The area of a triangle varies directly with the width and the height of the triangle. If 6 is the area when width = 4 and height = 3, what is the area of the triangle if width is 6 and height is 4?​

The estimate of the population proportion of defective in 10 different samples of 100 observations is A) 0.017

The estimate of the population proportion of defectives can be calculated as the sum of the number of defectives in all the samples divided by the total number of observations.

In this case, the number of defectives is 1 + 2 + 1 + 0 + 2 + 3 + 1 + 4 + 2 + 1 = 17, and the total number of observations is 10 * 100 = 1000.

Therefore, the estimate of the population proportion of defectives is 17/1000 = 0.017.

So, the answer is A. 0.017.

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When the two number of columns are added together, the result is 52. Therefore, 14 + 38 = 52.

14 + 38 =

The first step in determining the sum of 14 and 38 is to add the two numbers together.

14 + 38 = 52

The first step in determining the sum of 14 and 38 is to add the two numbers together. This is done by lining up the numbers according to their place values, and then adding the numbers in each column. In this case, the ones column is 4 and 8, which adds up to 12. The tens column is 1 and 3, which adds up to 4. When the two columns are added together, the result is 52. Therefore, 14 + 38 = 52.

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The probability that the visitor is a robot is 0.000 to three decimal places.

Probability is the likelihood that a particular event will occur. It is usually expressed as a number between 0 and 1. A probability of 0 means that the event will never happen, while a probability of 1 means that the event is certain to occur.

The formula for probability in decimal format is:

Probability (in decimal format) = Number of Possible Favorable Outcomes / Total Number of Possible Outcomes

given below

Step 1: When a visitor is flagged, it means that the website has identified the visitor as potentially suspicious or malicious.

Step 2: It is impossible to determine the exact probability that the visitor is a robot as this information is not available.

Step 3: Therefore, the probability that the visitor is a robot is 0.000 to three decimal places.

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Answer:

negative 10 and seven fifteenths

Answer:

1: negative 10 and seven fifteenths

The mistake is in the second step, and the correct option is the second one (counting from the top).

The solution of the system is (2, 1).

Here someone wants to solve the system of equations below:

2x + y = 5

3x - 2y = 4

On the first step, they isolate y on the first equation to get:

y = -2x + 5

Then they substitute that on the same equation, they get:

2x + (-2x + 5) = 5

5 = 5

That is trivial, we are replacing one equation into itself.

The substitution method needs to replace that on the other equation, so there is the mistake, then the correct option is the second.

The actual solution is given by:

3x - 2*(-2x + 5) = 4

3x + 4x - 10 = 4

7x = 4 + 10

x = 14/7 = 2

and the y-value is:

y = -2x + 5

y = -2*2 + 5 = 1

The solution is (2, 1).

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Answer:

5 units

Step-by-step explanation:

since the y- coordinates are equal, both 5, then this is a horizontal line.

the distance between the points is then the absolute difference of the x- coordinates, that is

distance = | - 3 - 2 | = | - 5 | = | 5 | = 5 units

or

distance = | 2 - (- 3) | = | 2 + 3 | = | 5 | = 5 units

Answer:

10 minutes 30 seconds

Step-by-step explanation:

begin by dividing the overall size of the tub by the amount of gallons per minute.

42/4=10.5

This means that in 10.5 minutes the tub would be full. .5 is half and half of one minute is 30 seconds.

It will take 0.6431 years or approximately 7.7 quarters for the investment to grow to $8935.

Raina deposited $5000 into an account with a 9. 4% annual interest rate, compounded quarterly.

To calculate the time it takes for an investment to grow to a certain amount at a given interest rate, you can use the formula:

T = [tex]\frac{log(\frac{A}{P}) }{log(1+\frac{r}{n}) }[/tex]

where:

T is the time in years

A is the final amount ($8935)

P is the initial amount ($5000)

r is the annual interest rate (9.4%)

n is the number of times compounded per year (quarterly = 4 times)

Plugging in the values, we get:

T = (log(8935 / 5000)) / (log(1 + 0.094 / 4))

T = [tex](\frac{log(1.787)}{log(1.0225)} )[/tex]

T = 0.6431 years or approximately 7.7 quarters (rounded to 2 decimal places).

Therefore, it will take 0.6431 years or approximately 7.7 quarters.

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k=2.081, f(x) is continuous at x=3. So correct option is A.

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous. Mathematicians up until the 19th century mostly used intuitive ideas of continuity and only took into account continuous functions. To formalize the idea of continuity, the epsilon-delta definition of a limit was established.

Since f(x)[tex]\left \{ {{k^{3}+x } for x < 3 \atop {\frac{16}{k^{2}-1 }for x\geq 3 }} \right.[/tex]

We have to check continuity at x=3, for the value of k.

So, [tex]\lim_{x \to-3 \ } f(x)= \lim_{x \to +3\ } f(3)[/tex], eq.(1)

[tex]\lim_{x \to -3\ } f(x)=k^{3} + 3\\ \lim_{x \to +3\ } f(x)= \frac{16}{k^{2}-3 } and f(3)=\frac{16}{k^{2}-3 } \\from eq.(1)\\k^{3}+3=\frac{16}{k^{2} -3}[/tex]

By option (A), put k= 2.081= 2.081³ + 3= [tex]\frac{16}{2.081^{2} -3}[/tex]

=9.01189744+3= [tex]\frac{16}{4.330561-3}[/tex]

=12.01189744=[tex]\frac{16}{1.330561}=12.0118974[/tex]

Hence, k=2.081, f(x) is continuous at x=3.

So, option A is correct.

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For the matrix [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex] , the LU-factorization is option D:  [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

Lower-upper (LU) decomposition, also known as factorization of a matrix, is the process of breaking a matrix into its lower and upper triangular components.

The given matrix is - [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex].

Generate a matrix A = LU such that L is the lower triangular matrix with principal diagonal elements being equal to 1 and U is the upper triangular matrix.

Take a matrix I =  [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Apply the elementary row operation such that - R2 → 3R1 + R2

So, it is obtained that I = [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex]

Here, lower matrix is [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex].

Here. upper matrix is  [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

Therefore, the matrix is  [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

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Answer: C.

Step-by-step explanation:

Ur getting paid for both per month. So you would add the together.

Then they had to be greater then or equal to 100.

The correct answer to the inequality representing how much you want to earn from tutoring Math and English is '15x + 10y ≥ 100', where 'x' and 'y' represent the hours you spend tutoring Math and English, respectively, multiplied by their respective rates. You aim to earn at least $100, so the total should be equal to or exceed $100.

The question is about inequalities that represent the money you want to earn from tutoring in Math and English. 'x' represents tutoring hours in Math and 'y' represents tutoring hours in English.

We multiply these by their respective rates ($15 for Math and $10 for English) and sum them up. As you want to earn at least $100, this sum should be equal to or greater than $100.

Therefore, the correct inequality that represents this scenario is 15x + 10y ≥ 100 since you're adding, not subtracting, the possible earnings from each subject and that total needs to be greater than or equal to your desired weekly wage of $100.

So, the correct answer is C: 15x + 10y ≥ 100.

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The function C(x) that gives the total cost in a day as a function is C(x) = 0.03x + 1000

The inverse function is C^-1(x) = 100/3x - 100000/3

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

Rate = $3 for every 100 reams

Initial cost = $1000

So, we have

C(x) = 3/100 * x + 1000

Evaluate

C(x) = 0.03x + 1000

To do this, we make x the subject

So, we have

0.03x = C(x) - 1000

This gives

3/100 x = C(x) - 1000

So, we have

x = 100/3 C(x) - 100000/3

Express as inverse function

C^-1(x) = 100/3x - 100000/3

This inverse function gives the number of reams of paper produced as a function of the total cost.

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Sara drank approximately 16.25 teaspoons of sugar in her 20-oz. bottle of soda.

