full method please
-8+27÷(-3)-(-2)​

Answer:

The cost per ounce of the small cup is $0.269

Step-by-step explanation:

To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.

Cost per ounce = Cost of the cup ÷ Number of ounces in the cup

Cost of the cup = $2.69

Number of ounces in the cup = 10 oz

So,

Cost per ounce = $2.69 ÷ 10 oz

Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)

Therefore, the cost per ounce of the small cup is $0.269.

Answer:

A = 11.4 ft²

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the height between the bases

here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²

The probability of passing at least one will be 0.70.

We know that,

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

here, we have,

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

so, we get,

Probability of passing at least one will be

⇒ 0.59 + 0.60 – 0.49

⇒ 0.70

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complete question:

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?

Answer:

3,000

Step-by-step explanation:

v = lwh

v = (25)(10)(12)

v = 3000

Helping in the name of Jesus.

The equation of smallest degree with integer coefficients will be f(x) = x^2 - (3 + √7)x + 3√7

It should be noted that to begin, let us establish the following:

x = √(8 - 1) which is equal to √7.

y = √(8 + 1) which is equivalent to √9. Therefore, y equals 3.

For the value of x, its conjugate coincides with √7; hence:

(x - x') × (x - y') = (x - √7)(x - 3)

Equation expansion yields:

f(x) = x^2 - (3 + √7)x + 3√7

By substituting for both values x and y in the equation above, we can show that f(x) satisfies the given specifications:

When x takes on a value of √7:

f(√7) = (√7)^2 - (3 + √7)√7 + 3√7 = 7 - 7 = 0

With an input value of 3:

f(3) = 3^2 - (3 + √7)(3) + 3√7 = 9 - 9 - 3√7 + 3√7 = 0

The lowest degree polynomial with rational coefficients having √(8 - 1) and √(8 + 1) as its roots is: f(x) = x^2 - (3 + √7)x + 3√7

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The graph that correctly shows the boundary line for y ≤ 2x − 4, is B. Graph B.

The inequality y ≤ 2x − 4, shows that the y - intercept is - 4. What this means is that the boundary line must pass through ( 0, - 4 ). As Graphs C and D do not cross ( 0, - 4 ), neither of them can be the boundary line.

Also, when representing an inequality on a graph, the signs of ≤ and ≥ are presented with a solid line. > and < are the ones presented with a broken line. This means that Graph A cannot the boundary line for the inequality.

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Answer:To solve this problem, we need to use the formulas for the area and perimeter of a triangle.

Let's start by using the formula for the area of a triangle:

Area = (base x height) / 2

where base and height are the length and height of the triangle's base, respectively.

Let's assume that the base of the triangle is x meters, and the height is y meters. Then we have:

Area = (x*y)/2 = 0.45 m²

Solving for y, we get:

y = (2*0.45)/x

y = 0.9/x

Now, let's use the formula for the perimeter of a triangle:

Perimeter = a + b + c

where a, b, and c are the lengths of the three sides of the triangle.

Since we know that the perimeter is about 325 cm, we can assume that the three sides are close to each other in length. Let's assume that each side has a length of 325/3 = 108.33 cm.

Converting to meters, we get:

a = b = c = 108.33/100 = 1.0833 m

Now, we can use the formula for the area of a triangle again to solve for x:

Area = (base x height) / 2

0.45 = (x * 0.9/x) / 2

0.9 = x²

x = √0.9 = 0.9487 m

Therefore, the base of the triangle is approximately 0.9487 meters, and the height is approximately 0.9/0.9487 = 0.9487 meters.

So the triangle has sides of length 1.0833 meters and a base of length 0.9487 meters, which gives us a perimeter of approximately 3.215 meters (rounded to three decimal places).

Step-by-step explanation:

Answer:6

Step-by-step explanation: It’s 6 because it’s only greater than, not greater than or equal to

The angle of incline of the tram is 19.4 degree.

