Ten letter tiles are placed in a bag. Once a tile has been drawn, it is not placed back in the bag. What is the probability that someone will randomly select the letter tiles in order to spell STATISTICS?

The amount of money you get paid if  the coin comes up heads 3 times is $12.

You flip a coin 3 times,

If you get o heads then $0

If you get 1 heads then $2

If you get 2 heads then $ 4

So if you toss the coin 3 times and 3 heads come up then

1 heads = $2

2 heads = $ 4

3 heads = $ 6

So , amount of money you get paid if  the coin comes up heads 3 times is $12.

The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, assessed at x. It is employed to describe a table's random variables' probability distribution. And with this data, we can quickly make a CDF graphic on an Excel spreadsheet.

So, CDF determines the cumulative probability for the specified value.

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The quotient of 47.61 and 15.87 has the result given as follows:

47,61 : 15,87 = 3.

The operation for this problem is defined as follows:

47,61 : 15,87 =

The : symbol means that the operation is a division, that is, we must obtain the quotient of dividing 47.61 by 15.87.

Using a calculator, we have that 47.61 is three times 15.87, hence the result of the quotient is given as follows:

47,61 : 15,87 = 3.

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The solution is Option C.

The value of the quadratic equation is 5x² + 2x = 7

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

5x² + 2x = 7  

On simplifying the equation , we get

Subtracting 7 on both sides of the equation , we get

5x² + 2x - 7 = 0   be equation (1)

Now , the roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -2 ± √ ( 4 - 4 ( 5 ) ( -7 ) ] / 10

x = [ -2 ± √ ( 144 ) ] / 10

x = ( -2 ± 12 ) / 10

So , the two roots of the equation are

x = ( -2 + 12 ) / 10

x = 10/10 = 1

And , x = ( -2 - 12 ) / 10

x = -14/10

x = -7/5

Hence , the roots of the quadratic equation are 1 and -7/5

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Water vapor is created when liquid water evaporates, and this water vapor then develops into clouds and falls back to earth as rain and snow.

Weather is the culmination of the present meteorological variables, such as temperature, wind speed and direction, precipitation amount and kind, weather is great hours, etc. The weather dictates a little window of time up over several days.

What you perceive outside when any given day is the weather. Therefore, for instance, it may be 20 ° with heavy snow or it could be 75 degrees and sunny. That is the climate. The average of the weather is the climate.

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B and E are both right angles.

C is an acute angle.

B and E are both 90⁰ as they are marked with a square on the angle. C is acute as it can not be larger than 90⁰ as angles in a triangle add up to 180⁰.

The length of the rectangular patio is 57 ft.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is that the perimeter of a rectangular patio is 204 feet and the width of the patio is 45 feet.

We can write -

2(L + B) = 204

L + B = 102

L = 102 - 45

L = 57

Therefore, the length of the rectangular patio is 57 ft.

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{Question in english -

The perimeter of a rectangular patio is 204 feet if the width of the patio is 45 feet what is the length of the patio}

The model product, P(16), predicts the number of moose to be 3545 in 1997 and 2970 in 2009.

The odds that a happening will happen or a claim will be true is measured by probability theory, a branch od arithmetic. The probability of an item is a number between 0 but also 1, where about 0 represents how frequently the event is to occurring and 1 represents certainty. A risk is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities may be expressed as percentages ranging from 0percent to 100% as well as from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a whole set of equally plausible options that lead to a specific occurrence.

given

We'll choose x on the graph to represent the number of years since 1990 and y to represent the number of moose.

On the graph, there are two points: (4, 4290) and (8, 3850)

We can determine the slope of this line using the slope formula (m = [y2 - y1]/[x2 - x1]):

Replacement: m = (3850 - 4290)/(8 - 4)

m = -440/4 Solve the parenthesis's subtraction puzzles.

m = -110 Reduce the percentage

Since we know the line's slope, we can apply the point-slope formula (y - y1 = m[x - x1]) to determine the line's equation.

