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