According to the question:

h=(10450-6311)ft

= 4139 ft

We know that, sinθ=Opposite/Hypotenuse

So, sinθ=h/12463

sinθ= 4139/12463

sinθ= 0.3321

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

θ=19.39

θ≈19.4°

Therefore, the angle of incline of the tram is 19.4 degree.

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Since we can't have a fractional number of lines, Citywide can sign up for a maximum of 1 line and still stay within their budget.

Let's start by calculating the total amount Citywide pays for their telephone costs without the federal excise tax. We can do this by subtracting the 3% tax from the total budget:

$190 / 1.03 = $184.47

The $96 budget plan includes 4,000 minutes, which means that each minute costs:

$96 / 4,000 = $0.024

If Citywide wants to stay within their budget, they need to make sure that the total cost of the lines they sign up for plus the federal excise tax is less than or equal to $190.

Let's represent the number of lines Citywide signs up for as "n". The total cost of the lines plus tax can then be represented as:

n * $96 * 1.03

Setting this expression less than or equal to $190, we get:

n * $96 * 1.03 <= $190

Simplifying, we get:

n <= $190 / ($96 * 1.03)

n <= 1.945

Thus, Citywide can sign up for a maximum of 1 line and still stay within their budget.

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The values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.

From the given right triangle hypotenuse= 17 units and legs of triangle are 15 units and 8 units.

We know that, sinθ = Opposite/Hypotenuse

sinθ = 8/17

We know that, cosθ = Adjacent/Hypotenuse

cosθ = 15/17

We know that, tanθ = Opposite/Adjacent

tanθ = 8/15

Therefore, the values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.

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The true statements are

To find the true statements about the graph that represents y = -2x(x - 11), we need to analyze the equation and its properties.

x-intercepts by setting y = 0 and solving for x:

form the equation we have y = -2x(x - 11)

0 = -2x(x - 11)

0 = x(x - 11)

x = 0

x = 11

The x-intercepts are at (0,0) and (11,0).

Now let's find the vertex of the parabola. The vertex is located at the x-coordinate x = -b / 2a,

y = -2x^2 + 22x

given that

a = -2,

b = 22

x coordinate of the vertex is found by

= -22 / (2 * -2)

= 22 / 4

= 5.5

so we can say that  the true statement is: The x-coordinate of its vertex is 5.5

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The distribution of the numbers of siblings is best described as skewed to the right so, the median will be a more appropriate measure of the center than the mean

If data is positively skewed - which means that the tail of the distribution leans towards higher values - the median will often be a superior indicator for ascertaining the center than the mean.

This advantage can be attributed to the fact that the median outright ignores extreme values, unlike the median which may become influenced by them and thus pulled towards the extremes of the overall set. Since it is simply the middle value obtained upon sorting the data, its sensitivity to conspicuous outliers is more limited.

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The number of ways they can is 40,320.

The number of ways Larry can arrive first and Sarah can arrive last is 720.

The probability that Larry arrives first and Sarah arrives last is 0.01786.

We have,

a)

Since each person can arrive at any time, the number of ways they can arrive is equal to the number of permutations of 8 people, which is:

= 8!

= 40,320

b)

To calculate the number of ways Larry can arrive first and Sarah can arrive last, we can fix their positions and then permute the remaining 6 people in the middle.

= 1 x 6! x 1

= 720

c)

To find the probability that Larry arrives first and Sarah arrives last, we need to divide the number of ways they can arrive in the desired order (720) by the total number of ways they can arrive (40,320):

= P(Larry first and Sarah last)

= 720 / 40,320

= 0.01786

So the probability is approximately 0.01786, or about 1.8%.

Thus,

The number of ways they can is 40,320.

The number of ways Larry can arrive first and Sarah can arrive last is 720.

The probability that Larry arrives first and Sarah arrives last is 0.01786.

