Which of the following expressions does cos(x − y) − cos(x + y) simplify to?

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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Answer:

8x+30 for the first. 8x-20 for the second.

Step-by-step explanation:

The first is 2(-x+3)+10x+24

Second is 4(2x-5)

Answer: 14.2638366937

Step-by-step explanation:

A geometric sequence is a sequence in which each term is multiplied by a number, called the common ratio, to get the next term.

So, if the first term of the geometric sequence is 10 and the common ratio is 0.3, the sequence would be 10, 0.3(10), 0.3 x 0.3 x 10... and so forth. This becomes:

10, 3, 0.9, 0.27, 0.081, 0.00243, 0.00729, 0.002187, 0.0006561, 0.00019683, 0.000059049, 0.0000177147...

You add these first 12 terms to get 14.2638366937.

An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).

In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:

x = a(y - k)² + h.

Where:

By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:

h = 0

k = 0

a = positive.

x = a(y - k)² + h.

x = a(y - 0)² + 0.

x = ay²

Therefore, a possible equation is x = 1/12(y²).

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To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

7850

Step-by-step explanation:

Answer:

7850 cm squared

Step-by-step explanation:

The formula for area of a circle is 3.14(r^2)

The radius is 50 cm.

3.14(50^2)

7850

The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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Answer:

you could fit 7776 people on the gym floor for an event.

Step-by-step explanation:

The Locust Grove gymnasium has an area of 54 yd x 40 yd = 2160 square yards. To find the number of people that can fit on the gym floor, we need to convert the area of the gym floor to square feet and divide it by the number of square feet each person takes up.

We know that 1 yard = 3 feet, so we have to convert the area of the gymnasium in square yards to square feet by multiplying it by (3*3) = 9.

So the area of the gymnasium in square feet is 2160*9 = 19440 square feet.

To find the number of people that can fit on the gym floor, we divide the area of the gym floor by the number of square feet each person takes up.

19440 square feet / 2.5 square feet/person = 7776 people

Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

9514 1404 393

Answer:

  0

Step-by-step explanation:

The forces are equal and opposite, so the net force is zero.

  5N -5N = 0

1) product is not defined.
2) product is undefined.
3)  [  -9 ]
    [  5  ]      
    [ -11 ]

Explanation:

1) product is not defined.
because no of column of 1st matrix (2)  is not same as no of row of second matrix.(3)

2) product is undefined.
because no of column of 1st matrix (1)  not same as no of row of second matrix (2).


3)  [    6     5 ]                           [    6  -15    ]                    [  9     ]
    [   -4    -3 ]  X  [ 1  ] =            [     -4   +9  ] =                [   5    ]
    [    7     6 ]       [ -3 ]              [      7  -18   ]                  [   -11   ]   
           

A matrix is a rectangular array of numbers (or other mathematical objects) that defines operations like addition and multiplication. A matrix over a field F is typically a rectangular array of scalars, each of which is a member of F.

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Answer:

2.5 hours or 2 hours and 39 min

Step-by-step explanation:

22.50/9

Answer:

Step-by-step explanation:

area of a rectangular piece of cloth 3 1/4m by 25 cm

the area of ​​the rectangle is found by making the base by the height, we convert the meters into centimeters

3 1/4 m = 3.25m = 325 cm

we find the area

325 × 25 = 8125 cm² (or 0.8125 m²)

The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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Answer:

7:10

Step-by-step explanation:

63/7=9

90/9=10

a/////

63÷90 = 7÷10

j’espere que ca pourra t’aider <3

The rock will be 125  feet above the beach at: The values of t are 3.911 or 1.28 and (b) The minimum height is h= 346 feet

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

The given parameters are

h = -16t² + 79t + 50

In the equation put h = 125 to find t

125 = -16t² +79t+50

Rearrange the equation to have

16t²-79t -50 +125 = 0

this is also written as 16t² -79t + 75 =0

Solving for t we have

[-b±√b²-4ac]/2z

[79 ±√79²-4*16*75]/2*16

[(79 ±√6241-4800)] / 32

Simplify further to get

[79 ±√1441] / 32

(79 ±38) / 32

117/32 or 41/32

The values of t are 3.911 or 1.28

The minimum height of the rock at t = 1.28 is

h = -16(3.28)² + 79( 3.28)+ 50

h = -16(10.7584) + 79(3.28) +50

h = -  172.1344 +259.12 + 50

h= 346 feet

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Answer:

85............................

