Ted earns a salary of $900 a month and a commission of 10% on all sales over $5,000. This month his sales were $36,000. What were his total earnings for the month?

Answer:

1/6

Step-by-step explanation:

If we're assuming that this is a six-sided die, then we can find that the results can be 1,2,3,4,5,6. Only 1 of those 6 numbers are 5, so the probability of the cube landing on 5 would be 1/6.

Answer:

2.24

Step-by-step explanation:

5 is not a perfect square and therefore its square root is not an integer.

it is a decimal which can partly be presented as 2.236068. the digits after the decimal point occupy the following decimal spaces

2-tenths

3-hundredths

6-thousandths.

If the digit in the thousandths position is 5 or greater then we add one to the digit in the hundredths position to get the nearest hundredth while if it is less than 5 we truncate at the hundredth position and retain the digit at this position as the nearest hundredth.

in this question, the digit in the thousandth position is 6 thus we add 1 to the digit in the hundredth position that is,3 to get 4

therefore the square root of 5 to the nearest hundredth is 2.24

Answer:

1,760

Step-by-step explanation:

A mile is 5280 feet

3 feet in a yard

so     5280/3=1760

your answer is A) 1,760 yards

Answer:  y = x

Step-by-step explanation:

First, find the point where 5x - 2y + 3 and 4x - 3y + 1 intersect using the Elimination Method.

5x - 2y + 3 = 0  →  3(5x - 2y + 3 = 0)  →  15x - 6y + 9 = 0

4x - 3y + 1 = 0   → -2(4x - 3y + 1 = 0)  →   -8x + 6y - 2 = 0

                                                                 7x         + 7 = 0

                                                                 7x               = -7

                                                                   x               = -1

5x - 2y + 3 = 0

5(-1) - 2y + 3 = 0

-5 - 2y + 3 = 0

    -2y  - 2 = 0

    -2y        = 2

        y        = -1

(-1, -1)

Next, find the point where x = y and x = 3y + 4 intersect using the Substitution Method.

x = y

x = 3y + 4    →    y = 3y + 4

                      -2y = 4

                         y = -2

x = y

x = -2

(-2, -2)

Now, find the line that passes through (-1, -1) and (-2, -2) using the Point-Slope formula.  (x₁, y₁) = (-1, -1)  and m = 1

y - y₁ = m(x - x₁)

y + 1 = 1(x + 1)

    y = x

In an acute triangle ABC Inscribed angles in a circle with another triangle MNP formed by the intersections of tangents to the circle at points A, B, and C, the angles of triangle MNP are the sum of the opposite angles of triangle ABC. Therefore, ∠M = α + γ, ∠N = β + α, and ∠P = γ + β.

The question is about an acute triangle ABC inscribed in a circle and another triangle MNP formed by the intersections of tangents to the circle at points A, B, and C.

From the properties of circle and geometry, in such a scenario, the angles of triangle MNP correspond to sum of the opposite angles of triangle ABC.

The measures of angles in △MNP are as follows:

∠M = α + γ

∠N = β + α

∠P = γ + β

This relation comes from the fact that the exterior angle of a triangle is equal to the sum of the opposite interior angles.

Learn more about Inscribed angles here:

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Answer:

639

Step-by-step explanation:

put the 71 on the top then the 9 on the bottom then 9x1=9 then 9x7=63

639!

ANSWER

[tex](0,-2), (1,0)[/tex]

EXPLANATION

The first equation is

[tex]y = {x}^{2} + x - 2[/tex]

The second equation is

[tex]y = 2x - 2[/tex]

We equate both equations to get,

[tex] {x}^{2} + x - 2 = 2x - 2[/tex]

[tex] {x}^{2} + x - 2x - 2 + 2 = 0[/tex]

Simplify

[tex] {x}^{2} - x = 0[/tex]

Factor

[tex]x(x - 1) = 0[/tex]

Either

[tex]x = 0[/tex]

Or

[tex]x - 1 = 0[/tex]

[tex]x = 1[/tex]

Put x=0 or x=1 into the second equation to get,

[tex]y = 2(0) - 2 = - 2[/tex]

