A 12-ounce soda can has a height of 4.875 inches. What is its average diameter in
inches?
8 ounces = 1 cup, 16 cups = 1 gallon,
7.48 gallons = 1 ft3, 1 foot = 12 inches.

Let the width be [tex]w[/tex] inches and the length be [tex]w+15[/tex] inches.

So, the dimensions of the box are [tex]w-6[/tex], [tex]w+9[/tex], and [tex]3[/tex] inches.

[tex]3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21[/tex]

Rejecting the negative case, [tex]w=21[/tex].

So, the dimensions are 21 by 36 inches.

Answer:

(a) sin() = 1/2

degrees: 30, 150

radians: π/6, 5π/6

(b) sin() = − 1/2

degrees: 210, 330

radians: 7π/6, 11π/6

Note that these solutions are in the interval of 0 to 360 degrees or 0 to 2 radians. Also note that these are the primary solutions, there are infinitely many solutions that can be obtained by adding multiples of 360 degrees or 2π radians to these values.

Answer:

Step-by-step explanation:

You want the measures of 5 marked angles in the figure showing two transversals crossing parallel lines.

Angle 1 forms a linear pair with the angle marked 88°, so is supplementary to it.

  Angle 1 = 180° -88°

  Angle 1 = 92°

Angle 3 is a corresponding angle to the one marked 64° where the horizontal transversal crosses the parallel lines. Corresponding angles are congruent.

  Angle 3 = 64°

Angles 2 and 3 are "remote interior angles" with respect to the exterior angle marked 88°. Hence their sum is 88°.

  Angle 2 = 88° -Angle 3 = 88° -64°

  Angle 2 = 24°

Angles 3, 4, and 81° combine to form a straight angle of 180°.

  Angle 4 = 180° -64° -81°

  Angle 4 = 35°

Angle 5 is an alternate interior angle with respect to the one marked 81° where the downward-sloping transversal crosses the parallel lines. Alternate interior angles are congruent.

  Angle 5 = 81°

It is proved that m = √n.

To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:

m^2 ≤ n < (m + 1)^2.

So, after taking the square root, it will be:

m ≤ √n < m + 1

From that we can see m = √n is the unique m.

A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.

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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.

On solving the provided question we can say that probability, P' = 1 - P( P' < 0.80 ) = 1 - P( P'- 0.80/0.06235 < 0.80-0.80/0.06235 )  => P' = 0.5

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

the proportion of days when particular mutual fund out performed the S&P 500 index = 29/40 = 0.0.725 = 0.8

Let P' denotes the sample proportion for random sample size of n = 40

now, probability, P' = 1 - P( P' < 0.80 ) = 1 - P( P'- 0.80/0.06235 < 0.80-0.80/0.06235 )

P' = 1 - P(Z)

P' = 1 - 0.5

P' = 0.5

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The equation of the linear function represented by the table in slope intercept form is f(x) = 2x + 2.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Equation of the linear function in slope intercept form can be represented as y = mx + d, where m is the slope and d is the y intercept.

Slope is the change in y coordinates divided by the change in x coordinates.

y intercept is the point on the line where the line touches the Y axis.

Given points are (-2, -2), (2, 6), (6, 14) and (10, 22).

Consider the points (-2, -2) and (2, 6).

Slope, m = (6 - -2) / (2 - -2) = 8 / 4 = 2

So the equation becomes y = 2x + d

Substituting one of the points (2, 6) in the above equation,

6 = (2 × 2) + d

d = 2

So the equation is y = 2x + 2.

Hence the given linear function can be represented as f(x) = 2x + 2.

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Answer:

The x intercept is going to be (-43/4) and the y intercept is going to be (0,-43)

Step-by-step explanation:

hope this helped

Answer:

Yolanda served 13 times , Kareem served 38 times and Jose served 19 times.

Step-by-step explanation:

No of orders served by Yolanda = x

No of orders served by Kareem = y

No of orders served by Jose = z

x + y + z = 82  ------------- (1)

y = 2z  ------------ (2)

x = z - 6  ---------(3)

substituting (2) and (3) in (1) :-

z - 6 + 2z + z = 82

4z - 6 = 82

4z = 76

z = 19

y = 2(19)

y = 38

x = 19 - 6

x = 13

Answer:

The expression 10√3 can be written as a single surd as (10√3) = (10 √3/1) = (10 √3)¹/¹ = (10√3)^(1/1) = 10√3.

Answer:

[tex] \frac{1}{24} [/tex]

Step-by-step explanation:

When you're dividing a fraction, you multiply the denominator

For example, taking this question

[tex] \frac{1}{4} \div 6[/tex]

The dominator is 4

You're dividing by 6

So multiply the denominator and what you're dividing by

[tex]4 \times 6 = 24[/tex]

Now that you have that, 24 will be the new denominator

[tex] \frac{1}{24} [/tex]

As an asset account, the furniture account is debited as its balance increases.