P(16) = 2970

The model product, P(16), predicts the number of moose to be 3545 in 1997 and 2970 in 2009.

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Answer: Yes at x = 2.

Step-by-step explanation: There are two ways to do it. Graph the function or solve it. Since im on a computer solving would be easiest for me to explain. To find a point where the two lines meet, you should set the two equations equal to each other. When you solve by subtracting 1/2x on both sides, the result is 3/2x = 3. This means that x=2. When you graph you should see that when x =2 the answer is right.

Answer:

19/8

Step-by-step explanation:

[tex]a\frac{b}{c}=\frac{ac+b}{c}\\\\2\frac{3}{8}=\frac{2(8)+3}{8}=\frac{16+3}{8}=\frac{19}{8}[/tex]

Answer:

= 19/8

Step-by-step explanation:

2 = 16/

2 3/8 = 2+3/8 = 16/8 + 3/

= 19/

The solution to the system of equations in this problem is given as follows:

(-5, 4).

The system of equations for this problem is defined as follows:

Applying linear combination, we can add the equations and remove the variable y, hence the solution for x of the system of equations is obtained as follows:

3x = -15.

x = -15/3

x = -5.

Then the solution for y is given as follows:

-5 - 4y = -21

4y = 16

y = 16/4

y = 4.

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The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

a) The equation is given as,

4 / 8 = 3 / (y - 1)

1/2 = 3 / (y - 1)

y - 1 = 6

y = 7

b) The equation is given as,

5 / (7 + 2x) = 2 / (x + 2)

5(x + 2) = 2(7 + 2x)

5x + 10 = 14 + 4x

5x - 4x = 14 - 10

x = 4

The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.

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The required cost of carpet is $1,148.

Hence option (c) is correct.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Cost of carpet of dimension 10 ft x 6 ft = $1230

Then cost of carpet of area 60 ft² = $1230

The cost of carpet per unit area = 1230/60

                                                      = $20.5

Area of carpet 7 ft x 8 ft =  56 ft²

Then the cost of this carpet

= 56x20.5

= 1,148

Therefore, the cost of carpet of dimension 7 ft x 8 ft = $1,148

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Answer:

You would have to buy three raffle tickets to have a chance to receive all three pieces of merchandise.

Step-by-step explanation:

Each raffle ticket gives you a chance to win one of the three pieces of marching band merchandise: T-shirt, hat, or shorts. To have a chance of winning all three pieces, you would need to buy three separate raffle tickets, each with a chance to win a different piece of merchandise. This way, you would increase your chances of receiving all three pieces through the random selection process of the raffle.

If each raffle ticket has an equal chance to win any of the three pieces of merchandise, then you would have a 33% chance of winning any one piece of merchandise with each ticket you buy. To have a greater chance of winning all three pieces, you would need to buy multiple tickets.

For example, if you buy three tickets, the chance of winning all three pieces of merchandise would be (1/3) * (1/3) * (1/3) = 1/27. This means that you have a 1 in 27 chance of winning all three pieces of merchandise with three raffle tickets.

Answer:3 i d k

Step-by-step explanation:

The data are discrete because the data can only take on specific values, So correct option is B.

Discrete data refers to data that can only take on specific, separate values. It is a type of data that can be counted or enumerated, but not measured. In other words, the values can't be expressed as fractions or decimals between two whole numbers. Some examples of discrete data include the number of siblings in a family, the number of pets owned by an individual, and the number of correct answers on a test. Discrete data is distinct from continuous data, which can take on any value within a certain range.

The data are discrete because the data can only take on specific values (e.g. a time of 20 minutes, 21 minutes, 22 minutes, etc.). They cannot take on any value in an interval, such as 20.5 minutes. Discrete data represent a countable number of values, while continuous data can take on any value within a given range.

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The value of cot(θ - π/2) is 1.52.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.

There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their respective angles using trigonometric ratios.