Or

[tex]y = 2(1) - 2 = 0[/tex]

Therefore the solutions are;

[tex](0,-2), (1,0)[/tex]

Answer:

Step-by-step explanation:

I got it right on the test... Have a great day :)

Answer:

[tex]V=12\ ft^{3}[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem

[tex]P*V=k[/tex]

step 1

Find the value of K

For [tex]P=24\ psi ,V=15\ ft^{3}[/tex]

substitute

[tex]24*15=k[/tex]

[tex]k=360[/tex]

the equation is [tex]P*V=360[/tex]

step 2

For [tex]P=30\ psi ,V=\ ft^{3}[/tex]

substitute in the equation

[tex](30)*V=360[/tex]

[tex]V=360/30=12\ ft^{3}[/tex]

Using Boyle's law, which states volume and pressure of a gas at constant temperature are inversely proportional, we find that at a pressure of 30 pounds per square inch, the volume will be 12 cubic feet.

The concept behind your question involves Boyle's law, which states the volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured. This means as pressure increases, volume decreases and vice versa while maintaining the same temperature.

To solve this, we can use the mathematical expression for Boyle's law: P₁V₁ = P₂V₂.

Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Applying these values: 24 pounds per square inch * 15 cubic feet = 30 pounds per square inch * V₂. By rearranging the equation and solving for V₂, we get: V₂ = (24 pounds per square inch * 15 cubic feet) / 30 pounds per square inch = 12 cubic feet.

Therefore, when the pressure is 30 pounds per square inch, the volume will be 12 cubic feet.

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Answer:

Number 7 is 40

Step-by-step explanation:

set up a proportion 5/1 = x/8 cross multiply a divide and you get 40

Answer:

Last option

[tex]d>3[/tex] or [tex]d<-3[/tex]

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function [tex]f(x) = |x|[/tex]  x> 0 for all real numbers.

Then the inequation:

[tex]|d|> 3[/tex] has two cases

[tex](d)[/tex]    if [tex]d>0[/tex]  (i)

[tex]-(d)[/tex]    if [tex]d< 0[/tex] (ii)

We solve the case (i)

[tex]d> 3[/tex]

We solve the case (ii)

[tex]-d>3\\d < -3[/tex]

Then the solution is:

[tex]d>3[/tex] or [tex]d<-3[/tex]

Answer:

Last choice is the correct graph.

Step-by-step explanation:

We have been given inequality [tex]|d|>3[/tex]. Now we need to find out which of the given number lines shows the correct solution set for [tex]|d|>3[/tex].

We know that [tex]|x|>a[/tex] can be broken into :

[tex]x>+a[/tex] or [tex]x<-a[/tex]

Same way we can break [tex]|d|>3[/tex] into two parts as:

[tex]d>+3[/tex] or [tex]d<-3[/tex]

Since it has only < symbol but not equal so we make an open circle at both +3 and -3.

Hence last choice is the correct graph.

True

A linear recurrence relation involving a sequence of numbers [tex]a_n[/tex] is one of the form

[tex]\displaystyle\sum_{k=0}^nc_{n-k}a_{n-k}=c_na_n+c_{n-1}a_{n-1}+\cdots+c_2a_2+c_1a_1=c[/tex]

where [tex]c_1,c_2,\ldots,c_n[/tex] and [tex]c[/tex] are any fixed numbers.

The given recurrence can be rearranged as

[tex]a_n=a_{n-1}+2\implies 1\cdot a_n+(-1)\cdot a_{n-1}=2[/tex]

A nonlinear recurrence would have a more "exotic" form that cannot be written in the form above. Some example:

[tex]a_n+\dfrac1{a_{n-1}}=1[/tex]

[tex]a_na_{n-1}=\pi[/tex]

[tex]{a_n}^2+\sqrt{a_{n-1}}-\left(\dfrac{a_{n-2}}{\sqrt{a_n}}\right)^{a_{n-3}}=0[/tex]

The query pertains to 'linear recurrence relations' in Mathematics, particularly concerning high school algebra and series expansions, such as the binomial theorem, and plotting data on a logarithmic scale.

