In a middle school library, there are currently 6 boys and 7 girls. If two students are selected at random what is the probability that both are boys?

Answer:

(2, -3)

Step-by-step explanation:

You must choose from the 3 ways to solve the system of equations:

1. Substitution

2. Elimination

3. Graphing (least recommended)

My example is going to be substitution, as folllows:

2x - y = 7

(Add y to both sides)

2x = y + 7

(Subtract 7 from both sides)

y = 2x - 7

Now, we are able to use substitution in the next equation with the other equation!

3x + 4y = -6

(Replace y with what y equals -- other equation)

3x + 4(2x -7) = -6

(Simplify the parantheses)

3x + 8x - 28 = -6

(Add 28 to both sides)

3x + 8x = -6 +28

3x + 8x = 22

(CLT - Combine like terms)

11x = 22

(Divide 11 from both sides)

x = 2

Now, we will find what y is by plugging x into the other equation.

y = 2x - 7

x = 2

y = 2(2) - 7

y = 4 - 7

y = -3

y = -3

x = 2

Since we found both of the variables' values, we found our coordinate pairs to solve this equation!

Answer: (2, -3)

Therefore, when h = 6 and j = 5, the value of hj - h² is -6.

Arithmetic operations are basic mathematical operations that involve manipulating numbers to perform calculations. There are four main arithmetic operations:

Addition: Adding two or more numbers together. The symbol used to represent addition is "+", and the result is called the sum.

Subtraction: Subtracting one number from another. The symbol used to represent subtraction is "-", and the result is called the difference.

Multiplication: Multiplying two or more numbers together. The symbol used to represent multiplication is "×" or "*", and the result is called the product.

Division: Dividing one number by another. The symbol used to represent division is "÷" or "/", and the result is called the quotient.

These operations can be combined to perform more complex calculations. Additionally, there are other arithmetic operations, such as exponentiation (raising a number to a power) and finding roots, which involve using arithmetic principles.

by the question.

To evaluate the expression hj - h² for h = 6 and j = 5, we simply substitute these values into the expression and perform the arithmetic operations:

hj - h² = (6)(5) - 6²

= 30 - 36

= -6

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The result of the division in ordinary decimal notation is 300.

Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.

To perform the indicated operation, we need to divide 0.00036 by 0.0000012.

First, let's express both numbers in scientific notation

0.00036 = 3.6 x 10^(-4)

0.0000012 = 1.2 x 10^(-6)

Now we can divide the two numbers and simplify

3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)

Finally, we can convert this result back to ordinary decimal notation

3 x 10^(2) = 300

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The given question is incomplete, the complete question is:

Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012

For the first question, the equation for the line is y = -x + 11. This comes from the fact that the slope for a line perpendicular to the line x = 5 is -1. From there, we can use the point (5,6) to calculate the y-intercept, which is 11.

For the second question, the equation for the line is y = 7x. This comes from the fact that the slope for a line parallel to the line 7x - y = -7 is 7. Since the point (0,0) is already on the line, the equation is already solved.

For the third question, the equation for the line is x = 8. This comes from the fact that the slope for a line with an undefined slope is 0. Since the point (8,2) is already on the line, the equation is already solved.

The first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get 118096.

What is Geometric Progression?

A progression of numbers with a constant ratio between each number and the one before

Let the first term of the geometric progression be denoted by "a" and the common ratio be denoted by "r".

We know that the 4th term is 108, so we can use the formula for the nth term of a GP to write:

a*r³ = 108 .....(1)

We also know that the 8th term is 8748, so we can write:

a*r⁷ = 8748 .....(2)

To find the sum of the first 10 terms, we can use the formula for the sum of a finite geometric series:

S = a(1 - rⁿ)/(1 - r)

where S is the sum of the first n terms of the GP. We want to find the sum of the first 10 terms, so we plug in n = 10:

S = a(1 - r¹⁰)/(1 - r)

We now have two equations (1) and (2) with two unknowns (a and r). We can solve for a and r by dividing equation (2) by equation (1) to eliminate a:

(ar⁷)/(ar³) = 8748/108

r⁴ = 81

r = 3

Substituting r = 3 into equation (1) to solve for a, we have:

a*3³ = 108

a = 4

Therefore, the first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get:

S = 4(1 - 3¹⁰)/(1 - 3)

S = 4(1 - 59049)/(-2)

S = 4(59048)/2

S = 118096

Therefore, the sum of the first 10 terms of the GP is 118096.