Given that tan θ = -1.52.

The given expression is

cot(θ - π/2)

= - cot(π/2 - θ)

Now applying the trigonometry identity cot(π/2 - θ) = tan θ:

= - tan θ

Now putting the value of tan θ = -1.52:

= - (-1.52)

= 1.52

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Answer:

84.8 squared centimeters

Step-by-step explanation:

You know the height is 8 cm

You know one of the bases has a length of 15.5 cm

You know one of the bases has a length of 5.7 cm

Formula to find a trapezoid:

[tex]\frac{b_{1}+b_{2}}{2}[/tex]×h

so...

substitute!!!!!

As a result, f(x-3) = x² - 6x + 13, as well as the simplified expression for f(x) = x² +4.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided.

Here,

To simplify the expression f(x-3), we need to substitute x-3 for x in the original expression f(x) = x² + 4.

So, f(x-3) = (x-3)² + 4

= x² - 6x + 9 + 4

= x² - 6x + 13

Therefore, f(x-3) = x² - 6x + 13 and also the simplified expression for f(x) = x² +4.

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the matrix equation for the given vector equation is:

[tex][ [5 0] [5 2] [-3 3] [4 -2] ] [z_1, z_2, z_3, z_4]^T = [-3 19]^T[/tex]

An equation of the form Av = b, in which A is a m by n matrix known as the coefficient matrix, v is a n by 1 column vector, and b is a m by 1 column vector, is known as a matrix equation (also known as a matrix-vector equation).

Given the vector equation:

[tex]z_1 [5 0] + z_2 [5 2] + z_3 [-3 3] + z_4 [4 -2] = [-3 19][/tex]

We can write this as a matrix equation by defining a matrix A and a vector x, such that:

A = [ [5 0]

[5 2]

[-3 3]

[4 -2] ]

[tex]x = [z_1, z_2, z_3, z_4]^T[/tex]

The vector equation then becomes:

[tex]Ax = [-3 19]^T[/tex]

So the matrix equation for the given vector equation is:

[tex][ [5 0] [5 2] [-3 3] [4 -2] ] [z_1, z_2, z_3, z_4]^T = [-3 19]^T[/tex]

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Dan spent 1.25 at each table.

The formula used to solve this problem is m = 16 - 6/8. The calculation is as follows: 16 is the total amount of money Dan spent, 6 is the admission fee, and 8 is the number of tables. The equation is set up to find the amount of money Dan spent at each table. Taking the total amount of money spent, 16, and subtracting the admission fee, 6, leaves us with 10. We then divide this amount, 10, by the number of tables, 8, to find the amount of money spent at each table, which is 1.25. Therefore, Dan spent 1.25 at each table.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3690.37\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]3690.37 = 3000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{3690.37 }{3000}=\left(1+\cfrac{r}{100} \right)^4 \\\\\\ \sqrt[4]{\cfrac{3690.37 }{3000}}=1+\cfrac{r}{100}\implies \sqrt[4]{\cfrac{3690.37 }{3000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{3690.37 }{3000}}=100+r\implies 100\sqrt[4]{\cfrac{3690.37 }{3000}}-100=r\implies \boxed{5.3\approx r}[/tex]

Answer:

5.3 is about r

Step-by-step explanation:

The p-value for the test is  0.0062

To determine the p-value for Kara's hypothesis test, we need to calculate the test statistic and then find its corresponding p-value.

Let's start by calculating the sample mean and standard deviation of the given data:

Sample mean x = (46+43+41+48+51+51+52+42+51+54+40+53+46+46+46+39+47)/17 = 46.529

Sample standard deviation (s) = 4.547

We can use these values to calculate the t-statistic for the one-sample t-test:

t = (x - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (50 hours), n is the sample size (17).

t = (46.529 - 50) / (4.547 / sqrt(17)) = -3.15

Using a t-distribution table with 16 degrees of freedom (n-1), we find that the p-value for a two-tailed test with a t-statistic of -3.15 is approximately  0.0062.

