How do you write 0.327 as a percentage

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Hence, a shift register with a minimum of 8 stages would be necessary to generate the given sequence.

To determine the minimal number of stages of a shift register necessary for generating the given sequence, we need to find the length of the shortest feedback shift register (FSR) capable of generating the sequence.

Looking at the sequence 0 1 0 1 0 1 1 0, we can observe that it repeats after every 8 bits. Therefore, the minimal number of stages required for the shift register would be equal to the length of the repeating pattern, which is 8.

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Answer:

The probability of winning directly is, as you calculated, 8/36, and the probability of losing directly is (1+2+1)/36=4/36.

For the remaining cases, you need to sum over all remaining rolls. Let p be the probability of rolling your initial roll, and q=6/36=1/6 the probability of rolling a 7. Then the probability of rolling your initial roll before rolling a 7 is p/(p+q), and the probability of rolling a 7 before rolling your initial roll is q/(p+q). Thus, taking into account the probability of initially rolling that roll, each roll that doesn't win or lose directly yields a contribution p2/(p+q) to your winning probability.

For p=5/36, that's

(536)25+636=2511⋅36,

and likewise 16/(10⋅36) and 9/(9⋅36) for p=4/36 and p=3/36, respectively. Each of those cases occurs twice (once above 7 and once below), so your overall winning probability is

836+236(2511+1610+99)=244495=12−7990≈12−0.007.

Step-by-step explanation:

Suppose you throw a 4 and let p(4) your winning probability. At your next roll you have a probability 3/36 of winning (you throw a 4), a probability 6/36 of losing (you throw a 7) and a probability 27/36 of repeating the whole process anew (you throw any other number). Then:

p(4)=336+2736p(4),so thatp(4)=13.

Repeat this reasoning for the other outcomes and then compute the total probability of winning as:

ptot=836+336p(4)+436p(5)+…

Answer:

315

Step-by-step explanation:

You're welcome
Answer above is rounded btw

Full number is:315.24444

The type of nonprobability design that is most likely to yield a representative sample is a stratified random sampling.

In stratified random sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables that are relevant to the research objective. Then, a random sample is selected from each stratum proportionally to the size or importance of that stratum in the population. This approach ensures that the sample reflects the diversity and heterogeneity of the population.

By stratifying the population and using random sampling within each stratum, the stratified random sampling design increases the likelihood of obtaining a representative sample. It allows for accurate representation of different groups within the population, which can help reduce sampling bias and provide more precise estimates of population characteristics.

However, it's important to note that even with stratified random sampling, there may still be limitations and potential sources of bias. Factors such as nonresponse rates and the accuracy of the population data used for stratification can impact the representativeness of the sample. Nevertheless, when properly implemented, stratified random sampling is a valuable nonprobability design for achieving representativeness in a sample.

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The smallest positive angle that is equivalent to A=343 degrees is 703 degrees.

To find the measure of the least positive angle that is coterminal with A, we need to determine the equivalent angle within one full revolution (360 degrees) of A.

A is given as 343 degrees. To find the coterminal angle within one revolution, we can subtract or add multiples of 360 degrees until we obtain a positive angle.

Let's subtract 360 degrees from A:

343 - 360 = -17

The result is a negative angle, so we need to add 360 degrees instead:

343 + 360 = 703

Now, we have a positive angle of 703 degrees, which is coterminal with 343 degrees.

The measure of the least positive angle that is coterminal with A is 703 degrees.

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Answer:  34

(2)(2)(1) + (5)(-3)(-2) = 34

    4     +      30       = 34

Answer:

2·2·1+5·(-3)·(-2)= 34

Step-by-step explanation:

Answer: y = -5 - 1/2 x

Step-by-step explanation:

Slope intercept form: y=mx+b

2x+4y=-20

Isolate the y.

4y=-20-2x

Divide by 4.

y=-20/4-2x/4

y = -5 - 1/2 x

Answer:

Negative

Step-by-step explanation:

A positive divided by a negative will always be negative.

Answer:

if they are both positive its positive

if ones positive and ones negitive its negative

if they are both negative its positive

Step-by-step explanation:

9514 1404 393

Answer:

  (1, 7)

Step-by-step explanation:

Fill in x=1 and do the arithmetic.

  h(1) = 4(1) +3 = 7

The coordinate pair is ...

  (x, h(x)) = (1, h(1)) = (1, 7)

To find the probability that a randomly selected patient is 0-12 years old given that the patient suffers from knee pain,

we need to use conditional probability.The conditional probability formula is:P(A|B) = P(A ∩ B) / P(B)where P(A|B) denotes the probability of A given that B has occurred. Here, A is "patient is 0-12 years old" and B is "patient suffers from knee pain".

Thus, the probability that a randomly selected patient is 0-12 years old given that the patient suffers from knee pain can be expressed as:P(0-12 years old | knee pain) = P(0-12 years old ∩ knee pain) / P(knee pain)The joint probability of 0-12 years old and knee pain can be busing the multiplication rule:P(0-12 years old ∩ knee pain) = P(0-12 years old) × P(knee pain|0-12 years old)where P(knee pain|0-12 years old) is the probability of knee pain given that the patient is 0-12 years old. We are not given this value, so we cannot calculate the joint probability.

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Answer:

Opens upward and is wider.

Step-by-step explanation:

Given:

The equation is

\(y=1.55x+110,419\)

Here, y approximates the total amount, in dollars, spent by a household to raise a child in the United States from birth to 17 years, given the household’s annual income, x.

To find:

The approximate average yearly cost of raising a child in a household with an annual income of $33,000.

Solution:

We have,

\(y=1.55x+110,419\)

Put x=33000 to get the total amount, in dollars, spent by a household if annual income of $33,000.

\(y=1.55(33000)+110,419\)

\(y=51150+110,419\)

\(y=161,569\)

So, total amount spent by a household to raise a child in the United States from birth to 17 years is $161,569.

Divide this total amount by 17 to get the average yearly cost of raising a child in a household with an annual income of $33,000.

\(\dfrac{161,569}{17}=9504.05882353\)

\(\dfrac{161,569}{17}\approx 9504.06\)

Therefore, the average yearly cost of raising a child in a household with an annual income of $33,000 is $9504.06.

Answer:

yearly cost $9,504

Step-by-step explanation:

1.55(33,000)+110,419 =161,569

161,569/17= 9,504.058823529412

took the test

Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

The system of inequalities are: y< -4x+1 and y≥(1/2)x-1

An inequality is a non-equal comparison between two numbers or other mathematical expressions in mathematics. It is most commonly used to compare two numbers on a number line based on their size.

We need to find the equations of the two lines in order to determine the graphed system of inequalities. The equations can then be used to write the inequalities.

The formula for the equation of a line is,

y=mx +c

Where m represents the slope and c is the y -intercept.

Therefore, from the given graph

m=4/-1

m=-4

And c=1

So, the equation of the lines is,

y= -4x+1

Here the line is not solid, so the inequalities are:

y< -4x+1 or y> -4x+1

From the graph one of the solution sets is the origin, which has coordinates, (0, 0)

We can test the two inequalities with this point to determine the right one. That is,

0< -4(0)+1 or 0> -4(0)+1

0< 0+1 or 0>0+1

0<1 or 0>1

We can see that the first statement is true but the second is false.

This implies that the right inequality is;

y< -4x+1

With the solid line, the slope is

m=1/2 and c= -1

Therefore, the equation is

y=(1/2)x-1

Since the line is solid, the inequalities that are possible are:

y≥(1/2)x-1 oy y≤(1/2)x-1

We have to test with the origin again, we get

0≥(1/2)(0)-1 or 0≤(1/2)(0)-1

0≥ -1 or 0≤ -1

Therefore, the second statement is true

So, the solid line inequality is,

y≥(1/2)x-1

Hence, the system of inequalities are:

y< -4x+1 and y≥(1/2)x-1

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If derivative of \(f(x)=ln(x+4+e^{(-3x)})\), then f '(0) = -2/5.

What is derivative?

In calculus, the derivative of a function is a measure of how the function changes as its input changes. More specifically, the derivative of a function at a certain point is the instantaneous rate of change of the function at that point.

To find f'(0), we first need to find the derivative of f(x) with respect to x. Using the chain rule, we get:

\(f'(x) = 1 / (x+4+e^{(-3x)}) * (1 - 3e^{(-3x)})\)

Now we can find f'(0) by substituting the value x=0:

\(f'(0) = 1 / (0+4+e^{(-3(0))}) * (1 - 3e^{(-3(0))})\)

f'(0) = 1 / (4+1) * (1 - 3)

f'(0) = -2/5

Therefore, f'(0) = -2/5.

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From the diagram, we know that:

Then, using the proportionality theorem:

Now, using the values of each segment:

The circumcenter of the triangle that has vertices at (1, 10), (-5, 2), and (7, 2) is (1, 3.75)

The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the three sides of the triangle.

The distance from the circumcenter to each of the three vertices are congruent.

The coordinates of the circumcenter can found using the as follows;

Let (x, y), represent the coordinates of the circumcenter, we get;

The distance of the circumcenter from the vertices of the triangle is the same for the three vertices, therefore;

The specified vertices of the triangle are; (1, 10), (-5, 2), and (7, 2)

The distance of the circumcenter, (x, y), from (1, 10), is therefore;

D₁ = √[(x - 1)² + (y - 10)²]

The distance of the circumcenter, (x, y), from (-5, 2), is therefore;

D₂ = √[(x - (-5))² + (y - 2)²]

The distance of the circumcenter, (x, y), from (7, 2), is therefore;

D₃ = √[(x - 7)² + (y - 2)²]

The properties of the circumcenter indicates that we get;

D₁ = D₂ = D₃

D₁ = √[(x - 1)² + (y - 10)²] = D₂ = √[(x - (-5))² + (y - 2)²] = D₃ = √[(x - 7)² + (y - 2)²]

D₁ = D₂ indicates;

√[(x - 1)² + (y - 10)²] = √[(x - (-5))² + (y - 2)²]

(x - 1)² + (y - 10)² = (x - (-5))² + (y - 2)² = (x + 5)² + (y - 2)²

(x - 1)² + (y - 10)² = (x + 5)² + (y - 2)²

x² - 2·x + y² - 20·y + 101 = x² + 10·x + y² - 4·y + 29

According to the addition and subtraction properties of equality, we get;

x² - 2·x + y² - 20·y + 101 - (x² + 10·x + y² - 4·y + 29) = 0

√[(x - 1)² + (y - 10)²] = √[(x - 7)² + (y - 2)²]

(x - 1)² + (y - 10)² = (x - 7)² + (y - 2)²

x² - 2·x + y² - 20·y + 101 = x² - 14·x + y² - 4·y + 53

x² - 2·x + y² - 20·y + 101 - (x² - 14·x + y² - 4·y + 53) = 0

Equation (1) and (2) indicates;

12·x + 16·y - 72 = 12·x - 16·y + 48

12·x - 12·x + 16·y - (-16·y) = 48 - (-72) = 48 + 72 = 120

16·y - (-16·y) = 16·y + 16·y = 32·y = 120

y = 120 ÷ 32 = 3.75

y = 3.75

12·x - 16·y + 48 = 0...(2)

12·x - 16 × 3.75 + 48 = 0

12·x - 12 = 0

12·x = 12

x = 12/12 = 1

x = 1

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Solution

For this case we have the following, the sum of the angles needs to be 360 since we have a circumference:

10a-4 +6a-2 +8a+6=360

Regrouping we have:

10a +6a +8a -4 -2 +6= 360

24a= 360

a= 360/24= 15

Given △FGH ~ △LMN,  all the statements that are true are options A, B , C and E

Since the two triangles are similar, their corresponding angles are going to be congruent and the sides would be proportional as well. This makes A correct

Given that FH ~ LN then the second option is correct

Option C is correct due to the definition of singularity

Option E is correct because ∠H ≅ m∠N

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Answer:  A. \(\dfrac{1}{120}\)

Step-by-step explanation:

Total digits on keypad = 5

According to permutation,

If repetition of digits is not allowed then the number of 5-digits passwords can be formed = 5!

= 5 x 4 x 3 x 2 x 1         [n!=n x (n-1) x (n-2)x ... x 1]

=120

The probability that someone guesses the correct code = \(\dfrac{\text{Number of correct codes}}{\text{Total possible codes}}\)

\(=\dfrac{1}{120}\)

Hence, the correct option is A.

The given cost function is C = 485 + 6.75x^(2/3).The marginal cost for producing x units is given by the expression 4.5x^(-1/3) dollars per unit.

Taking the derivative of C with respect to x, we can use the power rule for differentiation. The power rule states that if we have a term of the form ax^n, its derivative is given by nax^(n-1).