The term linear recurrence relation refers to a sequence of numbers where each term is a linear combination of previous terms. The relationship is defined by two aspects: the number of terms that go into the combination (order of the relation), and the coefficients of each of those terms. A classic example of a linear recurrence relation is the Fibonacci sequence, where each term is the sum of the two preceding terms.

When addressing series expansions like the binomial theorem, it is an expression that allows us to expand polynomials raised to a power in a series format. The theorem is a key concept in algebra and is particularly useful for calculating powers of binomials and deriving coefficients of individual terms within expanded polynomials.

To plot data like the recurrence interval on a logarithmic scale, it is essential to understand that each increment on the axis represents a multiplication by a certain factor, rather than a linear addition. This type of representation is particularly useful when dealing with data that varies by orders of magnitude.

Answer:

A = 75°

B = 90°

C = 15°

Step-by-step explanation:

The diagram tells us that C = 15°.

The diagram places a square in the angle of B, showing you the angle is a 90° right angle.

You can solve for A because all angles of a triangle must equal 180°. 180° - 90° (B) = 90°. 90° - 15° (C) = 75°, the measure of A.

Answer:

g(f(0)) = 6

Step-by-step explanation:

Evaluate f(0 ) and substitute this value into g(x)

f(0) = 0² = 0 and

g(0) = 0 + 6 = 6

⇒ g(f(0)) = 6

The value of g(f(0)) is 6.

If two functions f(x), g(x) are present , then (f o g) of x is also known as a composite function and it is mathematically denoted as f(g(x)) or (f ∘ g)(x). It means that x = g(x) should be substituted in f(x). It is an operation that combines two functions to form another new function.

Given , f(x) = [tex]x^{2}[/tex]  and  g(x) = x + 6

We have to find g(f(0)).

To get the value of this composite function g(f(x)), we first have to find the value of f(x) at the given value x = 0 and then substitute the value of f(x) into g(x).

⇒ f(0) = 0.

∴ g(f(0)) = g(0) = 0 + 6 = 6.

Therefore we have the value of g(f(0)) as 6.

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To find the probability of not rolling factors of 6 on both six-sided dice, multiply the individual probabilities of rolling a 4 or 5 on each die. The probability is 1/9.

The factors of 6 are 1, 2, 3, and 6. Therefore, the outcomes that are not factors of 6 are 4 and 5.

Since each die has six faces, the total number of possible outcomes when rolling two dice is 6 x 6 = 36.

Of these 36 possible outcomes, we need to count how many do not involve factors of 6. For each die rolled independently, we have 2 outcomes that are not factors of 6: {4, 5}.

So, we need to calculate the product of these individual probabilities to find the probability of both dice showing a non-factor of 6.

For a single die, the probability of rolling a non-factor of 6 (either a 4 or a 5) is 2/6 or 1/3, since we have 2 favorable outcomes out of 6 possible ones.

To find the probability for both dice, we multiply these individual probabilities:

Probability of not rolling a factor of 6 on both dice = (1/3) x (1/3) = 1/9.

This is the product rule in probability, which tells us that the probability of two independent events both happening is the product of their individual probabilities.

Therefore, the probability of not rolling a factor of 6 on both dice is 1/9.

Answer:   There are two points of intersection (2, 4) and (-4, -2)

Step-by-step explanation:

x - y + 2 = 0     →       x = y - 2

Use Substitution Method:

x² + y² = 20

(y - 2)² + y² = 20              replaced x with (y - 2)

y² - 4y + 4 + y² = 20        expanded (y - 2)²

2y² - 4y + 4 = 20             added like terms

2y² - 4y - 16 = 0               subtracted 20 from both sides

y² - 2y - 8 = 0                  divided both sides by 2

(y - 4)(y + 2) = 0               factored

y - 4 = 0    and      y + 2 = 0       applied Zero Product Property

y = 4        and       y = -2

Input the y-values into x = y - 2 to solve for x.

y = 4;   x = 4 - 2                      y = -2;    x = -2 - 2

           x = 2                                         x = -4

      (2, 4)                                         (-4, -2)

Answer:

N = 3

Step-by-step explanation:

I don't know what the whole thing above is, but just disregard that.

All it is here is cross multiplication.

So 28N = 21 * 4

Multiply...

28N = 84

And divide each side by 28

N = 3

Answer: The answer is B.

Step-by-step explanation: "Poly" means "many", and "nomial", in this case, meaning "term".

B is the only one with 3 or more different terms.

(negative number, whole number, two unknowns, and a square root)

The expression which is a polynomial is:

              [tex]-6x^3+x^2-\sqrt{5}[/tex]

A polynomial expression is a expression of the form:

          [tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+........+a_1x+a_0[/tex]

where n belong to non-negative integers and [tex]a_i's[/tex] are real numbers.

1)

[tex]4x^2-3x+\dfrac{2}{x}[/tex]

This is not a polynomial because the third term:

[tex]\dfrac{2}{x}=2x^{-1}[/tex] has a negative poswer of x which violates the definition of polynomial.

2)

[tex]-6x^3+x^2-\sqrt{5}[/tex]

In this each of the term satisfy the definition of polynomial and hence the expression is a polynomial expression.

3)

[tex]8x^2+\sqrt{x}[/tex]

Here the second term is not a integer power and hence violate the definition of polynomial.

4)

[tex]-2x^4+\dfrac{3}{2x}[/tex]

which could also be written as:

[tex]-2x^4+\dfrac{3}{2}x^{-1}[/tex]

Here the second term contain a negative power of x and hence is not a polynomial.

Answer:

B. 5

Step-by-step explanation:

Each edge of the base has one triangular face attached to it (which then come together). Since it is a square base, this gives you 4 faces, and the base itself makes 5 faces.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Probability is measured as

[tex]\frac{favourableoutcome}{count}[/tex]

The favourable outcome is obtaining roll > 4, that is a 5 or 6

P( > 4 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

The area of the L-shaped figure formed is 225 square inches.

To find the area of the L-shaped figure formed after cutting corners, start by calculating the area of the square from which the corners were removed.

The larger square has sides of length 15 inches, so its area is 15 x 15 = 225

When you cut corners of 9 inches by 9 inches from each corner of the larger square, you effectively create a smaller square. Since each side of the smaller square is 9 inches shorter than the larger square, its side length is -

15 - 2 x 9

= - 3

However, a negative side length is not possible, so we adjust it to zero. This implies that there's no square left after cutting off such large corners.

The area of the L-shaped figure is the difference between the area of the larger square and the area of the smaller square:

Area of L-shaped figure=Area of larger square−Area of smaller square

= 225 - 0

= 225

Thus, the area of the L-shaped figure formed is 225 square inches.

Final answer:

Ms. Gordon will need 1 1/3 cups of melted butter, 16 cups of marshmallows, and 8 2/3 cups of cereal.

Explanation:

To find how much of each ingredient Ms. Gordon needs, we need to use the information provided in the recipe and the fact that she is only using 2/3 of the recipe.

For each ingredient, multiply the original amount by 2/3.

So, Ms. Gordon will need:

Answer:

your answer is 8 cups. to find the answer first make the fraction in to a improper fraction. that will give you 8/3 cups. then multiply by 3. that will give you 24/3. then simplify it. you will get 8

Step-by-step explanation:

Answer:

[tex]\large\boxed{C.\ \dfrac{7}{2}}[/tex]

[tex]\large\boxed{B.\ \$3,600}[/tex]

Step-by-step explanation:

[tex]orange\ area-35\%\\\\light\ blue\ area-10\%\\\\the\ ratio:\ \dfrac{35}{10}=\dfrac{35:5}{10:5}=\dfrac{7}{2}[/tex]

[tex]Food-18\%\ of\ \$20,000.\\\\p\%=\dfrac{p}{100}\to18\%=\dfrac{18}{100}=0.18\\\\18\%\ of\ \$20,000\to0.18\cdot\$20,000=\$3,600[/tex]

The volume of a hemisphere with a radius of 5 inches is calculated by first determining the volume of a full sphere using the formula V = (4/3)πr³, and then dividing that by 2. The final volume of the hemisphere is 261.7994 cubic inches.