Therefore, the p-value for this hypothesis test is  0.0062

Since the p-value is less than the commonly used alpha level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the true mean work week for engineers in start-up companies is less than 50 hours.

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The distribution is b) skewed.

The sum of the probabilities is: 1

In a binomial distribution, p represents the probability of success. Success in the sense that the event of interest happens. In the model presented, the probability of success p is 0.4 since we are informed that 40% of adults watch a particular television show.

The next quantity of significance in a binomial model is the number of independent trials, n.

In our case there are 6 independent trials since we are told that 6 adults were selected at random. If we let the random variable K denote the number of adults out of the 6 who watch the television show, then K is a binomial random variable with parameters;

n = 6 and p = 0.4

A binomial distribution is only symmetric when either p is 0.5 or n is large. In the presented scenario none of these conditions is met since p is 0.4 while n is just 6 which is relatively small.

Thus we conclude that the distribution is not symmetric but rather skewed.

The sum of the probabilities is any discrete probability distribution such as the Bernoulli, binomial, negative binomial, Poisson, or the geometric distribution is always equal to 1. That's a rule of thumb.

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By solving the equation 3x = x² - 4, we know that the positive solution of the given problem is x = 4.

Using the equal symbol, they are linked.

For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

So, using the given  information, form the following equation:

3x = x² - 4

Now, solve this equation as follows:

3x = x² - 4

0 = x² - 3x - 4

0 = (x-4)(x+1)

Then, x = 4 and x = -1

Therefore, by solving the equation 3x = x² - 4, we know that the positive solution to the given problem is x = 4.

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By using the relationship between quantities, the missing values in the table are:

A = 750

B = 1,250.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be represented by this mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in this 2-column table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 250/1

Therefore, a linear equation for this proportional relationship can be correctly written as follows:

y = kx

y = 250x

When x = 3, the value of A is given by:

y = 250(3) = 750.

When x = 5, the value of A is given by:

y = 250(5) = 1,250.

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Answer:

A.  (0, 0)

Step-by-step explanation:

To find the center of the circle that can be circumscribed about the given triangle, find the triangle's circumcenter.

A circumcenter of a triangle is:

A perpendicular bisector is a line that divides another line segment into two equal parts at a right angle.

Add perpendicular bisectors to the sides of the triangle (shown in green on the attached diagram).

The point of intersection of the perpendicular bisectors is (0, 0).

Therefore, the center of the circle that can be circumscribed about the triangle is (0, 0).

Answer:

The area of the region inside both the square and the rectangle is 37 square units.

Step-by-step explanation:

The area of the region inside both the square and the rectangle can be found by subtracting the areas of the four triangles outside the square from the area of the rectangle.

The area of the rectangle is 4 * 8 = 32 square units. The area of each triangle can be found using the formula for the area of a triangle, which is (base * height) / 2. The base of each triangle is half the length of the side of the square, which is 5 / 2 = 2.5 units. The height of each triangle is the difference in height between the rectangle and the square, which is 4 - 5 = -1 unit. The area of each triangle is (2.5 * -1) / 2 = -1.25 square units. The area of the four triangles outside the square is 4 * -1.25 = -5 square units.

The area of the region inside both the square and the rectangle is 32 + 5 = 37 square units.

The work done by the force 4i−3j+2k is the scalar product of the force vector and the displacement vector between the two points. In this case, the displacement vector is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units.

Work is the scalar product of the force and displacement vectors. The force vector in this problem is given as 4i−3j+2k, while the displacement vector (the vector from the starting point to the end point) is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units. This means that the work done by the force is 15 units.

The work done by a force is the energy transferred to an object by the force. It is calculated by taking the scalar product of the force and displacement vectors. This scalar product gives the magnitude of the work done by the force, which in this case is 15 units. This means that the force transferred 15 units of energy to the object by moving it from the starting point to the end point.

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Answer:

b

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb