If the wholesale price of an item is $250 and the markup is 20%, find the retail price of the item.

9514 1404 393

Answer:

  6. step 2; terms are improperly combined; it should be -61n-8=-8

  7. no; point (2, 5) is not part of the solution in the left graph

Step-by-step explanation:

6. Step 2 should be ...

  -61n -8 = -8 . . . . . because -5n-56n = -61n, not -51n

__

7. The boundary lines of both graphs go through the point (2, 5). In the left graph, the line is dashed, indicating that points on the line are not part of the solution set. The point (2, 5) on the dashed line is not a solution to that inequality.

The solid boundary line indicates that the points on the line are part of the solution set. The point (2, 5) on the solid line is a solution to that inequality.

The point (2, 5) is not a solution to both inequalities.

Answer:

30 sq inches

Step-by-step explanation:

1.5 x 20 is 30

Therefore, the vector ⟨1,2⟩ of length 2 in the direction opposite to 4−13 is -4⟨1,2⟩/5.

The vector ⟨1,2⟩ of length 2 in the direction opposite to 4−13 is -4⟨1,2⟩/5.

Firstly, the magnitude of the vector, |v| is given as 2, i.e.|v| = 2

The vector whose direction is to be found is 4−13, i.e. ⟨4,-13⟩.

Let us represent the direction of vector 4−13 as a unit vector.

Step 1: Calculate |4−13|, which is the magnitude of the vector:|4−13|=√{(4)^2 + (-13)^2}=√{16 + 169}=√185

Step 2: Find the unit vector of 4−13 by dividing it with its magnitude: i.e., u⟨4,-13⟩ = 1/√185⟨4,-13⟩

Step 3: Scale the unit vector by multiplying it with the given magnitude 2, and multiplying it with -1 to get the opposite direction of the vector 4−13.

That is, v= -2 u⟨4,-13⟩= -2/√185⟨4,-13⟩

Multiplying both the numerator and the denominator by 2 gives the expression as -4⟨4, -13⟩/5 = ⟨-16/5, 52/5⟩.

Therefore, the vector ⟨1,2⟩ of length 2 in the direction opposite to 4−13 is -4⟨1,2⟩/5.

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An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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Answer:

\(f(x) = - 3x + 10 \\ f( - 5) = - 3( - 5) + 10 \\ = 15 + 10 = 25\)

\(g(x) = x ^{2} - 7x \\ g(2) = {2}^{2} - 7 \times 2 \\ = 4 - 14 \\ = - 10\)

Solving the given functions for the asked value, we get

f(-5) = 25, g(2) = -10

A function is a rule defining the relationship between two variables, one is dependent and the other independent.

To solve the given functions for asked values, we put in the value asked for in place of the variable determining the function.

Two given functions are:

f(x) = -3x + 10

g(x) = x² - 7x.

We are asked for values of f(-5) and g(2).

To calculate the value of f(-5), we substitute x with (-5) in the function f(x), that is,

f(-5) = -3(-5) + 10 = 15 + 10 = 25.

To calculate the value of g(2), we substitute x with (2) in the function g(x), that is,

g(2) = (2)² - 7(2) = 4 - 14 = -10.

∴ f(-5) = 25, g(2) = -10

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Answer:

3  ( x  +  29 )

Step-by-step explanation:

The best I can do is factor them, hope it helps!

The three angles of the triangle are approximately 61°, 33°, and 69°.

To find the three angles of the triangle with vertices P(2, 0), Q(0, 3), and R(3, 4), we can use the distance formula and the Law of Cosines.

First, let's calculate the lengths of the sides of the triangle:

Side PQ:
d(PQ) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((0 - 2)^2 + (3 - 0)^2)
= √((-2)^2 + 3^2)
= √(4 + 9)
= √13

Side QR:
d(QR) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((3 - 0)^2 + (4 - 3)^2)
= √(3^2 + 1^2)
= √(9 + 1)
= √10

Side RP:
d(RP) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((2 - 3)^2 + (0 - 4)^2)
= √((-1)^2 + (-4)^2)
= √(1 + 16)
= √17

Next, let's use the Law of Cosines to find each angle:

Angle P:
cos(P) = (d(QR)^2 + d(RP)^2 - d(PQ)^2) / (2 * d(QR) * d(RP))
= (10 + 17 - 13) / (2 * √10 * √17)
= 14 / (2 * √10 * √17)
≈ 0.486

Angle Q:
cos(Q) = (d(PQ)^2 + d(RP)^2 - d(QR)^2) / (2 * d(PQ) * d(RP))
= (13 + 17 - 10) / (2 * √13 * √17)
= 20 / (2 * √13 * √17)
≈ 0.836

Angle R:
cos(R) = (d(PQ)^2 + d(QR)^2 - d(RP)^2) / (2 * d(PQ) * d(QR))
= (13 + 10 - 17) / (2 * √13 * √10)
= 6 / (2 * √13 * √10)
≈ 0.357

Finally, we can find the angles by taking the inverse cosine (arccos) of each value:

Angle P ≈ arccos(0.486) ≈ 61°
Angle Q ≈ arccos(0.836) ≈ 33°
Angle R ≈ arccos(0.357) ≈ 69°

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Explanation:

If we start off with $100 and decrease by 15%, then we are decreasing by $15 since 15% of 100 = 0.15*100 = 15

We start with $100 and drop to 100-15 = 85. Dividing this over the original 100 gets us 85/100 = 0.85

Put another way, 100% - 15% = 1 - 0.15 = 0.85

The decimal multiplier for "decrease by 15%" is 0.85; this sort of thing is useful if you wish to apply multiple discounts to a product.

Side note: the 0.85 can be thought of as 85%, so the product's new value is 85% of its original value

A tree of n vertices has (n-1) edges.

In a tree, each vertex is connected to exactly one other vertex through an edge, except for the root of the tree which has no incoming edges. Since there are n vertices in the tree, there will be (n-1) edges connecting them.

The reason behind this is that a tree is defined as a connected acyclic graph. In order for a graph to be connected, each vertex must be reachable from every other vertex through a path. However, in order for the graph to be acyclic, it should not contain any cycles or loops. If we assume that there are n vertices in the tree, the maximum number of edges that can be present without creating a cycle is (n-1).

Therefore, a tree of n vertices will have (n-1) edges. This property holds true for all trees, regardless of their specific structure or arrangement of vertices.

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Answer:

25.20

Step-by-step explanation:

Answer:

25 6/29

Step-by-step explanation:

use long division, and cancel common factors

Answer:

8.778 or 8.8

Step-by-step explanation:

20% of 43.89 is 8.778

math: 43.89*(20/100) = 8.778

Answer:

\( {g}^{ - 1} (2) = 0\)

\( {h}^{ - 1} (x) = 11x + 13\)

\(h( {h}^{ - 1} (x)) = h(11x + 13) = \frac{11x + 13 - 13}{11} = x\)

\(h( {h}^{ - 1} ( - 1)) = - 1\)

Answer: move the point or decimal

Step-by-step explanation: you just remove the decimal that means the point the devide and put it back

Answer:

The answer isn't in the options anyway I'll write it. the answer is 46.

Step-by-step explanation:

According to BODMAS rule - addition should be done first so

4+36= 40 and -3 +7 = 4 so 40+4 ,= 44

then we should do subtracting so, 10-8 = 2

to conclude we should bring the equation to an end so,

44+2 = 46

HOPE THIS HELPS YOU

The process to subtract the mixed fractions with the whole numbers is explained below.

The Mixed Fractions are defined as type of fraction that consists of a whole number and a proper fraction.

Step(i) : We multiply whole number by denominator of fraction and add numerator.

For example, if mixed fraction 2(1/3), we multiply 2 by 3 and add 1 to get 7. So, 2(1/3) is equivalent to improper fraction 7/3.

Step(ii) : Find a common denominator for fractions. We find least common multiple (LCM) of denominators.

For example, if you want to subtract 2(1/3) from 5, denominators are 3 and 1, and LCM is 3.

Step(iii) : Convert whole number to a fraction with same denominator as common denominator.

For example, if LCM is 3 and we want to subtract 2(1/3) from 5, we will convert 5 to fraction 15/3.

Step(iv) : Rewrite each fraction with common denominator.

For example, if we want to subtract 2(1/3) from 5, we rewrite 2(1/3) as 7/3 and 15/3 as 5.

Step(v) : Subtract the fractions.

For example, to subtract 7/3 from 5, we subtract numerators and keep the denominator: 15/3 - 7/3 = 8/3.

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The best explanation to give for the button on the backpack that reads FBLA-PBL is FBLA-PBL prepares students for careers.

FBLA-PBL which stands for, Future Business Leaders of America-Phi Beta Lambda is a career organization in the United States that was founded to help students prepare for their future careers in a variety of fields.

These fields range from being great employees to running one's own business. They help out by organizing talks and seminars for middle school all the way to college.

In conclusion, the purpose of the Future Business Leaders of America-Phi Beta Lambda is to prepare students for careers.

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Answer:

Karen jogged 2.32 kilometers more than Morgan.

Step-by-step explanation:

Calculate the difference:

53.52 - 51.2 = 2.32

Answer:

2.32 km

Step-by-step explanation:

Take the amount that Karen jogged and subtract the amount that Morgan jogged

53.52 - 51.2

2.32

Answer:

864 ft3

Step-by-step explanation:

length = 12 ft

width = 8 ft

depth = 9 ft

Volume = ? = length * width * depth

Answer:

($14.37 was the original price)

Step-by-step explanation:

Answer:

alternate exterior angles

Step-by-step explanation:

so are 2 & 8

Practical difficulties such as undercoverage and nonresponse in a sample survey cause additional errors. These errors can affect the accuracy and representativeness of the survey results.

Undercoverage refers to when certain groups or individuals in the target population are not adequately represented in the sample. This can lead to biased estimates and inaccurate conclusions. Nonresponse occurs when selected participants choose not to respond to the survey, which can introduce bias and decrease the precision of the results.

To minimize these errors, researchers can use appropriate sampling techniques, employ effective survey design, and implement strategies to increase response rates. It is important to address these practical difficulties in order to obtain reliable and valid data in a sample survey.

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Given:

The different types of triangles.

Required:

Classify each triangle.

Explanation:

First, we need to gather some information about triangles

Now, lets classify triangles

Answer:

answered the question.

Answer:

x=6

Step-by-step explanation:

Add five to both sides:2x-5+5=7+5

Simplify: 2x-5+5=7+5

               2x=7+5

                2x=12

Divide both side by the same factor: 2x/2=12/2

Simplify:x=12/2

divide 12 by 2 = 6

hope I helped you!!!

The difference is statistically significant at a level of 0.05 because the p-value is less than 0.05. the p-value is less than 0.05, so we reject the null hypothesis and conclude that the proportion of Americans who prefer spicy flavoring has increased significantly since 2013 at a significance level of 0.05.

The null hypothesis for this test is that the proportion of Americans who prefer spicy flavoring is equal to 0.54, while the alternative hypothesis is that the proportion is greater than 0.54.
The z-statistic for this test can be calculated using the formula:
z = (p - P) / SE

Where p is the sample proportion (0.557), P is the hypothesized population proportion (0.54), and SE is the standard error of the proportion, which can be calculated as:
SE = sqrt [ P(1-P) / n ]
where n is the sample size (2430).
SE = sqrt [ 0.54(1-0.54) / 2430 ] = 0.010
z = (0.557 - 0.54) / 0.010 = 1.701


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A minimum sample size of 1069 is required to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle such that the margin of error is no more than 0.03 for a 95 percent confidence interval.

In order to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle, a researcher in campaign finance law wants to determine the minimum sample size such that the margin of error is no more than 0.03 for a 95 percent confidence interval.

Assuming that the researcher wants to establish a 95% confidence interval, the level of significance (α) is 1 - 0.95 = 0.05. Furthermore, we can assume that there is no prior knowledge of the population proportion, which is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. The standard deviation of a proportion is calculated using the following formula:

\(σ_p=√(p(1−p)/n)\)

Here, n is the sample size and p is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. Because there is no prior knowledge of p, it is assumed that the sample proportion, p-hat, is equal to 0.5.

Using these values, we can calculate the minimum sample size required for a margin of error of 0.03 for a 95 percent confidence interval.

α/2=0.025 can be determined by dividing the level of significance (α) by two. This will allow us to calculate the appropriate critical value. To calculate the critical value, we can look up the value of 0.025 in a standard normal distribution table.

Z_α/2=1.96 is the corresponding z-value for a 95% confidence interval.With the critical value, we can now calculate the minimum sample size using the formula below:

\(n = (Z^2) (p) (1 - p) / (E^2)\)

where, Z = critical valueα = level of significance (0.05)

E = margin of error (0.03)

p-hat = 0.5

The minimum sample size for a 95% confidence interval with a margin of error of 0.03 and no prior knowledge of the population proportion is as follows:

\(n = (1.96)^2 (0.5) (0.5) / (0.03)^2n = 1068.44444 ≈ 1069\)

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The length of arc PS is;

⇒ PS = 31.5 ft

Now, We have to given that;

Point T is the center of the circle and line TR is the radius of the circle.

Additionally, the angle subtended by,

⇒ arc PS = 180 - m ∠PS

⇒ arc PS = 180 - 16 = 164⁰.

This follows from the fact that line PR is a diameter.

On this note, the length of arc PS is;

arc PS = (164/360) × 2 × 3.14 × 11.

arc PS = 31.5ft.

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The expression that shows how many cupcakes the baker decorated is:

c/2.

A mathematical expression is a combination of numbers, symbols, and/or variables that represents a mathematical relationship or operation. It can be written using various mathematical symbols and notation to convey a specific meaning or instruction.

Mathematical expressions can also include functions, exponents, logarithms, and other mathematical operations that represent specific relationships or computations. They are commonly used in algebra, calculus, geometry, and other branches of mathematics to represent and solve mathematical problems.

The number of cupcakes the baker decorated can be found by dividing the total number of candy eyes by the number of candy eyes needed per cupcake.

If the baker used c candy eyes in total and each cupcake needed 2 candy eyes, then the expression that shows how many cupcakes the baker decorated is:

c/2

Dividing c by 2 gives the number of cupcakes the baker decorated, since each cupcake required 2 candy eyes.

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The number of cupcakes is the total number of candy eyes divided by 2.

What is equation?

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.

The number of cupcakes decorated is equal to the total number of candy eyes divided by the number of candy eyes used per cupcake. So, if c is the number of candy eyes, then the expression that shows how many cupcakes the baker decorated is:

c/2

This is because each cupcake needs 2 candy eyes.

Therefore, the number of cupcakes is the total number of candy eyes divided by 2.

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Answer:

∡3 = 142°

Step-by-step explanation:

28° + 10° + ∡3 = 180° (Sum of angles in a triangle)

38° + ∡3 = 180°

∡3 = 180° - 38°

∡3 = 142°

Alternate method:

38° + ∡3 = 180° (Sum of angles on a straight line)

∡3 = 180° - 38°

∡3 = 142°

Answer:

38 degree + 180 degree = [ sum of angle on a straight line]

3= 180 degree - 38 degree

3= 142 degree.

·

The area of the region that lies inside both curves is 27/10 square units.

To find the area of the region that lies inside both curves, we need to set the equations equal to each other and find the points of intersection:

3 cos(theta) = sin(theta)

Dividing both sides by cos(theta) (since cos(theta) cannot be zero), we get:

3 = tan(theta)

Taking the arctangent of both sides, we get:

theta = arctan(3)

So the curves intersect at theta = arctan(3).

To find the area of the region, we integrate the equation for the smaller curve (r = sin(theta)) squared from 0 to arctan(3), and subtract the integral of the equation for the larger curve (r = 3cos(theta)) squared from 0 to arctan(3):

\(Area = ∫[0, arctan(3)] (sin(theta))^2 d(theta) - ∫[0, arctan(3)] (3cos(theta))^2 d(theta)\)

Simplifying and evaluating the integrals, we get:

Area = (9/4)sin(2arctan(3)) - 27/2

Using the trigonometric identity \(sin(2arctan(x)) = (2x)/(1+x^2),\) we get:

Area = (27/5) - 27/2

Area = 27/10

Therefore, the area of the region that lies inside both curves is 27/10 square units.

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