I have a system of equations I don’t remember how to do :|

I forgot how to solve this, and I forgot how to find the slope…

Answer:

picture?

Step-by-step explanation:

The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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Answer:

FE is not congruent to FG.

Step-by-step explanation:

FE is 49 and FG is 111.

So, because these two numbers are not equal,

FE is not congruent to FG.

Answer:

she sold 15 candy bars every hour

Step-by-step explanation:

The length of the straw will be 9.89949 inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula

\(X^2=l^2+b^2+h^2\)

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 5 inch , b= 8 inch , h= 3 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

\(X^2+l^2+b^2+h^2\)

\(X^2=5^2+8^2+3^2\)

\(X^2=25+64+9\)

\(X^2=98\)

\(X=\sqrt{98}\)

X= 9.89949 (in radical form)

Hence, the length of the straw will be  9.89949 inches.

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Answer:

Step-by-step explanation:

I think is x-1

It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.

The area of rectangle.

Area of rectangle = Length × Breadth

\(\sf=2\dfrac{5}{6}\times4\dfrac{4}{7}\)

\(\sf=\dfrac{17}{6}\times\dfrac{25}{7}\)

\(\sf=\dfrac{17\times25}{6\times7}\)

\(\sf=\dfrac{425}{42}\)

The first system of linear equations has one solution, the second system has infinitely many solutions, and the third system has no solution.

To determine the number of solutions for each system of linear equations, we can examine the equations and solve them using various methods.

In the first system, -3x + y = 7 and 2x - 4y = -8, we can solve the equations using substitution or elimination. Regardless of the method used, we find that the solution is x = 2 and y = 1. Therefore, this system has one unique solution.

In the second system, y = -4x - 5 and y = -4x + 1, we can observe that the equations represent two parallel lines with the same slope (-4). Since parallel lines never intersect, there are no common solutions. Therefore, this system has no solution.

In the third system, 3x - y = 4 and 6x - 2y = 8, we can simplify the second equation by dividing both sides by 2 to get 3x - y = 4. Notice that this equation is the same as the first equation in the system. The two equations represent the same line, meaning they have infinitely many points of intersection. Therefore, this system has infinitely many solutions.

By analyzing the coefficients and constants in each system of linear equations, we can determine the number of solutions and match them accordingly: one solution, no solution, and infinitely many solutions.

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Answer:

Im pretty sure they are

Step-by-step explanation:

Answer:A, C, and F

Step-by-step explanation: A requirement for a polygon is that its a polygon which basically means no gaps or missing sides and only A, C, and F serve those requirements

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

Here is your answer

s= 9/4

A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.

Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.

The diameter of the semicircle is also the length of the rectangle, so it is 3x.

The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.

The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:

3x^2 + (9/8)πx^2 = 750

(21/8)πx^2 = 750

x^2 = 750/(21/8)*π

x = √(750/(21/8)*π)

To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:

x = √(750/(21/8)*3.14)

= √(750/6.71)

= √(112.64)

= approximately 10.65 inches.

The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.

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Answer: 6

Step-by-step explanation:

Just some simple ratios

P = Pizza People = Pl

P: Pl

2 : 9

x: 27

We want to find x.

Since 27/9 is equal to 3, we multiply 2 by 3 as well!

2x3=6, our desired amount.

Work done in pumping water out of a circular pool Work done in pumping all the water over the side of a swimming pool can be obtained by calculating the gravitational potential energy of water and can be calculated as follows:

Therefore, the amount of work required to pump all the water over the side is 5745600 J.2. Work done in pumping water out of a conical tankLet V be the volume of water in the conical tank and H be the height of water. Since the tank is conical, the volume of water in the tank at height h is given by.

Where R is the base radius of the tank. Therefore, the volume of water in the tank is given by: The mass of water is given by:

m = density of water × volume

of Since the pipe is always leveled at the surface of the water, the work done to lift water from height h to height H is given by: W = mghwhere g is the acceleration due to gravity and h is the height of the water being pumped out.

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Answer:

A

Step-by-step explanation:

Inverse means that the function is reversed from the original function, f(x).

To find the inverse function of f(x)=5x-11, add 11 to x, then divide the expression by 5.

This would be (x+11)/5.

So, you know that A is true.

Try the other selections too.

B: \(g(x)=x^3/2\)       The x should be tripled before being divided by 2; FALSE

C: \(g(x)=7/(x+9)\)     7 should by in the numerator; FALSE

D: \(g(x)=6(x+8)\)    8 should be added before being multiplied by 6; FALSE

I hope this helps!!!

