A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 3 shots. Let x = the number of shots that he makes. What is the probability that she makes 0 shots?.

P(x) = -14 + 30x + 26x⁴ has four roots. The solution has been obtained by using properties of polynomials.

What is a polynomial?

The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

We are given a polynomial as P(x) = -14 + 30x + 26x⁴.

It is a polynomial of degree 4 as the highest power is 4.

We know that the number of roots is equal to the degree of the polynomial.

Here, since the degree is 4, so it has 4 roots.

Hence, P(x) = -14 + 30x + 26x⁴ has four roots.

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The probability of selected exactly three girls is A 0.022

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this case, the probability of an event us usually represented as a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

In this situation, the probability of selected exactly three girls is 0.022. This can easily be seen in the table.

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Answer:

1. 4

2. [tex]cos^2(sin^2(0))tan^2(0)[/tex]

3. sec^2 theta

Hope it helped!

The required point slope of the line shown in the graph is y + 4 = 2(x - 3).

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
From the graph, we have two points on the line (3, -4) and (6, 2)

The slope of the line, with the help of the two-point, is given as,

m = (y₂ - y₁) /  (x₂ - x₁)

m = 2 + 4 / 6 - 3
m = 6/3
m = 2

Now,
The equation of the line having a slope of m = 2 and passing through (3, -4) is given as

y - y₁ = m (x - x₁)

y + 4 = 2(x - 3)
y = 2x - 6 - 4
y = 2x - 10

Thus, the required point slope of the line shown in the graph is y + 4 = 2(x - 3).

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Answer:

193 1/3

Step-by-step explanation:

First, we need to convert [tex]\frac{145}{3}[/tex] into a mixed number.

Now, we can add them together:

Therefore, the answer is [tex]193\frac{1}{3}[/tex].

By proportion formula and Pythagorean theorem, the length of line segment AB is equal to 8 units.

Herein we find a geometric system formed by two similar right triangles, then we can determine the length of side BD by following proportion formula:

BD / AD = CD / BD

BD² = AD · CD

BD = √(AD · CD)

And the length of the line segment AB can be determined by Pythagorean theorem:

AB = √(BD² + AD²)

If we know that AD = 4 and CD = 12, then the length of the line segment AB is:

BD = √(4 · 12)

BD = √48

BD = 4√3

AB = √[(4√3)² + 4²]

AB = 8

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Answer:

x = 54

Step-by-step explanation:

See picture below :)

Answer:

a. Possible outcomes for this chance experiment are:

(Here, D means a defective battery, and N means a nondefective battery.)

b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.

c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.

A linear relationship between two quantities can be modeled using a mathematical function.

Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.

The form of the function is generally expressed as y = mx + b, where y is the dependent variable, m is the slope of the line, x is the independent variable, and b is the y-intercept. The slope of the line, m, can be calculated from two points on the line using the formula m = (y2-y1)/(x2-x1). The y-intercept, b, can be calculated by substituting any point into the equation y = mx + b and solving for b.

Once the slope and y-intercept are known, the equation can be used to predict the value of the dependent variable given a certain value of the independent variable. For example, if the equation is y = 3x + 4, then for any given value of x, the corresponding value of y can be calculated. For x = 5, the corresponding value of y is 19 (5 x 3 + 4 = 19). This equation can also be used to graph the linear relationship between the two variables; by plotting the equation, a straight line is produced.

By using a function to model a linear relationship between two quantities, it is possible to calculate the relationship between them and predict values for either one given the other. This can be a useful tool for understanding the data and for making predictions about the data.

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The solution is, the function is  g(x) = (x -5)² + 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

we know that,

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

"a" is the vertical stretch

-a is a reflection over the x-axis

h is the horizontal shift (positive = right, negative = left)

k is the vertical shift (positive = up, negative = down)

given that,

f(x) = (x-2)² + 1

now we have,

Given: 3 units left   -->   h = -3

so, we get,          

g(x) = (x - 2- 3)² +1

       =(x-5)² + 1

Hence, The solution is, the function is  g(x) = (x -5)² + 1.

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This equation demonstrates the distributive property of multiplication

What is distributive property ?