This calculation is determining the amount of sugar that was consumed by Sara in her 20-oz. bottle of soda. The amount of sugar is given as 65 grams, and we are converting this quantity from grams to teaspoons.

One teaspoon of sugar is equivalent to 4 grams of sugar, so we divide the number of grams by 4 to find the number of teaspoons. The calculation is 65 grams divided by 4 grams/teaspoon, which gives us 16.25 teaspoons.

There are approximately 4 grams of sugar in a teaspoon, so 65 grams of sugar is equal to:

65 grams / 4 grams/teaspoon = 16.25 teaspoons

So, Sara drank approximately 16.25 teaspoons of sugar in her 20-oz. bottle of soda.

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The probability of 2 being the outcome when picking a random card is; P(2) = 40%

The outcomes of the results on the cards are either, 1, 2, 3 or 4 or more.

Now, the total possible outcome will be gotten by adding the frequencies of occurRence to get;

Total Outcome = 6 + 12 + 9 + 3

= 30

Now, the frequency of occurrence of 2 out of the total outcome is 12. Thus;

Probability of 2 being the outcome is;

P(2) = 12/30 = 0.4

Expressing in percentage gives 40%

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The value of z if the area to the right of z is 0.9803 is -2.06.

The area to the right of a standard normal random variable (z) can be calculated using the cumulative probability of the normal distribution. This can be done by using the formula P(z≤x) = Φ(x), where Φ is the cumulative probability of the normal distribution.

Since the area to the right of z is 0.9803, this implies that P(z≤x) = 0.9803.

Using the formula, this can be rearranged to solve for x. The rearranged equation is Φ(x) = 0.9803, which can then be solved using a standard normal table.

From the standard normal table, the value of x is found to be 2.06. This means that the value of z for the given area to the right of z is -2.06.

Therefore, the value of z if the area to the right of z is 0.9803 is -2.06.

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The value of a 45 degree angle in an isosceles right angled triangle is: 1

In an isosceles right angled triangle, where AB = BC = x, the sides AB and BC form the hypotenuse, and the remaining side AC forms one of the legs.

For the 45 degree angle (let's call it angle A), the sine function can be used to find the ratio of the opposite side to the hypotenuse:

Since the triangle is isosceles, AC = AB = x, therefore:

So the sine of a 45 degree angle in an isosceles right angled triangle is 1.

Note: The cosine and tangent of 45 degrees can also be found using the other trigonometric ratios, but since only sine was requested, I only provided the sine value.

Complete Question:

"ABC is an isosceles right angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios:

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The quadratic equation whose solution set is {0, 2}, is: x²-2x = 0

A Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given that, the solution of a quadratic equation is {0, 2},

The equation of a quadratic polynomial in form sum and product of solutions is given by,

x²-(α+β)x+αβ = 0, where α, β = solution of equation

α+β = 0+2

α+β = 2

αβ = 0×2

αβ = 0

Therefore, equation is x²-2x+0 = 0

Hence, the quadratic equation whose solution set is {0, 2}, is: x²-2x = 0

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As x = -7 & x = 2 are zeroes of  y=2x²+5x−24, option b. (5) and option d. (7) are NOT a potential zero.

Finding a polynomial's zeros requires the use of the rational zero theorem and synthetic division.

To generate a list of all the function's potential rational zeros, use the Rational Zero Theorem.

Analyze potential zeros via synthetic division.

The result is a zero if the remainder is 0.Any rational zero must take the form p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient, if the coefficients of a polynomial function are integers and stated in descending order of the exponents.

P(x)= x² + 5x -14

p(x) = (x+7)(x-2)

y = (x+7)(x-2)

0 = (x+7)(x-2)

x+7 = 0 , x-2=0

x = -7 , x = 2

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Use the Rational Zero Theorem to find all potential rational zeros of the polynomial y=2x2+5x−24. Which of these is NOT a potential zero?

a. x = -7

b. x = 5

c. x = 2

d. x = 7

By Using the Rational Zero Theorem, All of these are not the potential zeros of the polynomial y = 2x² + 5x - 24

The Rational Zero Theorem states that if a polynomial has rational zeros, then the zeros must be the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the potential rational zeros are:

For example:- constant term = 24 and Leading coefficient = 2.