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The function is :

[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex] the inverse function is:

Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

Domain: (-[tex]\infty[/tex],9]

Range: [tex](-\infty,0][/tex]

If the inverse function of f is the function g, then x = f(x) gives x = g(y). We just need to reverse the function.

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.

If f and g are inverse functions, then f(x) = y if and only if g(y) = x

The function is :

[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]

We have to find the inverse of the function.

The inverse, interchange the variables solve for y,

Now,

[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]

[tex]f^-^x(x)=\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

So, [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

Hence,

Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

Domain: (-[tex]\infty[/tex],9]

Range: [tex](-\infty,0][/tex]

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Answer:

cmon man

Step-by-step explanation:

We want to show that sinθ cosθ = cotθ is not true for all values of θ. To do this, we just need to find one counterexample, i.e., one value of θ for which the equation is not true.

Recall that cotθ = cosθ/sinθ. So, the equation sinθ cosθ = cotθ can be rewritten as sinθ cosθ = cosθ/sinθ.

Multiplying both sides by sinθ, we get:

sin^2θ cosθ = cosθ

Dividing both sides by cosθ, we get:

sin^2θ = 1

Taking the square root of both sides, we get:

sinθ = ±1

So, we need to find a value of θ such that sinθ is equal to ±1. This occurs when θ = π/2 + kπ, where k is an integer.

Now, let's check whether sinθ cosθ = cotθ is true for this value of θ. We have:

sin(π/2 + kπ) = ±1

cos(π/2 + kπ) = 0

cot(π/2 + kπ) = undefined (since cos(π/2 + kπ) = 0)

Therefore, sinθ cosθ = cotθ is not true for θ = π/2 + kπ, and we have found a counterexample. This shows that sinθ cosθ = cotθ is not a trigonometric identity.

The domain can be written as follows:

R - {x = n*12pi or m*4pi | n, m ∈ Z}

where pi = 3.14 and R is the set of real numbers.

Here we want to find the domain of the function:

y = tan(x/8)

The tangent is the quotient between the cosine and the sine, then we will get:

sin(x/8)/cos(x/8)

The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.

The zeros are:

cos(x/8) = 0

We know that cos(pi/2) = cos(3pi/2)  = 0

Then:

x/8 = pi/2

x = 4pi

x/8 = 3pi/2

x = 12pi

So the domain is the set of all real numbers except the ones in the next set:

{x = n*12pi or m*4pi | n, m ∈ Z}

Where Z is the set of integers.

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Answer:

$5.50(2/3)π(6.5^3) = $3,163.45

$5.50(2/3)(3.14)(6.5^3) = $3,161.85

$3,161.85 is the correct answer.

The statement that correctly describes the expression |x^3|+5 is 5 more than the absolute value of the cube of a number.

Given this expression: |x^3|+5

| | = This sign means Absolute value,

x^3 = x³ = x × x × x

Hence, the statement that correctly describes the expression |x^3|+5 is : 5 more than the absolute value of the cube of a number.

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Some solutions for the given system of inequalities are:

(5, 12)

(6, 12)

(7, 13)

And so on.

Here we have the following system of inequalities:

x > 4

y  ≥ 12

We want to see which ordered pair, of the form (x, y), is a solution for the system.

A solution is a pair that makes both inequalities true.

So, x must be larger than 4.

y can be equal to 12, or larger than 12.

Then some solutions are:

(5, 12)

(6, 12)

(7, 13)

And so on.

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Sebastian can choose between 4,320 different sweaters.

to find the total number of different sweaters, we need to take the product between the numbers of options for each of the given selections, we have the numbers:

Color = 10 options.

Pattern = 4 options.

Letter type = 12 options.

Image = 9 options.