In mathematics, the distributive property is a property of binary operations that applies to numbers, sets, or other mathematical objects. It governs how to perform the operation of multiplication over addition or subtraction. The distributive property states that for any numbers a, b, and c:

a × (b + c) = a × b + a × c (multiplication distributes over addition)

or

a × (b - c) = a × b - a × c (multiplication distributes over subtraction)


The property demonstrated in this equation is the distributive property of multiplication over addition. This property states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. In other words, a(b + c) = ab + ac.

In this case, 15 is being multiplied by the sum of 5 and 7, which is equivalent to multiplying 15 by 5 and 15 by 7 separately and adding the results. So, we have:

15(5 + 7) = 15 x 5 + 15 x 7

This equation demonstrates the distributive property of multiplication over addition.

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The period of the sine function is given as follows:

2π.

Hence the frequency is given as follows:

0.5/π Hz.

The standard definition of a sine function is given as follows:

y = Asin(Bx + C) + D.

The parameters are given as follows:

A: amplitude.

B: the period is 2π/B.

C: phase shift.

D: vertical shift.

From the function defined in this problem, the parameter B is given as follows:

B = 1.

Hence the period of the function is given as follows:

P = 2π/1 = 2π.

The frequency is the inverse of the period, hence it is given as follows:

f = 1/p

F = 1/(2π)

F = 0.5/π Hz.

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The decibel measurement for the quiet room is 54 dB.

To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.

Next, we can use the formula for decibel measurement:

dB = 10 log (I/I0)

where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.

Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:

dB = 10 log (500/1)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.

To correct this mistake, we need to use the formula for decibel measurement with the correct values:

dB = 10 log (500 * I0/I0)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.

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To determine Kristina's refund or tax liability, we need to calculate her total tax liability and compare it to the total amount of federal withholding that was taken out of her paychecks throughout the year.

From the previous question, we know that Kristina's federal tax liability for the year is $668.00.

To calculate her total federal withholding, we need to multiply the amount taken out of each biweekly paycheck by the number of pay periods in a year. If $89.50 was taken out of each biweekly paycheck, then the total federal withholding for the year would be:

$89.50 x 26 = $2,327.00

To determine Kristina's refund or tax liability, we subtract her total federal withholding from her total tax liability:

$2,327.00 - $668.00 = $1,659.00

Since the result is a positive number, it means that Kristina will have a tax liability when she files her taxes. Specifically, she will need to pay $1,659.00 in federal taxes for the year.

Therefore, the answer is option B) Pay $1,011.75.

The point that is a solution to the system of inequalities y < −2x + 10 and y < 1/2x − 2 is point E at (4, -2). This is because point E satisfies both inequalities.

When we plug in the x and y values of point E into the first inequality, we get -2 < -2(4) + 10, which simplifies to -2 < 2, which is true.

When we plug in the x and y values of point E into the second inequality, we get -2 < 1/2(4) - 2, which simplifies to -2 < 0, which is also true. Therefore, point E is a solution to the system of inequalities.

For question 7, the correct answer is −10 < x < 35 and 0 < y ≤ 38. This is because the temperature must be between -10 and 35 degrees, and there must be between 0 and 38 people on the trip.

For question 8, the correct answer is 2x + 3y < 60. This is because a small rug requires 2 hours for dyeing and a medium-size rug requires 3 hours for dyeing, and the total time must be less than 60 hours.

For question 9, the correct answer is the graph with a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above.

This is because the solution to the system of inequalities is the area where both inequalities are true, which is the area where they have shading in common. In this case, it is the area above both dashed lines.

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The difference quotient expression for the given function is

[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]

The expression in single-variable calculus is usually referred to as the difference quotient.

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.

The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.

Consider the difference quotient formula,

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

Evaluate the function at x = x + h

replace the variable x with (x + h) in the given expression

[tex]f(x+h)=\sqrt{(x+h)^2-1}[/tex]

simplify the result ,

[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]

find the components of the definition,

[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]

[tex]f(x)=\sqrt{(x+1)(x-1)}[/tex]

plug in the components,

[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]

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Answer: 3/8

Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.

The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.

The process involves two steps:

Here,
First, we need to prove the statement is true for the base case n=0,

When n=0, we have,

[tex]\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2[/tex]

and

[tex]n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2[/tex]

Therefore, the statement is true for n=0.