So, p/q = ±1, ±2, ±3, ±4, ±6, ±12, ±24

To determine which of these is not a zero, we can substitute each into the polynomial and check if the result is zero. For example, when we substitute x = 1 into the polynomial, we get:

y = 2x² + 5x - 24

At x = 1

y = 2(1)² + 5(1) - 24

y = 2 + 5 - 24

y = 19 ≠ 0

At, x = 1 it is not possible.

Check, on x = 2

y = 2(2)² + 5(2) - 24

y = 8 + 10 - 24

y = -6 ≠ 0

y = 2 is also not possible.

Check, on x = -2

y = 2(-2)² + 5(-2) - 24

y = 8 - 10 - 24

y = -26 ≠ 0

y = -2, is also not possible.

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Use the Rational Zero Theorem to find all potential rational zeros of the polynomial y=2x2+5x−24. Which of these is NOT a potential zero?

a. x = 1

b. x = 2

c. x = -2

d. all of these

Answer:

m=log(l)n. is the equation equivalent.

Considering that Parker uses 1 gallon of gas for every 0.026 miles he drives, he can travel 1.149 miles on 44.2 gallons of fuel.

The unitary is a method of troubles that entails calculating the value of a single unit, multiplying that value, and then calculating the required value. To sum it up, the unit method is employed to obtain a single unit quantity from a specified multiple. One writer costs 400 rupees, and 40 pens would cost 400 rupees. Perhaps there is a regular procedure for carrying it out. merely one nation. anything featuring a distinctive component. Algebra of matrices or operators, linear programming, applied mathematics, and its homologue and reciprocal are all equivalent.

given

For 34 miles and 1305, Parker's mileage is directly proportionate to the amount of gallons used.

1 gallon equals 0.026 miles, so 6 gallons are required.

Consequently, 1.149 miles equal 44.2 gallons of gas.

Considering that Parker uses 1 gallon of gas for every 0.026 miles he drives, he can travel 1.149 miles on 44.2 gallons of fuel.

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The values of A,B,C are 1/4,0.-1/8 respectively.

If the degree of both f(x,y) and g(x,y) are the same, a differential equation of the form f(x,y)dy = g(x,y)dx is said to be homogeneous. For k>0, a homogeneous function of degree n is a function of type F(x,y) that may be expressed in the form kn F(x,y). As a result, f and g are the same-degree homogeneous functions of x and y.

The characteristic equation of homogeneous problem and its zeros:

r²+4=0

r= ±2i

Homogeneous solution:

yc=c1 cos 2t+ c2 sin 2t

set Y1= At²+ Bt+C

Plugging in Y1 into the starting equation:

2At+ 4At²+ 4Bt+4C=t²

A=1/4

B=0

2A+4C= 0

4C= -1/2

C= -1/8

Thus, the values of A,B,C are 1/4,0.-1/8 respectively

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The value of expression to represent stickers Niu has left is,

⇒ 24 - 4x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Niu has decorated x cards.

He started with 24 stickers, and he used 4 stickers per card.

Now, Number of used stickers in x cards =  4x

Hence, The value of expression to represent stickers Niu has left is,

⇒ 24 - 4x

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Answer:

[tex]x > -5[/tex]

Step-by-step explanation:

Flip the equation over- [tex]10x+16 > 9x+11[/tex]

Now do [tex]10x-9x=x[/tex]

So the equation now looks like this [tex]x+16 > 11[/tex]

Now subtract 16 from both sides to give you the answer [tex]x > -5[/tex]

Answer: [tex]x > \Large\boxed{-5}[/tex]

Step-by-step explanation:

Given inequality

[tex]9x+11 < 10x+16[/tex]

Subtract 9x on both sides

[tex]9x+11-9x < 10x+16-9x[/tex]

[tex]11 < x+16[/tex]

Subtract 16 on both sides

[tex]11 -16 < x+16-16[/tex]

[tex]-5 < x[/tex]

[tex]x > \Large\boxed{-5}[/tex]

End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.

Here,

End behavior of a function f specifies how the function's graph behaves at the "ends" of the x-axis. In other words, when we look to the right end of the x-axis (as x approaches +) and to the left end of the x-axis (as x approaches ), the end behavior of a function explains the graph's trend.

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The difference between the two girl at first is 120 - 24 = 96 weet.

I determined the answer by using algebra. I started by defining the original number of weet that Sally had as x. Then, I used the information given in the problem to set up two equations:

       x = 24

Now that I know that Sally originally had 24 weet, I can use that information to find the original number of weet that Devi had. According to the problem, Devi had five times as many weet as Sally, so:

Finally, I subtracted Sally's original number of weet (24) from Devi's original number of weet (120) to find the difference between the two:

So, the difference between the two girls at first was 96 weet.

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There are 4 possible nitrogenous bases, so for each position in the DNA sequence there are 4 options to choose from. Therefore, in a single base position there are 4 possible mutations. In a double base position, there are 4 * 4 = 16 possible mutations. This means that for 11 double base positions, there are 11 * 16 = 176 possible double letter mutations.

DNA (Deoxyribonucleic Acid) is the genetic material that encodes the instructions for the development and function of all living organisms. DNA is made up of four nitrogenous bases: adenine (A), cytosine (C), guanine (G), and thymine (T).

The sequence of these nitrogenous bases is what determines the genetic information of an organism. Mutations are changes in the DNA sequence that can occur naturally or as a result of environmental factors.

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Answer:

6

Step-by-step explanation:

70 sign up

11.5 each visit  assuming w visits

so to get to 139

11.5w +70=139

11.5w =69

w= 6

The complete sentence:

Produce per pound costs less than meat per pound because the slope of the graph for meat is greater to that of the graph for produce.

The slope of the graph tells you the unit rate in dollars per pound.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

Given:

The graph's x-axis displays weight in pounds and the y-axis the cost in dollars.

The slope of a line is constant and indicates the unit rate of change.

The graph's slope, then, shows the unit rate in dollars per pound.

Also, the slope is higher on the steeper line (closer to the y-axis).

Considering the graph,

The graph of the line shows that the price of meat per pound is higher than the price of vegetables per pound.

Therefore, the line for meat is larger than the graph for produce, the price of meat per pound is higher than the price of produce per pound.

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The complete question is given in the attached image.

[tex]\huge\begin{array}{ccc}A.&\left(\frac{f}{g}\right)(x)=\frac{\sqrt[3]{2x}}{2x+1},&x\neq-\frac{1}{2}\end{array}[/tex]

We have the functions:

[tex]f(x)=\sqrt[3]{2x}\\\\g(x)=2x+1[/tex]

Let's define the domain of the functions:

[tex]D_f:x\in\mathbb{R}\\\\D_g:x\in\mathbb{R}[/tex]

Make the function

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{\sqrt[3]{2x}}{2x+1}[/tex]

Let's define the domain of the function:

[tex]D:2x+1\neq0\\\\2x+1-1\neq0-1\\\\2x\neq-1\\\\\dfrac{2x}{2}\neq\dfrac{-1}{2}\\\\x\neq-\dfrac{1}{2}[/tex]

The solution for a for the expression in this problem is given as follows:

a = 2.4.

The expression for this problem is defined as follows:

3/4(12a + 8) = 27.6.

We want the solution for the variable a, hence the variable a must be isolated.

Applying cross multiplication, we have that:

3(12a + 8) = 27.6 x 4.

Now with the distributive property, we have that:

36a + 24 = 110.4

36a = 110.4 - 24

a = (110.4 - 24)/36

a = 2.4.

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