Then the total number of different options is:

D = 10*4*12*9 = 4,320

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The area of the triangle is equal to 1337 square feet. (Correct choice: A)

In this problem we must determine the area of the triangle given the lengths of all sides, this can be done by using Heron's formula:

A = √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

If we know that a = 47 ft, b = 59 ft and c = 65 ft, then the area of the triangle is:

s = 0.5 · (47 ft + 59 ft + 65 ft)

s = 85.5 ft

A = √[(85.5 ft) · (85.5 ft - 47 ft) · (85.5 ft - 59 ft) · (85.5 ft - 65 ft)]

A = 1337.252 ft²

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The area of triangle LMN is 49.61 square units.

We have,

To find the area of triangle LMN.

Area = (1/2) x base x height

where the base and height are the sides of the triangle perpendicular to each other.

First, we need to find the length of side L.

We can use the Law of Cosines.

L² = M² + N² - 2MNcos(132°)

L² = 6² + 8.3² - 268.3cos(132°)

L² = 36 + 68.89 + 99.36

L² = 204.25

L = √204.25

L = 14.28

Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.

Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.

Let's call the foot of the perpendicular point P.

Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:

M∠LMP = 180° - M∠M

M∠LMP = 180° - 132°

M∠LMP = 48°

We can use trigonometry to find the length of MP:

tan(48°) = h/6

h = 6 x tan(48°)

h = 6.93

The area of triangle LMN is:

Area = (1/2) x base x height

Area = (1/2) x 14.28 x 6.93

Area ≈ 49.61

Thus,

The area of triangle LMN is 49.61 square units.

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The other endpoint is (11, 1).

We have,

Midpoint = (6, 2) and endpoint = (1, 3).

and, ratio of m: n = 1 :1

Using section formula

6 = ( 1 + a) / (1+1)

6 = (1+a)/2

1 + a = 12

a = 11

and, 2 = (3 + b) / (1+1)

2 = (b + 3) /2

b +3 = 4

b = 1

Thus. the other endpoint is (11, 1).

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Rewriting the expression based on the information will be 72(1 + z/72).

In order to transform 72 + z into a product based on 72, we can apply the distributive property of multiplication over addition. Essentially, this property maintains that:

a x (b + c) = a x b + a x c

By extension, we can create the following equation:

72 + z = 72 + 1 x z

In order to produce an equivalent expression as a multiple of 72 and another factor, we would then need to use the distributive rule once again:

72 + 1 x z = 72 x 1 + 72 x z/72

Simplification leads us to arrive at:

72 + z = 72(1 + z/72)

Our end result is expressed as a synthesis between 72 and the expression (1 + z/72), namely:

72(1 + z/72).

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We can factor each of the given terms so that 4x^2 shows up

8x^5 = 4x^2*2x^3

12x^3 = 4x^2*3x

20x^2 = 4x^2*5

This shows how 4x^2 is the GCF of 8x^5, 12x^3, and 20x^2

-----------------

Here's how to find the GCF of terms involving variables.

First, find the GCF of the coefficients 8, 12 and 20.

List the prime factorizations

Then circle "2*2" since it is found in all three factorizations. Do not circle 3 because it's not found in 8 or 20. Do not circle 5 since it's not found in 8 or 12.

Therefore, the GCF of {8,12,20} is 2*2 = 4.

As for the variable terms, we look for the smallest exponent.

The exponents for x^5, x^3, x^2 are 5,3,2 in that order. The smallest exponent is 2, so x^2 is part of the GCF.

----------------

Summary:

We found the GCF of the coefficients was 4.

The GCF of the variable terms was x^2

That's how we arrive at the GCF of 4x^2

For the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively

The given function is h(x) 4x+5

h of x equal to four times of x plus five

We have to find the values of h(x) for different values of x

x=0, h(x) = 5

x=1, h(x)=9

x=2, h(x)=13

x=3, h(x)=17

x=4, h(x)=21

x=5, h(x)=25

Hence, for the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively

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Answer:

Dividing both sides by 4, we get:

4m/4 = 28/4

Simplifying, we get:

m = 7

Therefore, the answer is D. 7.