Cash and bank amount are assets accounts as well, and when furniture is purchased percentage , they are credited for the amount that has been deducted from them.

Record in journal

A/C for furniture is $50,000.

A/C Cash: DR 2,000,000.

To Capital, 2.5 million

(The beginning of a business with money and furniture)

Note: Since cash and furniture are investments in the business, they are capital, and when capital increases, it is credited. Furniture is our asset, and if it increases, it will be debited. Cash is also our asset, and as it is arriving in the firm, it is increasing, therefore it will be debited.

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The complete question is " Explain Journal entry for started business with cash Rs 200000 and furniture Rs 50000. "

Answer:

1

Step-by-step explanation:

Quotient of 24 and -8 gives you -3. Hence, 4 added to -3 is 1, which is the answer.

Answer: $270

Step-by-step explanation: You multiply 3*750, then multiply the product by 0.12 because 0.12 = 12%.

Answer:

23

Step-by-step explanation:
If x-16=7

Then X= 23

Let me know I’d this answer is incorrect

The equation of the quadratic function that contains the point (1,1) is

y = 2x² - 1.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree. A quadratic function must contain at least one term of the second degree.

Given  the quadratic function that contains the point (1,1)

x = 1 and y = f(x) = 1

the shape of the equation is the same as f(x) = 2x²

a quadratic equation is given by

y = a(x - k)² + h

here (k, h) is the vertex of the function

given vertex is on the y-axis,

so k = 0

y = ax² + h

and a = 2 from f(x) = 2x²

y = 2x² + h

substitute x= 1 and y = 1

1 = 2 + h

h = 1 - 2 =  -1

equation of function is y = 2x² - 1

Hence equation of the function is y = 2x² - 1.

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The number of boxes that would fit into the trunk is 70.

The box is known as a cuboid. A cuboid is a three-dimensional shape that has six faces, 12 sides and 6 vertices.

In order to determine the number of boxes that would fit into the trunk, divide the volume of the trunk by the volume of one box.

Volume is the product of the length, width and height of an object. It measures how much space is in object.

Number of boxes that can fit into the trunk = volume of the trunk / volume of one of the boxes

40,480 /  576 = 70.28 boxes or 70 boxes

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The unknown measures in similar triangles in which x is 24 in.

What is a similar triangle?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

We have given,

ΔABC ≈ ΔXYZ

In ΔABC

AC = 36 in, BC = 18 in and AB = x in

In ΔXYZ

XY = 16in, ZY = 12in and  XZ = 24in

We know that,

the side and angles of a similar triangle are in proportion to each other.

AC / XZ = 36 / 24 = 3/2

BC / ZY = 18 / 12 = 3/2

AB / XY = x / 16

AC / XZ = BC / ZY = AB / XY   --------(similar triangle)

x / 16 = 3/2

x  = 3/2 * 16

x = 3 * 8

x = 24

hence, the unknown measures in similar triangles in which x is 24 in.

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According to the question, the solution to the equation is x = -7.

The equation is a representation of a mathematical relation between two or more variables. It is usually expressed as an equation, where one side of the equation is equal to the other. For example, the equation y=mx+b is a linear equation with two variables, m and b, which are known as the slope and the y-intercept, respectively.

To solve this equation, we must first combine like terms on both sides of the equals sign.

-3x + 3 - x + 10 = -3x + 6

Next, we can subtract 3 from both sides of the equation to isolate the x-term.

-4x + 13 = -3x + 6

Finally, we can subtract -3x from both sides of the equation to isolate the constant term.

-7x = 7

We can then divide both sides of the equation by -7 to solve for x.

x = -7

Therefore, the solution to the equation is x = -7.

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On solving the provided question, we can say that an explicit equation for the geometric sequence t(n) = [tex]t^2+ 6t - 8[/tex] and a recursive equation for the geometric sequence; t(1) = -1

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

an explicit equation for the geometric sequence.

t(n) = [tex]t^2+ 6t - 8[/tex]

a recursive equation for the geometric sequence.

t(1) = -1

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The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

h(x) = √(x - 7) + 5

The value inside the square root should be greater than or equal to zero. Then we have

x - 7 ≥ 0

x ≥ 7

The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

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(a). The smallest quantity at which marginal cost is equal to 15 dollars per item is 2.76. (b). The positive value of q at which average variable cost is equal to marginal cost is [tex]\frac{15}{2}[/tex]. (c). The longest interval on which marginal revenue exceeds marginal cost is (1.8377, 8.1622). (d). The profit is increasing at 8.1622 at p(q) is maximum. (e). The maximum value of profit is 78.2455 dollars.