Next, we assume the statement is true for some arbitrary integer k, meaning:

[tex]\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2[/tex]

We want to show that the statement is also true for n=k+1,

[tex]\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2[/tex]

We can rewrite the left-hand side of the equation as,

[tex]=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2[/tex]

This last step used the assumption that the statement is true for n=k.

Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

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Answer:

48.

Step-by-step explanation:

Area of a rectangle formula is [tex]l[/tex]·[tex]w[/tex]

[tex]6[/tex] · [tex]8[/tex] [tex]= 48[/tex]

Thus, the area of the rectangle equals 48.

A researcher who examines the causal relationship between amount of exercise (randomly assigned as 30 minutes per day or none) and memory abilities is using the experimental research design.

The experimental research design involves the use of two sets of variables;

It is the process of carrying out research in an objective and controlled way in order to achieve precision and specific conclusions are drawn from the hypothesis statement.

Ultimately, the purpose of experimental research design is to establish the effect that a factor has a dependent variable.

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The distance from Megan to the point on the ground directly below the kite would be = 80yd

To calculate the distance, the Pythagorean formula should be used such as follows;

c² = a² + b²

a = 60yd

C= 100yd

b = ?

That is;

100² = 60² + b²

make b the subject of formula;

b² = 10,000 - 3600

b² = 6400

b= √6400

b = 80yd

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The percentage of amount paid toward principal is, 70.4%

And, the percentage of amount paid towards interest is,

⇒ 20.6%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

An individual borrowed $95,000 at an APR of 5%.

Hence,

The percentage of amount paid toward principal can be calculated as;

Percent amount = 95,000/(450 × 25 × 12) × 100

                         = 95,000 / 135,000 × 100

                         = 70.4%

Hence, And the percentage of amount paid towards interest will be:

⇒ 100% - 70.4%

⇒ 20.6%

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The types for each person are:

P1 belongs to type A

P2 belongs to type C

P3 belongs to type C

What is Statements?

Facts regarding a mixed company are key statements to add in the objective summary.

Let's assume that there are three possible types: A, B, and C. Then, we can use a process of elimination to determine the type of each person based on the given statements.

First, we know that P1 claims to belong to type A. Therefore, we can eliminate type A as a possibility for P2 and P3.

Next, P2 claims that P1 does not belong to type B. Since P1 has already claimed to be type A, we can eliminate type B as a possibility for P1. Therefore, we know that P1 belongs to type A and P2 does not belong to type B.

Finally, P3 claims that P2 does not belong to type B. Since we have already determined that P2 does not belong to type B, we can eliminate type B as a possibility for P3. Therefore, we know that P3 belongs to type C.

So the types for each person are:

P1 belongs to type A

P2 belongs to type C

P3 belongs to type C

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The best description of the expression 6(x + 10) is given as follows:

The product of a constant factor 6 and a 2-term factor x + 10.

The expression for this problem is defined as follows:

6(x + 10).

The 6 before the parenthesis means that the distributive property is applied, meaning that we have a product of two amounts, which are given as follows:

Meaning that the second option is the correct option.

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So, in response to the above question, we can state that  The differential equation has a second solution, which is this.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical.

When we differentiate y2(x) with regard to x, we obtain:

[tex]y2'(x) = v'(x)y1(x) plus v(x)y1' (x)\\v"(x)y1(x) + 2v'(x)y1'(x) + v(x)y1" = y2"(x) (x)\\y2'(x) - y2(x) = 6y2"(x)\\[v"(x)y1(x), 2v'(x)y1'(x), and v(x)y1'(x)] [v(x)y1'(x) + v'(x)y1(x)] - v(x)y1(x) = 0\\3 + 2ex/3)v'(x) + 6v"(x) = 0\\[/tex]

A first-order linear differential equation in v' is shown below (x).

[tex]e(x/2 + (2/9)e(x/3)) = u(x)\\3 + 2ex/3 + 6u(x)v"(x)\\u(x)v'(x) = 0\\6u(x)v'(x) = C1[/tex]

where C1 is an integration constant. Calculating v'(x), we obtain:

[tex]v'(x) = C1/(6u(x))[/tex]

the expression [tex]v(x) = C1e(-x/2 - (2/9)e(-x/3)) dx/6[/tex]

[tex]y2(x) = y1(x)e(-P(x) dx)e(-P(x) dx)y1(x)e(-2) dx[/tex]

where P(x) = (3 + 2ex/3)/6 is the differential equation's coefficient for y'(x). When we replace y1(x) = ex/3 and P(x), we obtain:

y2(x) = (ex/3)

∫e^(-∫(3+2ex/3)/6 dx)

[tex](e^{(-2x/3)/9)} ex/3 e(x/2 - (2/9)e(x/3)) dx y2(x) =[/tex]

[tex]y2(x) = C1y1(x) (x)[/tex]

[tex]"e" (-x/2 - (2/9)e" (-x/3)") dx/6[/tex]

where C1 is an integration constant. The differential equation has a second solution, which is this.

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Answer:

15 x [tex]3^{2}[/tex]

Step-by-step explanation:

since each side is increased by 3, total enlargement of area will be [tex]3^{2}[/tex] times

The data set is as follows, going from smallest to largest:

$1,2,000,000, $1.5,000,000, $1.5,000,000, $2.8,000,000, $3.5,000,000, and $18,9,000,000

The middle two figures are $2.8 million and $3.5 million because the data set has six items. These two values' average is:

($2.8 million plus $3.5 million) / 2= $1.35 million.

As a result, the median serves as the most accurate measure of the centre, and its value is $1.35 million. The median price is (A), or $1.35 million.

Standard deviation is a statistical measure that indicates how much the values in a dataset deviate from the mean or average value of the dataset. It measures the spread or variability of the data around the mean.

The standard deviation is calculated by taking the square root of the variance of the dataset. The variance is the average of the squared differences between each data point and the mean. In other words, it measures how much the data points vary from the mean squared.

The formula for calculating the standard deviation is:

Standard deviation = sqrt( Sum [tex](x - mean)^2[/tex] / (n - 1) )

where x is each data point in the dataset, mean is the average value of the dataset, and n is the number of data points in the dataset.

A higher standard deviation indicates that the values in the dataset are more spread out or have more variability, while a lower standard deviation indicates that the values are more tightly clustered around the mean.

Standard deviation is widely used in statistics and data analysis to measure the variability of data and to compare the spread of different datasets. It is used to assess the degree of risk and uncertainty associated with a given set of data, and it plays a crucial role in various fields, such as finance, engineering, and social sciences.

Given that we have a range and a standard deviation for the annual contracts obtained for the sports agent's clients, we can use these measures to determine the most appropriate measure of center.

The range is the difference between the largest and smallest values in the data set, which in this case is 17.7. The standard deviation is a measure of the spread of the data around the mean, which in this case is 6.3.

If the range is relatively small compared to the standard deviation, then the mean is the most appropriate measure of the center, since it takes into account the value of every data point. However, if the range is relatively large compared to the standard deviation, then the median is a more appropriate measure of center since it is less affected by extreme values in the data set.

In this case, the range of 17.7 is relatively large compared to the standard deviation of 6.3, which suggests that the median is the most appropriate measure of the center. We can find the median by arranging the data set in order from smallest to largest and finding the middle value. If there are an even number of values, we take the average of the two middle values.

The answer (B) mode; $1.5 million is incorrect because there are two modes ($1.5 million appears twice). The answers (D) mean; of $4.9 million and (E) mean; of $5.58 million are incorrect because the range is relatively large compared to the standard deviation, which indicates that the mean may be influenced by the extreme values in the data set.

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The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.

You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :

There are 12 teams overall, which is equal to the number of leaves.

The fraction of teams that raised additional funds is:

= 4 teams / 12 total teams

= ( 4 ÷ 4 ) / ( 12 ÷ 4 )

= 1 / 3

In conclusion, the fraction of teams which raised extra money was 1 / 3.

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Answer:

Below

Step-by-step explanation:

Due to vertical angles:

5x+21 =9x -55     shows x = 19°

then WOZ = 9x-55 = 116 degrees

WOZ and WOY  are supplemenrary (add to a 180 ° straight line)

116 + WOY = 180      so WOY = 64°