Which property is illustrated below?
5x 11 = 11x5
associative property of multiplication
commutative property of multiplication
distributive property
identity property of multiplication

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula \(n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}\), equivalent to the recurrence formula \(a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}\).

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

\(n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}\)      (1)

Now we prove that given expression contains the pattern:

n = 0

7

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula \(n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}\), equivalent to the recurrence formula \(a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}\).

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Answer:

C.) 2^10

Step-by-step explanation:

You would add the exponents which in this case are 3 and 7 getting 10 as your exponent.

Answer: C)

Step-by-step explanation: If you do 2^3 x 2^7 = 1024 also 2^10 = 1024

The difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.

To subtract the second polynomial from the first polynomial, we need to perform term-wise subtraction. Let's break down the process step by step:

The first polynomial is: 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n.

The second polynomial is: -6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n.

To subtract the second polynomial from the first, we need to change the signs of all terms in the second polynomial and then combine like terms.

First, let's change the signs of the terms in the second polynomial:

-(-6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n) = 6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n.

Now, we can combine like terms by adding or subtracting coefficients of similar monomials:

(11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n) - (6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n)

= 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n - 6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n

= (11m^(2)n^(5) - 6m^(2)n^(5)) + (-3m^(2)n^(3) + 3m^(2)n^(5)) + (5mn + m) + (-n + 2n)

= 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.

Therefore, the difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.

In summary, to find the difference, we changed the signs of all terms in the second polynomial and then combined like terms with the first polynomial. The resulting polynomial is the difference between the two original polynomials.

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Answer:

534 is the mean.

Step-by-step explanation:

to calculate the mean you add all the numbers together (for example this set of numbers):

785, 585, 465, 409, 495, 465

=3204

then divide the number of numbers that you added together , (in this case 6)

3204/6

=

534

When dividing a number by 10, the decimal point is moved one place to the left.

What is the arithmetic operation?

Arithmetic operations involve the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

When dividing a number by 10, the decimal point is moved one place to the left.

For example, if we divide 345.67 by 10, the result is 34.567.

Similarly, if we divide 345.67 by 100, the result is 3.4567.

If we divide 345.67 by 1000, the result is 0.34567.

In general, if we divide a number by 10^n (where n is a positive integer), the decimal point is moved n places to the left.

For example, if we divide 345.67 by 10^4, the result is 0.034567.

Hence, When dividing a number by 10, the decimal point is moved one place to the left.

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Answer:

proportional is the answer

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

hi

Step-by-step explanation:

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

x - 2y = -2

To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.

If x = 0, we have:

0 - 2y = -2

y = -2/-2 = 1

if x = 1 then:

1 - 2y = -2

1 + 2 = 2y

3 = 2y

3/2 = y

Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:

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The probability of being in the first or second position in a heat with 10 cars can be calculated by finding the total number of ways that the cars can be arranged in the heat and then dividing by the number of ways that result in being in the first or second position.

There are 10 cars in the heat, so there are 10 possible positions for the first car, and once that car has been assigned a position, there are 9 possible positions remaining for the second car, and so on. Therefore, the total number of ways that the cars can be arranged is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This is equivalent to 10! (read as "10 factorial"), which is the product of all the positive integers from 1 to 10.

To be in the first or second position, there are 2 possible positions out of the 10 total positions in the heat. So, the number of ways to be in the first or second position is:

2 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

which is equivalent to 2 x 9!, since we only need to consider the arrangements of the remaining 9 cars after we have assigned ourselves to one of the first two positions.

Therefore, the probability of being in the first or second position is:

(2 x 9!) / 10!

Simplifying this expression, we get:

(2 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

which simplifies further to:

2 / 10

or:

1 / 5

So, the probability of being in the first or second position is 1/5 or 0.2, which means that there is a 20% chance of being in one of those positions in any given heat.

Answer:

SAS

Step-by-step explanation:

Answer:

c looks like the right answer.

Step-by-step explanation:

Answer:

a.9

Step-by-step explanation:

Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

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Rounded to the nearest hundred, the perimeter is approximately \(20 + 2\sqrt{5} = 29.2\) units, so the answer is 2900 feet.

What is perimeter?

Perimeter is the distance around a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

To find the perimeter of the pentagon, we need to find the distance between each pair of adjacent vertices and add them together.

We can use the distance formula to find the distance between two points (x1, y1) and (x2, y2):

\(d = \sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)}\)

Using this formula, we can find the distances between the five pairs of adjacent vertices:

Distance between (0, 0) and (5, 0):

\(d1 = \sqrt{((5 - 0)^2 + (0 - 0)^2)} = 5\)

Distance between (5, 0) and (8, 4):

\(d2 = \sqrt{((8 - 5)^2 + (4 - 0)^2)} = \sqrt{(9 + 16)} = 5\)

Distance between (8, 4) and (4, 7):

\(d3 = \sqrt{((4 - 8)^2 + (7 - 4)^2) } = \sqrt{ (16 + 9)} = 5\)

Distance between (4, 7) and (0, 5):

\(d4 = \sqrt{ ((0 - 4)^2 + (5 - 7)^2)} = \sqrt{(16 + 4)} = 2\sqrt{5}\)

Distance between (0, 5) and (0, 0):

\(d5 = \sqrt{((0 - 0)^2 + (0 - 5)^2)} = 5\)

Now we can add these distances together to find the perimeter:

perimeter = d1 + d2 + d3 + d4 + d5

perimeter = 5 + 5 + 5 + \($2\sqrt{5}$\) + 5

perimeter = 20 + \($2\sqrt{5}$\)

Rounded to the nearest hundred, the perimeter is approximately \(20 + 2\sqrt{5} = 29.2\) units, so the answer is 2900 feet.