118096.

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The matrix A of the linear transformation T(M) with respect to the standard basis for U2×2 is given by:

T([1000]) = [8 0]

[0 0]

T([0010]) = [0 0]

[0 9]

T([0001]) = [0 1]

[0 0]

To find the matrix A of the linear transformation T(M), we need to apply T to each basis vector of U2×2 and express the result as a linear combination of the basis vectors for U2×2. We can then arrange the coefficients of each linear combination as the columns of the matrix A.

Let's begin by finding T([1000]). We have:

T([1000]) = [8097][1000][8097]^-1

= [8 0]

[0 0]

To express this result as a linear combination of the basis vectors for U2×2, we need to solve for the coefficients c1, c2, and c3 such that:

[8 0] = c1[1000] + c2[0010] + c3[0001]

Equating the entries on both sides, we get:

c1 = 8

c2 = 0

c3 = 0

Therefore, the first column of the matrix A is [8 0 0]^T.

Next, we find T([0010]). We have:

T([0010]) = [8097][0010][8097]^-1

= [0 0]

[0 9]

Expressing this as a linear combination of the basis vectors for U2×2, we get:

[0 0] = c1[1000] + c2[0010] + c3[0001]

Equating the entries on both sides, we get:

c1 = 0

c2 = 0

c3 = 0

Therefore, the second column of the matrix A is [0 0 0]^T.

Finally, we find T([0001]). We have:

T([0001]) = [8097][0001][8097]^-1

= [0 1]

[0 0]

Expressing this as a linear combination of the basis vectors for U2×2, we get:

[0 1] = c1[1000] + c2[0010] + c3[0001]

Equating the entries on both sides, we get:

c1 = 0

c2 = 1

c3 = 0

Therefore, the third column of the matrix A is [0 1 0]^T.

Putting all of this together, we have:

A = [8 0 0]

[0 0 1]

[0 0 0]

Therefore, the matrix A of the linear transformation T(M) is:

T([1000]) = [8 0]

[0 0]

T([0010]) = [0 0]

[0 9]

T([0001]) = [0 1]

[0 0]

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Based on the information in the image, the values of the symbols in order would be: 5, 9.86, 9.93, 7.91. 10.56.

To find the equivalent value of each symbol we must apply the Pythagorean theorem and find the value of the hopotenuse of all triangles as shown below:

Triangle 1:

Triangle 2:

Triangle 3:

Triangle 4:

Triangle 5:

According to the above, the values of the symbols in order would be:

5, 9.86, 9.93, 7.91. 10.56.

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There are infinitely many irrational numbers between 1 and 6. This is because between any two distinct rational numbers, there is an infinite number of irrational numbers.

In the case of the interval between 1 and 6, there are infinitely many rational numbers between them, and therefore there must be infinitely many irrational numbers between them as well. This is due to the fact that the set of real numbers is uncountable, meaning that there is no finite or countably infinite list that contains all of its elements.

Thus, the answer is rather a statement about the infinite nature of the set of irrational numbers between 1 and 6.

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Answer:

Find the area A of the sector shown in the picture

76 degrees

6

Step-by-step explanation:

To find the area of a sector, we need to know the measure of the central angle and the radius of the circle.

If the central angle of the sector is 76 degrees, and the radius of the circle is 6, we can use the formula for the area of a sector:

A = (θ/360) * π * r^2

where θ is the central angle in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14.

Plugging in the given values, we get:

A = (76/360) * π * 6^2

Simplifying:

A = (0.2111) * π * 36

A = 7.57 square units (rounded to two decimal places)

Therefore, the area of the sector is approximately 7.57 square units.

LaShawn's class donated $350 for the fundraiser.

LaShawn's class raised $500 for the fundraiser, and they used 10% of the money to cover the cost of materials. That means they spent:

[tex]$$0.1 \times 500 = 50$$[/tex]

So they spent $50 on materials. Next, they saved 20% of the money for the next fundraising project. That means they saved:

[tex]$$0.2 \times 500 = 100$$[/tex]

So they saved $100 for the next project. To find out how much money they donated, we can subtract the amount spent on materials and the amount saved from the total amount raised:

500 - 50 - 100 = 350

Therefore, LaShawn's class donated $350 for the fundraiser.

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By answering the question the answer is So the area of ​​the rectangle is area 1/2 square inch. 

The size of an area on a surface can be expressed as area. The open surface or boundary area of ​​a three-dimensional object is called the surface area, and the area of ​​the planar area or planar area refers to the area of ​​the shape or planar layer. The total amount of space occupied by a planar (2-D) surface or shape of an object is known as its area. Draw a square on paper with a pencil. two-dimensional character. The area of ​​a shape on paper is the space it occupies. Imagine a square made up of more compact unit squares.  

It's not entirely clear what shape is being referred to here, but assuming it's a 2 inch by 1/4 inch rectangle, you can calculate the area by multiplying the length and width of the rectangle.

Area = Length x Width

Area = 2" x 1/4"

Area = (2/1) inch x (1/4) inch

Area = 1/2 square inch

So the area of ​​the rectangle is 1/2 square inch. 

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By answering the question the answer is So the area of ​​the rectangle is area 1/2 square inch.

The size of an area on a surface can be expressed as area. The open surface or boundary area of ​​a three-dimensional object is called the surface area, and the area of ​​the planar area or planar area refers to the area of ​​the shape or planar layer. The total amount of space occupied by a planar (2-D) surface or shape of an object is known as its area. Draw a square on paper with a pencil. two-dimensional character. The area of ​​a shape on paper is the space it occupies. Imagine a square made up of more compact unit squares.  

It's not entirely clear what shape is being referred to here, but assuming it's a 2 inch by 1/4 inch rectangle, you can calculate the area by multiplying the length and width of the rectangle.

Area = Length x Width

Area = 2" x 1/4"

Area = (2/1) inch x (1/4) inch

Area = 1/2 square inch

So the area of ​​the rectangle is 1/2 square inch.

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Find the area of 2 inches long times 1/4

Answer:

Hence, factors are 3x,(x−4y).

Step-by-step explanation:

We need to factorise 3x 2 −12xy

Here we can take 3x common.

Thus we have 3x 2−12xy=3x(x−4y)

Hence, factors are 3x,(x−4y).

Answer: 3x ( x - 4y )

Step-by-step explanation:

Factorizing 3x²-12xy

3x ( x - 4y )

The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.

The minimum value of a set of numbers or a function is the smallest value within that set or range, while the maximum value is the largest value within the same set or range.

a) The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.

b) The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

a) The least value inside the target range is attained. when:

The two hikers in the 5 x 10 interval cover fewer than 6 miles.

The 8 hikers in the range 15-20-20 cover a distance of more than 17 miles.

As a result, the minimum is 9, or somewhere between 10 and 15 persons.

b) The maximum number in the desired range will be obtained when:

The two hikers in the 5 x 10 interval cover fewer than 6 miles.

Less than 17 miles are covered by the 8 hikers in the period of 15 to 20.

The maximum number is then determined as follows:

2 + 9 + 8 = 19 hikers.

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The polynomial function with the given zeros and numeric value at x = 1 is given as follows:

f(x) = x^4 - 7x³ + 16x² - 8x - 32

The zeros of the polynomial function are given as follows:

Then the linear factors of the function are given as follows:

According to the Factor Theorem, the function with leading coefficient a can be defined as a product of it's linear factors are follows:

f(x) = a(x + 1)(x - 4)(x - 2 - 2i)(x - 2 + 2i).

f(x) = a(x² - 3x - 4)(x² - 4x + 8)

f(x) = a(x^4 - 7x³ + 16x² - 8x - 32).

When x = 1, y = -30, hence the leading coefficient a is obtained as follows:

-30 = a(1 - 7 + 16 - 8 - 32)

-30a = -30

a = 1.