Using composite functions, it is found that the pair of functions that are inverse of each other is given by:

A. \(f(x) = 5x - 11\) and \(g(x) = \frac{x + 11}{5}\)

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

The composite of functions f and g is given by:

\((f \circ g)(x) = f(g(x))\)

Two functions f and g are inverse of each other if:

\(f(g(x)) = g(f(x)) = x\)

Item a:

\(f(x) = 5x - 11\)

\(g(x) = \frac{x + 11}{5}\)

\(f(g(x)) = f(\frac{x + 11}{5}) = 5(\frac{x + 11}{5}) - 11 = x + 11 - 11 = x\)

\(g(f(x)) = g(5x - 11) = \frac{5x - 11 + 11}{5} = \frac{5x}{5} = x\)

Since \(f(g(x)) = g(f(x)) = x\), these functions are inverse of each other.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Step-by-step explanation:

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.

for the slope a :

x changes by +10 (from -5 to 5)

y changes by +1 (from -4 to -3)

the slope is +1/+10 = 1/10

the equation looks now like

y = (1/10)x + b

let's use the first point.

-4 = (1/10)×-5 + b = -1/2 + b

-3 1/2 = -7/2 = b

the equation is

y = (1/10)x - 7/2

so, the second answer option is correct.

The probability is 0.4647.

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Answer:

7 dollars and 25 cents

Step-by-step explanation:

there is 8 quarts in 2 gallons then divide 58 dollars by 8 and you get 7 dollars 25 cents

Division is one of the four fundamental arithmetic operations. The price per quart is $7.25 per quart.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that A 2-gallon bucket of paint costs $58.00. Therefore, the price per gallon is,

Price per gallon = $58/2

Since a gallon is equal to 4 quarts. Therefore, the price per quart is,

Price per quart  = $58/(4×2) = $7.25 per quart

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Answer:

the answer is 80

Step-by-step explanation:

or, angleAFE =angleBFD [V.O.A]

or, 125=45+DFC

or, 125-45=DFC

or, 80 =DFC

Using the concepts of straight angle, ∠DFC = 80°.

A straight angle is an angle equal to 180 degrees. It is called straight because it appears as a straight line.

Since AD is a straight line.

∠AFE + ∠EFD = 180°

125° + ∠EFD = 180°

∠EFD = 180° - 125° = 55°

Now, EB is a straight line.

∠EFD + ∠DFC + ∠CFB = 180°

55° + ∠DFC + 45° = 180°

∠DFC = 180° - 100° = 80°

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Answer:

A. 120 ft

B. 119

C. 2100 ft

Step-by-step explanation:

A. (Slipt the shape into 2 parts so it will be simpler)

For the triangle : 1/2 (4x12)

And for the rectangle : 12x8

1/2 (4x12) = 24

12 x 8 = 96

24 + 96 = 120 ft

_________________________________

B. (this time we can split it into 3 parts)

Longer rectangle : 12x6

Short rectangle : 5x5

Triangle : 1/2 (4x11)

LR : 12x6 = 72

SR : 25

T : 1/2 44 = 22

72+25+22 = 119

______________________________________

C. (Like the first one, we can split it into 2 parts)

Rectangle : 50x30

Triangle : 1/2 40x30

R : 1500

T : 1/2 1200 = 600

1500 + 600 = 2100

Hope this helps :)

Answer:

y=17x-55

Step-by-step explanation:

y-(-4)=17(x-3)

y+4=17x-51

y=17x-55

The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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Answer:

Probability that a customer complains in percentage = 4% (Approx)

Step-by-step explanation:

Given:

Total number of customers = 669

Total number of complaints = 27

Find:

Probability that a customer complains

Computation:

Probability that a customer complains = 27 / 669

Probability that a customer complains in percentage = [27 / 669]100

Probability that a customer complains in percentage = [0.040358]100

Probability that a customer complains in percentage = 4.0358%

Probability that a customer complains in percentage = 4% (Approx)

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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26 square feet is the exact surface area of the composed figure with two cones.

The composed figure has two cones.

The formula to find the surface area of cone is A=πr(r+√h²+r²))

Where r is radius and h is height of the cone.

Both the cones have radius of 1 ft and height of 2ft and 4 ft.

Area of cone 1=3.14×1(1+√4+1)

=3.14(1+√5)

=10.16 square fee

Area of cone 2=3.14×1(1+√16+1)

=3.14(1+√17)

=16.01square feet.

Total surface area = 10.16+16.01

=26.17 square feet.

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