The total revenue: TR(q) = 30q

The total cost: Tc(q) = [tex]q^3-15 q^2+75 q+10$[/tex]

The change in cost is referred to as the change in the cost of production when there is a need for change in the volume of production.

(a).  Marginal cost MC[tex]=\frac{\partial}{\partial q}(T C)$[/tex]

[tex]$$=3q^2-30 q+75 \text {. }$$[/tex]

According to question.

[tex]$$\begin{aligned}& 3 q^2-30 q+75=15 \\& 3 q^2-30 q+60=0 \\& q^2-10 q+20=0 \\& q= \frac{10 \pm \sqrt{100-80}}{2} \\&= \frac{10 \pm 2 \sqrt{5}}{2}=5 \pm \sqrt{5}\end{aligned}[/tex]

[tex]$$$\therefore \quad q=5+\sqrt{5} \quad$ and $q=5-\sqrt{5}$[/tex]

we have to find smallest quantity.

[tex]$$\therefore \quad q=5-\sqrt{5}=2.76 \text {. }$$[/tex]

b)

[tex]$$\begin{aligned}& F C=T C(0)=10 \\& V C(q)=T C(q)-F C \\& =q^3-15 q^2+75 q . \\& \text { AVC(q) }=\frac{V C(q)}{q}=q^2-15 q+75 .\end{aligned}$$[/tex]

When AVC(q)=MC(q)

[tex]$$\begin{array}{ll}\Rightarrow & q^2-15 q+7 ;=3 q^2-30 q+75 \\\Rightarrow & 2 q^2-15 q=0 .\ \Rightarrow q(2 q-15)=0 . \\\Rightarrow & q=0, \frac{15}{2} \quad \Rightarrow \quad q=\frac{15}{2}\end{array}$$[/tex]

Therefore, the positive value of q at which average variable cost is equal to marginal cost is [tex]\frac{15}{2}[/tex].

(c).

[tex]& M R(q)=\frac{d}{d q}(T R)=30 . \\[/tex]

[tex]& M C(q)=3 q^2-30 q+75 . \\[/tex]

Let MR(a)>MC(q)

[tex]& \Rightarrow \quad 30 > 3 q^2-30 q+75 \text {. } \\[/tex]

[tex]& \Rightarrow \quad 3 q^2-3 p q+45 < 0 \\[/tex]

[tex]& \Rightarrow \quad q^2-10 q+15 < 0 \text {. } \\[/tex]

[tex]& \because \quad q=\frac{10 \pm \sqrt{100-60}}{2} \Rightarrow q=\frac{10 \pm 2 \sqrt{10}}{2} \\[/tex]

[tex]& q=(5 \pm \sqrt{10}) \\[/tex]

[tex]& \Rightarrow \quad(q-5+\sqrt{10})(q-5-\sqrt{10}) < 0 . \\[/tex]

[tex]& \Rightarrow \(q-5+\sqrt{10}) < 0 \quad \& \quad(q-5-\sqrt{10}) > 0 \text {. } \\[/tex]

[tex]& \text { or } \quad(q-5+\sqrt{10}) > 0 \quad \& \quad(q-5-\sqrt{10}) < 0 \text {. } \\[/tex]

[tex]& \therefore \quad \text { other } q < 5-\sqrt{10}=1.8377 ., q > 5+\sqrt{10}=8.1622 \text {. } \\[/tex]

[tex]& \Rightarrow \quad q < 1.8377 \& q > 0.1622 \text {. } \\[/tex]

[tex]& \text { or } q > 5-\sqrt{10} \quad \& \quad q < 5+\sqrt{10} \text {. } \\[/tex]

[tex]& \Rightarrow q > 1.8377 \quad < q < 8.1622 \text {. } \\[/tex]

The Interval is (1.8377, 8.1622).

(d).  P(q) =TR(q)-TC(q)

[tex]& =30 q-\left(q^3-15 q^2+75 q+10\right) \\& =-q^3+15 q^2-75 q-10+30 q \\& =-q^3+15 q^2-45 q-10 .[/tex]

on (1.8377,8.1622). we have to find a point such that p"(q)=0 and p"(q)<0.

[tex]& p^{\prime}(q)=-3 q^2+30 q-45 \\[/tex]

[tex]& \Rightarrow \quad-3\left(q^2-10 q+15\right)=0 \\[/tex]

[tex]& \Rightarrow \quad q^2-10 q+15=0 . \\[/tex]

[tex]& \quad q=1.8377 \text { and } \quad q=8.1622 . \\[/tex]

[tex]& \Rightarrow \quad p^{\prime \prime}(q)=-6 q+30 . \\[/tex]

[tex]& p^{\prime \prime}(1.8377)=-6(1.8377)+30 \\[/tex]

[tex]&=18.9738 \\[/tex]

[tex]& p^{\prime \prime}(8.1622)=-6(8.1622)+30 . &=-18.9732 < 0 .[/tex]

at 8.1622, p(q) is maximum.