Hence the function is:

f(x) = x^4 - 7x³ + 16x² - 8x - 32

The problem asks for the polynomial function with the given zeros and numeric value at x = 1.

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Mr. Woodstock will need to purchase 144 meters of wire to fully encircle his land. He will need to measure the length of the four sides of the land and add them together. The four sides measure 36 meters + 36 meters + 16 meters + 16 meters, which equals a total of 104 meters. He should buy enough wire to cover an additional 40 meters to account for any extra material he may need. Therefore, he needs to purchase 144 meters of wire for his fencing.

The value of h(x) using exponents are as follows:

For -1, the value of h(x)=1/10

For 0, the value of h(x) = 1

For 1, the value of h(x) = 10

For 2, the value of h(x) = 100

For 3, the value of h(x) = 1000

The exponent of a number tells us how many times the original value has been multiplied by itself. For instance, 2×2×2×2 can be expressed as [tex]2^{4}[/tex] the result of 4 times multiplying 2 by itself. Thus, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."

Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times. Here x is the base and n is the power.

Now here, as we put the value of x in the equation, h(x) we can get the value of h(x) for each value of x.

So,

For -1, the value of h(x)=1/10

For 0, the value of h(x) = 1

For 1, the value of h(x) = 10

For 2, the value of h(x) = 100

For 3, the value of h(x) = 1000

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29 = speed of the boat in still water

c = speed of the current

t = time it took each way

when going Upstream, the boat is not really going "29" fast, is really going slower, is going "29 - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "29" fast, is really going faster, is going "29 + c", because the current is adding its speed to it.

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&180&29-c&t\\ Downstream&342&29+c&t \end{array}\hspace{5em} \begin{cases} 180=(29-c)(t)\\\\ 342=(29+c)(t) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{180=(29-c)t\implies \cfrac{180}{29-c}=t} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{342=(29+c)\left( \cfrac{180}{29-c} \right)}\implies \cfrac{342}{29+c}=\cfrac{180}{29-c} \\\\\\ 9918-342c=5220+180c\implies 4698-342c=180c\implies 4698=522c \\\\\\ \cfrac{4698}{522}=c\implies \boxed{9=c}[/tex]

There are no points at which the function has its direction of fastest change along the vector i + j. This is because the equations lead to a contradiction.

The exercise asks to find all the points at which the function f(x, y) = x^2 + y^2 - 8x - 16y has its direction of fastest change along the vector i + j.

To find the points, we need to solve the equation:

(2x - 8)i + (2y - 16)j = k(i + j)

where k is a constant. Since the direction of fastest change is along the vector i + j, we know that the left-hand side of the equation represents the gradient vector of f(x, y).

Equating the x and y components of the gradient vector to the corresponding components of the vector i + j, we get:

2x - 8 = k

2y - 16 = k

Equating these two expressions for k, we get:

2x - 8 = 2y - 16

Solving for y in terms of x, we get:

y = x - 4

Substituting this expression for y into the equation of the gradient vector, we get:

2x - 8 = k

2(x - 4) - 16 = k

Simplifying, we get:

2x - 8 = k

2x - 24 = k

Substituting the first equation into the second, we get:

2x - 24 = 2x -

Simplifying, we get:

16 = 0

This is a contradiction, which means there are no points at which the function has its direction of fastest change along the vector i + j.

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6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94

Untuk Konsultasi Tugas Lainnya: WA 0813-7200-6413

Answer:

P = x(4x+7)/(x+2)(x+1)

Step-by-step explanation:

P = 2l + 2w. If x/x+2 = l and x/x+1 = w:

P = (2x/x+2) + (2x/x+1)

P = (2x(x+1)/(x+2)(x+1)) + (2x(x+2)/(x+1)(x+2))

P = (2x(x+1) + 2x(x+2))/(x+2)(x+1)

P = (4x squared + 7x)/(x+2)(x+1)

P = x(4x+7)/(x+2)(x+1)

The probability of obtaining a reading greater than 0.28°C is 0.3897.

What is standard normal distribution ?

The standard normal distribution is a specific type of probability distribution that has a mean of 0 and a standard deviation of 1. It is also called the Z-distribution or the Gaussian distribution.

The standard normal distribution is commonly used in statistics and probability theory to make comparisons and calculations across different normal distributions. To use the standard normal distribution for calculations involving a normal distribution with a different mean and standard deviation, the data must be standardized by subtracting the mean and dividing by the standard deviation.

According to the question:
To solve this problem, we need to standardize the value of 0.28°C using the standard normal distribution formula:

z = (x - mu) / sigma

where:

x = 0.28°C

mu = 0°C

sigma = 1.00°C

Substituting the values, we get:

z = (0.28 - 0) / 1.00

z = 0.28

Now, we need to find the probability of obtaining a reading greater than 0.28°C, which is the same as finding the area to the right of z = 0.28 on the standard normal distribution curve. We can use a standard normal distribution table or calculator to find this area.

Using a calculator or software, we find that the probability of obtaining a reading greater than 0.28°C is 0.3897, rounded to 4 decimal places.

Therefore, the probability of obtaining a reading greater than 0.28°C is 0.3897.

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Answer: -18

Step-by-step explanation:

Answer:

value of f is 6

Step-by-step explanation:

100% correct

the work is in the image below. Hope this help!

Answer:

The first discount of 50% means Jason paid 50/100 x £88 = £44 for the jacket.

Then, the second discount of 25% means he paid 75/100 x £44 = £33 for the jacket.

Therefore, the final sale price that Jason paid for the jacket was £33.

In response to the stated question, we may respond that As a result, the fraction length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).

A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions , and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.

We can calculate the length of the other leg of the right triangle, which is also half the side of the hexagon, using the Pythagorean theorem:

[tex]$(fracs2 )2 + (fracs2 )2 = 122$\\$fracs244 + fracs244 = 144$\\$\frac{s^2}{2} = 144$\\$s^2 = 288$\\$s = sqrt288 = about 16.97$[/tex]

As a result, the length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).

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Answer:

400 balcony seats

Step-by-step explanation:

We know 170 tickets have been sold which is 1/5 of the total tickets

We have to find the total number of seats by doing 170x5

Now we know that there are 850 seats (170x5)

We have to subtract the lower seats from the total number of seats to find b (balcony seats)

850-450 = 400

Therefore, b is equal to 400 balcony seats

Answer:

Let's call the speed of the jet in still air "j" and the speed of the wind "w".

When flying with the tailwind, the effective speed of the jet is j + w. We know that it can travel 2040 miles in 4 hours, so:

2040 = 4(j + w)

Simplifying this equation, we get:

j + w = 510

When flying into the headwind, the effective speed of the jet is j - w. We know that it can only travel 1560 miles in 4 hours, so:

1560 = 4(j - w)

Simplifying this equation, we get:

j - w = 390

Now we have two equations with two variables:

j + w = 510

j - w = 390

We can solve this system of equations using elimination. Adding the two equations, we get:

2j = 900

Dividing both sides by 2, we get:

j = 450

So the speed of the jet in still air is 450 mph.

Now we can use either equation to solve for the speed of the wind. Let's use the first equation:

j + w = 510

Substituting j = 450, we get:

450 + w = 510

Subtracting 450 from both sides, we get:

w = 60

So the speed of the wind is 60 mph.

Step-by-step explanation:

Answer:

Step-by-step explanation:

16350$

Answer:

16 407.1

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

We know

The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.

2x + 3x + 10 = 160

5x + 10 = 160

5x = 150

x = 30

If f is analytic and never zero on a domain D, then the graph (x,y,|f(x+iy)|) has no "pits". This follows from the fact that Re(f(z)) has no local minima in D.

Exercise 15 establishes the following result: if f is analytic and never zero on a domain D, then the the real part of f(z) has no local minima in D.

To use this result to establish the statement that |f(z)| has no local minima in D, we can use the fact that[tex]|f(z)|=\sqrt{real part of f(z))^2 + \ img part of f(z) )^2[/tex] . Since the sum of two non-negative functions is non-negative, it follows that if  the real part of f(z)  has no local minima in D, then |f(z)| has no local minima in D either.

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