Answer:

\(\frac{1}{10} \£\)

Step-by-step explanation:

We know that £1 equals 100p.

Knowing this relation, we can use the rule of three

\(30p \times \frac{ \£1}{100p} =0.3 \£\)

Then, we form the fraction

\(\frac{0.3 \£}{\£ 3.00} =\frac{3}{30} =\frac{1}{10} \£\)

Therefore, the fraction of of £3.00 is

\(\frac{1}{10} \£\)

Answer:

l

Step-by-step explanation:

Answer:

$1,945.91

Step-by-step explanation:

To find the amount a family would have spent to be at the 80th percentile, we can use the normal distribution.

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

\(\boxed{X \sim\text{N}(\mu,\sigma^2)}\)

Given that the average spending on a summer vacation is $1,600 and the standard deviation is $411:

We need to convert the problem to the standard normal distribution by calculating the z-score.

The z-score represents the number of standard deviations a data point is away from the mean. To find the z-score corresponding to the 80th percentile, we need to find the critical value or z-score that corresponds to an area of 0.80 under the standard normal curve.

Using a standard normal distribution table or a calculator, the z-score corresponding to an area of 0.80 is 0.84162084...

Next, we use the formula for the z-score:

\(\boxed{z = \dfrac{x - \mu}{\sigma}}\)

where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.

Substitute z = 0.84162084..., μ = 1600, σ = 411 into the z-score formula:

\(0.84162084... = \dfrac{x - 1600}{411}\)

Solving for x:

\(x=1945.90616...\)

Therefore, a family would have spent approximately $1,945.91 to be at the 80th percentile of spending on a summer vacation.

Answer:

$1,945.03

Step-by-step explanation:

To find the amount a family would have spent to be at the 80th percentile, we need to find the z-score that corresponds to the 80th percentile and then use that z-score to calculate the corresponding amount.

First, we find the z-score using the standard normal distribution table or a calculator:

z = InvNorm(0.8) ≈ 0.8416

Next, we use the formula for transforming a z-score to a raw score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the given values and solving for x, we get:

0.8416 = (x - 1600) / 411

x - 1600 = 0.8416 * 411

x - 1600 = 345.0256

x = 1945.0256

Therefore, a family would have spent about $1,945.03 to be at the 80th percentile.

If a researcher wants to predict the value of a dependent variable based upon known independent variables for a specific case, they would use unstandardized partial slopes

Here the researchers wants to predict the value of a dependent variable based upon known independent variables for a specific case.

The dependent variable is variable that affected by other variables and the independent variable is the variables that does not affected by other variables.

The unstandardized partial slopes is defined as the average changes in the y units change in x units, at the same time all other predictor variable held constant

Therefore, they would use unstandardized partial slopes

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The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

To determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.

1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.

2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.

3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.

To find the total number of possible outcomes, we multiply the number of outcomes for each event together:

Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)

Total number of outcomes = n × 6 × 52

Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

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Answer:

A - The exponent of 3 is 7/9.

Step-by-step explanation:

The expression 3^(7/9) can be read as "3 to the power of 7/9".
This means that the number 3 is being multiplied by itself 7/9 times.

For example
3^(2/3) can be written as cube root of 3, cube root of 3 is equal to 3^(1/3) .

When the exponent of an expression is a fraction, it can be written in radical form, with the denominator of the fraction as the index of the radical. However, it's not true in this case as the index is not 9 but 7.

So, the correct answer is A - The exponent of 3 is 7/9.

Answer:

B.

Step-by-step explanation: The answer is b because 65.04 is the answer we get from finding the difference of those irregular triangles and the circle.

P.S. They must be done seperately.