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A system of equations representing the number of adults and children attending the game is x + 2x = 45, and the number of children who were in the group is 30.

An equation is a mathematical statement showing that two mathematical expressions are equal or equivalent.

Equations are represented using the equation sign (=).

The total number of people who attended the game = 45

Let the number of children, who were twice as many as adults, C = 2x

Let the number of adults, who attended the game, A = x

Therefore, the total number of attendees, T = x + 2x = 45

x + 2x = 45

3x = 45

x = 15

C = 2x

= 2(15)

= 30

Check:

x + 2x = 45

Substitute x with 15

15 + 2(15) = 45

15 + 30 = 45

45 = 45

Thus, from the system of equations, we can conclude that 30 children attended the game, which is twice the number of adults.

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The water's height at 8:30 pm is 19.99 feet

From the question, we have the following parameters that can be used in our computation:

h(t) = 6cos(2π(t - 8)/12.4) + 14

Also from the question, we have

Time = 8:30 pm

When converted to hour, we have

Time = 20.5

Substitute the known values in the above equation, so, we have the following representation

h(t) = 6cos(2π(20.5 - 8)/12.4) + 14

This gives

h(t) = 6cos(6.33) + 14

Evaluate the expression

h(t) = 19.99

Hence, the height is 19.99 feet

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Complete question

at a seaport, the depth of the water during the day can be found using the equation h(t) = 6cos(2π(t - 8)/12.4) + 14

Where h is the depth of water in feet and t is the number of hours after midnight. at 8:30pm

What will be the water's height?

Answer:

67/100

Step-by-step explanation:

its the simpelist form

Step-by-step explanation:

F=400(1+0.05/1)^1*t

After 1 year= $ 400.20

2= 400.40

3=$ 400.60

4= $ 400.80

5=$ 401.00

6= $ 401.20

7=$ 401.40

8=  $ 401.60

9=$ 401.80

10= $ 402.00

The graph of the balance over every year is plotted. Here, we can see the increase in balance over the years.

"Compound interest is the addition of interest to the principal sum of a deposit, or in other words, interest on principal plus interest."

Here, the principal is (P) = $400

The interest rate(r) = 5% = 0.05

The time period is = n years

Therefore, after n years balance is = P(1 + r)ⁿ

After 1 year, balance is = $400(1 + 0.05)¹ = $420

After 2 years, balance is = $420(1 + 0.05)¹ = $441

After 3 years, balance is = $441(1 + 0.05)¹ = $463.05

After 4 years, balance is = $463.05(1 + 0.05)¹ = $486.20

After 5 years, balance is = $486.20(1 + 0.05)¹ = $510.51

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Hope this helps!! The answer and explanation are as shown above:))

Answer:

8

Step-by-step explanation:

line of symmetry indicates equal measurements between both sides, 4 from eye not nose and another 4 from the nose to eye

The period of the function f(t) = 2.3cos(0.25t) is 8π. Hence, the correct answer is d) period 8π.

To determine the period of the function f(t) = 2.3cos(0.25t), we need to consider the coefficient of t inside the cosine function.

In this case, the coefficient is 0.25, which represents the frequency of the cosine function. The period of a cosine function is given by the formula T = 2π/frequency.

Using this formula, we can calculate the period of the function f(t) as follows

T = 2π / 0.25

T = 8π

Therefore, the period of the function f(t) = 2.3cos(0.25t) is 8π.

Hence, the correct answer is d) period 8π.

The period of a function represents the length of one complete cycle or the distance between two consecutive identical points on the graph of the function. In this case, the function is a cosine function, and the period determines how long it takes for the function to repeat its values

The coefficient 0.25 in the function f(t) = 2.3cos(0.25t) affects the frequency of the cosine function. A smaller coefficient results in a slower oscillation, while a larger coefficient leads to a faster oscillation. In this case, since the coefficient is 0.25, it means that the function completes one full cycle within 8π units of time.

Understanding the period of a function is crucial for analyzing its behavior, identifying the frequency of oscillation, and studying its repetitive patterns.

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Answer:

A) 4.5x + 6y < 1600, x + y > 60

Explanation:

Let the number of pounds of regular coffee = x

Let the number of pounds of decaffeinated coffee = y

Cost of regular coffee = $4.50 per pound

Cost of decaffeinated coffee = $6.00 per pound.

If she can spend no more than $1600 to buy coffee for the next month, then:

The owner estimates she will need at least 60 pounds of coffee for the month..

Therefore:

Therefore, the inequalities that meet these conditions are:

Answer:

1. x=-6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(2x+3)−4x=−3

(3)(2x)+(3)(3)+−4x=−3(Distribute)

6x+9+−4x=−3

(6x+−4x)+(9)=−3(Combine Like Terms)

2x+9=−3

2x+9=−3

Step 2: Subtract 9 from both sides.

2x+9−9=−3−9

2x=−12

Step 3: Divide both sides by 2.

x=-6

Answer:

200 sheets

Step-by-step explanation:

Divide 5,000 by 25 to get 200 sheets of paper per box.

Answer:

750 pieces of paper

Step-by-step explanation:

can't

Step-by-step explanation:

first Pythagoras to get PT :

85² = 77² + PT²

7225 = 5929 + PT²

PT² = 1296

PT = 36

second Pythagoras to get ST :

39² = PT² + ST² = 36² + ST²

1521 = 1296 + ST²

ST² = 225

ST = 15

third Pythagoras to get TR :

97² = ST² + TR² = 15² + TR²

9409 = 225 + TR²

TR² = 9184

TR = 95.83318841... ≈ 96