In this case, the derivative of 6.75x^(2/3) with respect to x is (2/3)(6.75)x^((2/3)-1) = 4.5x^(-1/3).

Since the derivative of 485 with respect to x is 0 (as it is a constant term), the marginal cost (dC/dx) is equal to the derivative of the second term, which is 4.5x^(-1/3).

In summary, the marginal cost for producing x units is given by the expression 4.5x^(-1/3) dollars per unit.

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No, when writing the inductive step, we do not have to change the variable "n" to "k."

When using mathematical induction to prove a statement about natural numbers, we typically follow a two-step process: the base case and the inductive step. In the inductive step, we assume that the statement is true for a fixed value of "n" (the inductive hypothesis) and then prove that it holds for the next value, which we often denote as "n+1."

The choice of variable names, such as "n" or "k," is arbitrary and does not affect the validity of the proof. The value of "k" is not necessarily fixed or equal to any specific value from the base case. It simply represents the next value in the sequence after the inductive hypothesis is assumed to be true.

In mathematical induction, the focus is on the logic and structure of the proof rather than the specific function names used. As long as the inductive step correctly demonstrates the transition from one value to the next, the choice of variable name is a matter of preference and clarity.

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The sum of the equation is  = 5494000.

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

\(\sum_{j=1}^{200} 2 j(j+3)\)

simplifying them we get:

\(\sum_{j=1}^{200} 2 j^{2}+6 j\)

Split the summation into smaller summations that fit the summation rules.

\(\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j\)

\(\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}\)

The formula for the summation of a polynomial with degree 2

is:

\(\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}\)

Substitute the values into the formula and make sure to multiply by the front term.

\((2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$\)

we get: 5373400

Evaluating same as above : \(6 \sum_{j=1}^{200} j\)

we get: 120600

Add the results of the summations.

5373400 + 120600

= 5494000

The sum of the equation is  = 5494000.

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Answer:

√100 +4√10 +3 −8 √10 =  −4√10 + 13 TRUE

Step-by-step explanation:

Simplify the following:

sqrt(100) + 4 sqrt(10) + 3 - 8 sqrt(10)

Hint: | Simplify radicals.

sqrt(100) = sqrt(10^2) = 10:

10 + 4 sqrt(10) + 3 - 8 sqrt(10)

Hint: | Evaluate 10 + 4 sqrt(10) + 3 - 8 sqrt(10).

10 + 4 sqrt(10) + 3 - 8 sqrt(10) = 13 - 4 sqrt(10):

Answer:  13 - 4 sqrt(10)

Answer:

the answer is C

Step-by-step explanation:

please mark brainlist

Answer:

D.-26

Step-by-step explanation:

-26+12=-14 Hope this helps :)

If the relationship discovered is very similar to Y₁ = X and a linear regression is fit through the data points, we would expect the slope coefficient to be approximately 1.

The value of the regression R2 in this situation would likely be high, indicating a good fit.

Expectation for the slope coefficient:
If the relationship discovered is very similar to Y₁ = X, we would expect the slope coefficient of the linear regression to be close to 1. This is because the equation Y = X represents a direct proportional relationship between the dependent variable (Y) and the independent variable (X), where a unit increase in X corresponds to a unit increase in Y.

Expected value of the regression R2:
In this situation, the regression R2 value would likely be high. R2 measures the proportion of the total variation in the dependent variable (Y) that is explained by the independent variable (X). Since the discovered relationship is very similar to Y₁ = X, a linear regression through the data points would likely result in a good fit, capturing a large portion of the variation in Y.

Implications of fitting a linear regression to a non-linear relationship:
Fitting a linear regression to a non-linear relationship can lead to biased estimates and inaccurate predictions. While the R2 value might indicate a good fit, it’s important to remember that the underlying relationship is non-linear. Linear regression assumes a linear relationship between the variables, and if the true relationship is non-linear, the estimates of the slope coefficient and other parameters may not accurately represent the relationship.

To properly capture the non-linear relationship, alternative regression techniques such as polynomial regression, exponential regression, or non-linear regression models should be considered.


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Answer:

x + 5 = 8

Step-by-step explanation:

x + 5 = 8

Subtract 5 from both sides.

x + 5 - 5 = 8 - 3

x = 3

Answer: x+5=8

Step-by-step explanation: