Solve the following pair of equations for the vectors u and v. Assume i = (1,0) and j = (0;1).

Answer:

25

Step-by-step explanation:

$50

Cost=$6

Selling price=$8

Profit=$8-$6=$2

50/2=25

Answer: The cheapest option is Website B.

Step-by-step explanation:

The cost of 6 rechargeable batteries and a charger from each website is:

   Website A: 6 batteries * $52/battery = $312

   Website B: 6 batteries * $2.30/battery + $35/charger = $16.80 + $35 = $51.80

   Website C: 6 batteries * $49.60/battery = $297.60

   Website D: 6 batteries * $3.5 x + $28 = $63 + $28 = $91

The cheapest option is Website B with a cost of $51.80.

Answer:240!

16 xs 15 = 240

Step-by-step explanation:

Answer: 240

Step-by-step explanation:

16 x 15 = 240 :)

When 80 kg is converted to lbs it will be equal to 176.36980975 pounds (lb).

        Here in this case,

        80kg x 2.20462

         = 176.36980975 pounds.

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As the sides of the parallelogram are equal, the values of x and y that ensure each quadrilateral is a parallelogram are 2 and -3.

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a sort of quadrilateral with opposing pairs of sides that are parallel and equal. A parallelogram is a form of quadrilateral in geometry. It has four sides and is two-dimensional. A parallelogram's most significant qualities are that its opposite sides are parallel and congruent, and its opposite angles are equal.

Here,

3x-4y=18

5x+y=7

multiply 2nd equation by 4 and solve,

3x-4y=18

20x+4y=28

23x=46

x=2

5*10+y=7

y=-3

The values of x and y that ensure each quadrilateral is a parallelogram is 2 and -3 as the side of parallelogram are equal.

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For given expression, solution will be y=(t-1)/(1+t).

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is t^2dy/dt-t=1+y+ty

After differentiation : As (d/dx) (x^n ) = nx^{n-1}

2t-t=1+y+ty

t-1=y(1+t)

y=(t-1)/(1+t)

for y(1)=2

2+2t=1-t

3t=-1

t=-1/3

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Answer:

456.9 inches

Step-by-step explanation:

We can use the law of sines to find c:

c = (a / sin C) = (270 inches / sin 164°)

To find the sine of an angle in degrees, we can use a scientific calculator or a trigonometry table. Rounding to the nearest 10th of an inch, c = approximately 456.9 inches.

Answer: It's 534.7

Step-by-step explanation:

I sacrificed my chance of getting it right to see the answer. It's right That I guarantee. btw brainiest, please?

The volume of the region will be 4/3 cubic unit with the help of integration.

What is integration?

Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives. Integration is one of the two major calculus topics in Mathematics, apart from differentiation(which measure the rate of change of any function with respect to its variables).

Definite Integral

An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.

A definite Integral is represented as:

∫f(x)dx from a to b.

Indefinite Integral

Indefinite integrals are defined without upper and lower limits. It is represented as:

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

For volume

Integrate y=1-x^2 for x=-1 to 1.

volume=1-x^2.dx

V=x-x^3/3

=1-1/3+1-1/3

=2-2/3

Hence,

          Volume=4/3 cubic unit

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9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.

The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.

When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.

Finding the location of the lawn is the first stage.

Area: 110 feet by 260 feet.

28600 square feet.

Calculating how many bags of fertilizer to purchase is the next step.

Bags = Area x 3,000 feet

Bags: 28600 feet / 3000 feet

9.53 bags total are in the bag.

Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.

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It will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.

The decay rate of 137Cs is given by the formula:

A = A0 * e^(-λt)

Where A is the decay rate, A0 is the initial decay rate (10^10 decays per second), λ is the decay constant (ln(2)/30.1 years) and t is the time in years.

To calculate the time, t, required for the decay rate to decrease to 10^7 decays per second, we solve for t and substitute the given values into the equation:

[tex]t = (ln(A0/A))/λ\\t = (ln(10^10/10^7))/(ln(2)/30.1)\\t = 19.44 years[/tex]

Therefore, it will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.

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The algebraic expression representing the length of the desk as a function of the width is given as follows:

L = W + 6.

The two variables in the context of this problem are given as follows:

The length is 6 inches greater than the width of the desk, hence the algebraic expression representing the length of the desk as a function of the width is given as follows:L = W + 6.

The problem asks for the algebraic expression representing the length of the desk as a function of the width.

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Answer:

Factors

Step-by-step explanation:

To find the roots of a polynomial, [factors] help the process of finding them

Answer:

D

Step-by-step explanation:

1. Find which of these 4 (four) has a y-intercept of positive 4, in this case, B and D. Recall, that the y-intercept means when X is 0 (zero) what is the value of Y?

2. Find the slope of B and D
The formula to find slope is change in y/change in x (Y/X)

B:

X: 0 - 4 = -4
Y: 4 - 0 = 4

4/-4 = -1

D:

X: 0 - -4 = 4

Y: 4 - 0 = 4

4/4 = 1

Conditional statements using the theme of the real number system:

Conditional statements in if-then form:

Conditional statements are statements in logic and mathematics that assert the truth of a statement based on certain conditions. They are usually written in the form "if P, then Q", where P is a condition and Q is a conclusion that follows from P. Conditional statements are used to make decisions or test certain conditions in programming, mathematics, and everyday life.

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If the liquidity premium theory of the term structure of interest rates holds, 0.498% is the liquidity premium for year 2.

Any additional compensation that is necessary to attract investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. Because it is more difficult to sell than a short-term bond, a long-term bond, for instance, will have a higher interest rate. According to the principle of the liquidity premium, bond investors favour short-dated assets that are highly liquid and have a short sales cycle over those that are longer-dated. According to another tenet of the theory, fluctuations in interest rates provide investors with compensation for greater pricing and default risks.

Given that,

1 + 1R₂= {(1 + 1R₁)(1 + E(2r₁) + L₂)}1/2

or, 1.12 = (1.8)(1.14 + L₂)1/2

or, (1.12)2/1.18 = 1.14 + L₂

or, 1.898 = 1.14 + L₂

or, L₂ = 0.498%

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The average value is the intersection point between the function and the line, which is at (0,1+C).

The average value of a function on an interval can be calculated using the following formula: Average Value = (1/b-a)∫a b f(x)dx. In this case, the function is f(x) and the interval is [0,1]. To calculate the average value, we must first calculate the integral of the function on the given interval. The integral of f(x) is nx^n-1 + C, where C is a constant. Using the fundamental theorem of calculus, we can evaluate the integral from 0 to 1 to be 1 + C.

The average value of the function on the given interval is then (1/1-0)∫0 1 (1+C)dx, which simplifies to 1+C. Therefore, the average value of the function on the given interval is 1 + C.

Graphically, the average value of the function on the given interval can be seen by plotting the graph of the function, which is a parabola with a vertex at (0,0), and a line at y=1+C. The average value is the intersection point between the function and the line, which is at (0,1+C).

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The correct option is "will be centered around p, the true population proportion."

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

Given that, the students select their random samples and plot the results on a dot plot, the dots, represent the sample proportions obtained by the students,

Since, the dots are representing the sample proportions, we know,

The population proportion is equal to the mean of the sampling distribution of the sample proportion.

Hence, the correct option is "will be centered around p, the true population proportion."

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Team A needs to sell 255 bags of popcorn to reach their goal of $100.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Team A will sell the bags of popcorn for $0.50 each.

Team B will sell the cotton candy for $0.75 per stick.

Let the number of bags of popcorn sold by Team A be "x".

So, the total cost for the popcorn machine rental and supplies is

= $15 + 0.05x.

To reach their goal of $100

$100 = 0.5x - ($15 + 0.05x)

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45

x = 255 bags of popcorn

Thus, Team A needs to sell 255 bags of popcorn.

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By vertical angles theorem, ∠1≅∠3 and ∠2≅∠4. Therefore, option B is the correct answer.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

From the given figure,

By vertical angles theorem, we have

Angle 1 and angle 3 are congruent.

Angle 2 and angle 4 are congruent

Therefore, option B is the correct answer.

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A scale of 1:900,000 is 36 times smaller than a scale of 1:24,000.

This can be expressed mathematically as a ratio: 1:900,000 = 1:24,000 / 36. To calculate the scale factor between two maps, divide the denominator of the larger scale by the denominator of the smaller scale. In this example, the scale factor is 36.

A scale of 1:900,000 means that one unit on the map represents 900,000 units of the same type in the real world. For example, one centimeter on the map could represent 900,000 centimeters in real life, or 9 kilometers. A scale of 1:24,000 would mean that one unit on the map represents 24,000 units of the same type in the real world. For example, one centimeter on the map could represent 24,000 centimeters in real life, or 0.24 kilometers.

The scale factor is the number that is used to compare the size of one map to another. In this example, a map with a scale of 1:900,000 is 36 times smaller than a map with a scale of 1:24,000. This means that the features on the 1:900,000 map are 36 times smaller than the same features on the 1:24,000 map. Therefore, the 1:900,000 map is not as detailed as the 1:24,000 map.

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Answer:

Midpoint=(−12,−2)

As a decimal:

Midpoint=(−0.5,−2)

Step-by-step explanation:

M=(xM,yM)

M=(x1+x22,y1+y22)

M=(3+−42,3+−72)

M=(−12,−42)

M=(−12,−2)

As a decimal:

M=(−0.5,−2)

Distance Solution: Between Endpoints

d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

d=(−4−3)2+(−7−3)2−−−−−−−−−−−−−−−−−−√

d=(−7)2+(−10)2−−−−−−−−−−−−√

d=49+100−−−−−−−√

d=149−−−√

d=12.206556

The height of the tree is obtained as  27.7 m

We have to note that in the solution of the problem that the tangent of the angle is going to come in to play. The tangent if one of the trigonometric ratios and the other ratios are the cos and the sine.

We know that the tangent of the angle is;

tan 36 = opposite/adjacent

Opposite of the angle = x + 5

(Where x is the height of the tree)

Adjacent of the angle = 45 m

We would then have that;

tan 36 = x + 5/45

45 tan 36 = x + 5

x = (45 tan 36) - 5

x = 27.7 m

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The second derivative of a(x) is larger than the second derivative of b(x) for the given x values.

The second derivative of a function with respect to x is the rate of change of the first derivative with respect to x. The second derivative of a function measures the "curvature" of the graph. In the case of the two functions shown, the blue line represents a(x) and the pink line represents b(x). By looking at the graph, we can see that the first derivative of a(x) is steeper than that of b(x). Therefore, the second derivative of a(x) will be larger than the second derivative of b(x). This can be seen by looking at the graph and noting that the blue line has a greater curvature or "bend" than the pink line. In other words, the second derivative of a(x) is larger than the second derivative of b(x) for the given x values.

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Answer:

-16 - 5x = -16

-5X=-16+16

-5X=0

X=5

Step-by-step explanation:

The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.

here, we have,

The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.

Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.

The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

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The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.

An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.

Let A, B, C, and D be the collinear points. Then the condition of the collinear will be

AB + BC + CD = AD

The collinear points lie in the same plane. Then the points are coplanar too.

From the graph, the distance between points E, H, and J will be the same.

The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.

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Answer:2.12

Step-by-step explanation:

the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2

a) Average rate of change of the function over [6,8] = (f(8) - f(6))/(8-6) = (11(83) - 11(63))/2 = 882/2 = 441

b) Average rate of change of the function over [-1,1] = (f(1) - f(−1))/(1-(−1)) = (11(13) - 11(-13))/2 = 244/2 = 122

a) To find the average rate of change of the function f(x)=11x3 over the interval [6,8], first calculate the value of the function at x=6 and x=8. This gives us f(6) = 11(63) = 729 and f(8) = 11(83) = 1728. Then, the average rate of change = (f(8) - f(6))/(8-6). Substituting in the values of f(6) and f(8), we get (1728 - 729)/2 = 882/2 = 441.

b) To find the average rate of change of the function f(x)=11x3 over the interval [-1,1], first calculate the value of the function at x=-1 and x=1. This gives us f(-1) = 11(-13) = -143 and f(1) = 11(13) = 143. Then, the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2

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Total area of the enclosed figure is given as  66 sq. units.

The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm2 and m2 are used to measure area. A shape's area is a two-dimensional measurement.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The common ways to depict square units, which are the same as areas, are square inches, square feet, etc.

The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric forms.

In the shape there is 2 triangles and 3 rectangle

Area of the bottom triangle = 1/2 * 3*4 = 6 sq. units

Area of the top triangle = 1/2 * 4*2 = 4 sq. units

Area of the bottom rectangle = 8*3 = 24 sq. units

Area of the middle rectangle = 8*3 = 24 sq. units

Area of the top rectangle = 4*2 - 8 sq. units

Total area of the enclosed figure is given as 6+4+ 24+ 24+ 8 = 66 sq. units.

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