Volume of a Hemisphere

The question involves finding the volume of a hemisphere, which is half of a sphere, with a given radius of 5 inches. First, we would calculate the volume of a full sphere using the formula V = (4/3)πr³, and then divide that by 2 to get the hemisphere volume. Therefore, for a sphere with a radius of 5 inches:

Volume of the sphere, V = (4/3)π × 5³.

Volume of the hemisphere = V/2.

After performing the calculations:

Volume of the sphere, V = (4/3)π × 125 = 523.5988 cubic inches.

Volume of the hemisphere = 261.7994 cubic inches.

Answer:

b=4

Step-by-step explanation:

-14+2b= -2b+2​

Add 2b to each side

-14+2b+2b= -2b+2b+2

-14+4b =2

Add 14 to each side

-14+4b+14= 14+2​​

4b = 16

Divide each side by 4

4b/4 = 16/4

b =4

Answer:

8

Step-by-step explanation:

The answer is 8 but maybe it is 21

Answer:

The profit function would be p(x) = 7x - 20

Step-by-step explanation:

In order to find this, start by listing just as asked.

p(x) = r(x) - c(x)

Now input the functions where indicated

p(x) = 12x - (5x + 20)

p(x) = 12x - 5x - 20

p(x) = 7x - 20

Answer:

The value of [tex]p(x)=-5x-8[/tex]

Step-by-step explanation:

Given : The revenue from selling x shirts is [tex]r(x)=12[/tex]. The cost of buying x shirts is [tex]c(x)=5x+20[/tex]. The profit from selling x shirts is [tex]p(x)=r(x) - c(x)[/tex].

To find : What is p(x)?

Solution :

The revenue from selling x shirts is [tex]r(x)=12[/tex].

The cost of buying x shirts is [tex]c(x)=5x+20[/tex].

The profit from selling x shirts is [tex]p(x)=r(x) -c(x)[/tex]

Substitute the values in the formula,

[tex]p(x)=12 -(5x+20)[/tex]

[tex]p(x)=12 -5x-20[/tex]

[tex]p(x)=-5x-8[/tex]

Therefore, The value of [tex]p(x)=-5x-8[/tex]

Step-by-step explanation:

To find the median of a distribution, we first need to arrange the data in ascending order. Then, if the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.

Given the distribution: 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48

Arranging the data in ascending order: 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48

There are 15 data points, which is an odd number. The middle value is the 8th value, which is 35.

Therefore, the median of the given distribution is:

OE. 35

For the next one, also put the answers because they will not always give you the correct answer since they do not know what it will be :/

The median of the given distribution is the ninth number in the ordered set, which is 37.

To find the median of the given distribution, you will first need to order the data from smallest to largest, which has been done. The data set consists of 17 values, so the median will be the value in the middle position, which is the 9th value when the data is ordered. Since the data set is already in ascending order, you count nine values from the start, and the 9th value is the median.

The sequence of numbers is: 24, 26, 26, 28, 29, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48, 55, 56.

The median of the distribution is 37, which is the value in the middle of the ordered set.

Answer:

a=3

Step-by-step explanation:

This should be very simple, just substitute xy and y for 5 and 7 respectively, so 5a-2*7=1, or 5a-14=1, or 5a=15, if we divide both sides by 5, we get a=3

Answer:

A=3 5a-14=1

Step-by-step explanation:

Add 14 to both sides then divide 5 and 15 to get 3

Answer:

C. 45 degrees.

Step-by-step explanation:

The degree of the entire circle is 360 degrees, and the circle is divided into 8 equal sections, therefore x = 360/8 = 45 degrees.

The central angle of a regular octagon is computed by dividing the total degrees in the circle (360 degrees) by the number of sides in the octagon (8). Hence, the value of 'x' is 45 degrees.

The question is asking for the measure of 'x', which represents the angle in the center of the octagonal umbrella. To solve this, we need to remember that the total degrees in a circle (or in this case, an octagon) is 360 degrees. As a regular octagon consists of 8 equal angles, we simply divide 360 by 8 to find the measure of each angle. Therefore, 'x' equals to 45 degrees. This corresponds to option C.

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