(e).

Max profit-P(8.1622)

=78.2455 dollars

Therefore, the maximum value of profit is 78.2455 dollars.

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Answer:

Step-by-step explanation:

check the image

The values that, the function intersect the x axis at 2 different points is -4 < b < 4. So correct option is D.

A function in mathematics is a relationship between a set of inputs (also known as independent variables or arguments) and a set of outputs (also known as dependent variables or values). The output of a function is determined by the inputs, and the function assigns exactly one output value to each input value.

A function can be represented in many ways, including a formula, a table, or a graph. The formula of a function defines the relationship between the inputs and outputs, and can be used to calculate the output for a given input. A table lists input and output values, and a graph represents the function by plotting the input and output values.

Functions are a fundamental concept in mathematics and are used in many areas, including algebra, calculus, and other branches of mathematics, as well as in science, engineering, and other fields. Functions can be simple, such as linear functions, or complex, such as exponential functions or trigonometric functions.

For the function f(x) = x^2 + bx + 4 to intersect the z-axis at two different points, it must have two real roots. This means that the discriminant of the quadratic equation must be greater than 0. The discriminant of the quadratic equation is given by b^2 - 4(1)(4). Hence, b^2 - 16 > 0, or b^2 > 16, which simplifies to -4 < b < 4.

Therefore, the answer is D: -4 < b < 4.

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The correct solution for the area of this triangle is 20 inches².

The area of a triangle is a measure of the amount of two-dimensional space enclosed by its three sides. It is represented by the symbol A and is calculated by multiplying the base of the triangle by its height and dividing the result by 2.

A = (1/2)b×h

In other words, the height of the triangle is a line segment perpendicular to the base that divides the triangle into two smaller triangles of equal area. The area of a triangle is important in many real-world applications, such as in construction and architecture, where it is used to determine the amount of material needed for a project, and in geometry, where it is used to solve problems related to triangles.

No, Kevin's solution is not correct. The formula for the area of a triangle is

A = (b×h)/2, not A = b×h.

To find the area of this triangle, you would use the formula:

A = (8 × 5)/2 = 20 inches²

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The number of guitars sold each year in Montana is given as follows:

7075 guitars.

The number of guitars sold per year in Montana is obtained applying the proportions in the context of this problem.

Ohio's average is seven times Montana's average, hence Montana's amount is obtained dividing Ohio's amount by 7.

Ohio's amount is given as follows:

49525 guitars.

Hence Montana's amount is obtained as follows:

49525/7 = 7075 guitars.

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The equation of the circle that has a diameter with endpoints located at (5, –3) and (11, 5) is;   (x – 8)² + (y – 1)² = 25

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

The midpoint of the diameter of a circle is it's center.

As such; the coordinates of its center are;

x = (5+11)/2

x = 8

y = (-3 + 5)/2

y = 1

The coordinates of the center are then; (8, 1)

The radius of a circle is half the length of the diameter;

Radius, r = d/2

where; d = √(11-5)² + (5-(-3))²

d = √36 + 64

d = √100

d = 10

Therefore, radius, r = 10/2 = 5.

Therefore, the equation of the circle usually takes the form;

(x -f)² + (x -g)² = r²

In this scenario; the equation is;

(x – 8)² + (y – 1)² = 25.

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Answer:

The equation of a circle can be represented in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

A diameter of a circle is a straight line passing through the center of the circle and has endpoints on the circle.

Given that the equation of the diameter of a circle is x+y-14=0 and 2x-y-4=0, we can find the center of the circle by solving for the intersection of these two lines.

We can find the intersection point of these lines by solving the system of equations using the substitution method:

x+y-14=0 and 2x-y-4=0

x = 14/3, y = 10/3

So the center of the circle is (14/3, 10/3)

Since we know that the point (3,4) lies on the circle, we can use the distance formula to find the radius of the circle.

r = sqrt((x-h)^2 + (y-k)^2)

r = sqrt((3-(14/3))^2 + (4-(10/3))^2) = sqrt(5)

Therefore, the equation of the circle is (x-14/3)^2 + (y-10/3)^2 = 5^2

or (x-14/3)^2 + (y-10/3)^2 = 25

So, the equation of the circle passing through point (3,4) and having equation of its diameter x+y-14=0 and 2x-y-4=0 is (x-14/3)^2 + (y-10/3)^2 = 25