graph e(x) = √x − 10 .

Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.

A quadratic equation can be made together into perfect square trinomial simply adding or removing elements from both sides, a technique known as "completing the square."

You can use the square's completion as another mathematical tool to solve a variety of problems:

Given expression:

-3x² - 298 = 60x - 1

isolating the x values:

-3x² - 60x = 298 - 1

-3x² - 60x = 299

Taking -3 common from the left hand side:

-3(x² + 20x) = 299

x² + 20x = - 299/3

This, can be written as:

x² + 2*10x = - 299/3

add both side by 100

x² + 2*10x + 100 = - 299/3 + 100

On simplification:

(x + 10)² = (-299 + 300) /3

(x + 10)² = 1 /3

Comparing obtained expression with the given form: (x+a)²=b

a = 10 and b = 1/3

Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.

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$4,204.80

Interest is the amount of money an initial investment earns.

Simple Interest

The question states that this account has simple interest. This means that the interest is only earned on the principal (initial investment) and not compounded. For simple interest, we need to know 3 things: the principal, the rate of interest, and the time period. So, all we need to do is plug in the values we were given.

Interest Formula

The formula to find the amount of interest earned is I = Prt. In this formula, P is the principal, r is the rate as a decimal, and t is the time. Now, we can plug our values in.

So, over the course of 2 years, the account will earn $4,204.80.

if you're trying to solve for x, and it is equal to zero, then it would be -3. plug it in and it would all cancel out

After using the formula for the sum of an infinite geometric series, we conclude that the given infinite series does not converge to 1.

To prove that the infinite series ∑(i=1 to ∞) 2^(i-1) equals 1, we can use the formula for the sum of an infinite geometric series.

The sum of an infinite geometric series with a common ratio r (|r| < 1) is given by the formula:

S = a / (1 - r)

where 'a' is the first term of the series.

In this case, our series is ∑(i=1 to ∞) 2^(i-1), and the first term (a) is 2^0 = 1. The common ratio (r) is 2.

Applying the formula, we have:

S = 1 / (1 - 2)

Simplifying, we get:

S = 1 / (-1)

S = -1

However, we know that the sum of a geometric series should be a positive number when the common ratio is between -1 and 1. Therefore, our result of -1 does not make sense in this context.

Hence, we conclude that the given infinite series does not converge to 1.

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The sum of the number in the binary form is 1001010 and the values of m is 0 and n is 1.

Binary Number System: A binary number is a number that is stated in the binary system or base 2 numeral system, according to mathematics. It uses the symbols 1 (one) and 0 to represent different numeric values (zero). The notation with 2 as a radix is known as the base-2 system.

The binary number can be expressed in decimals as follows:

\(11111_2 = 1*2^4 + 1*2^3+1*2^2+ 1*2^1+1*2^0\\\\11111_2= 31\\\\10000_2= 1*2^4\\\\10000_2 = 16\)

The sum of all the numbers is:

27 + 31 + 16 = 74

To convert the decimal in the binary form, divide the number continuously and note the remainder until it cannot be divided any further.

74 ÷ 2= 37= 0

37 ÷ 2 = 18 = 1

18 ÷ 2 = 9 = 0

9 ÷ 2 = 4 = 1

4 ÷ 2 = 2 = 0

2 ÷ 2 = 1 = 0

1 ÷ 2 = 0 = 1

So, the number in the binary form is 1001010 and the value of m is 0 and n is 1.

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The sum of the other two numbers, x and y, is 120.

To solve this problem, we need to use the fact that the average of three numbers is the sum of the numbers divided by 3. Since the average of the three numbers is 50, and one of the numbers is 30, we can set up the equation:

(30 + x + y)/3 = 50

To solve for x and y, we need to multiply both sides of the equation by 3 to get:

30 + x + y = 150

We can then subtract 30 from both sides of the equation to get:

x + y = 120

So, the sum of the other two numbers, x and y, is 120.

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If the lowest number is 30, the sum of the other two numbers is 150

Let x1, x2 and x3 be three unique numbers with x1 is the lowest number and x3 is the largest number.

Let x{bar} be the average of numbers  x1, x2 and x3

Given that the average of three unique numbers is 50.  

So, x{bar} = 50

And the lowest number is 30

i.e., x1 = 30

Using the formula of average,

x{bar} = (x1 + x2 + x3) / 3

50 = (30 + x2 + x3)/3

50 × 3 = x2 + x3

x2 + x3 = 150

Therefore, the sum of the other two numbers is 150

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The solution to the initial value problem is dP dt molding sol = kP(1-P), where P(0) = 7 and P(2) = 4 is P(6.69) = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It involves the independent variable, the unknown function, and its derivatives. Differential equations are used to model various physical, biological, and social phenomena in the natural and social sciences.

Given,

the initial value problem as;

dP/dt = kP(1 - P),

P(0) = 7, P(2) = 4

To solve the initial value problem, we will integrate both sides of the given differential equation with respect to t;

we get,

P(t) / [P(t) - 1] = A * e^(kt)

where, A = P(0) / [P(0) - 1] = 7/6

Now, we can write

P(t) / [P(t) - 1] = 7/6 * e^(kt) ---(1)

Using P(2) = 4,

we have4 / (4 - 1) = 7/6 * e^(2k)6 / 7 = e^(2k)ln 6/7 = 2k

Therefore,

k = ln 6/14

Now, substituting k = ln 6/14 in equation (1),

we get

P(t) / [P(t) - 1] = 7/6 * e^(t * ln 6/14)P(t) / [P(t) - 1] = 7/6 * (e^(ln 6/14))^t

P(t) / [P(t) - 1] = 7/6 * (6/14)^(t/2)

P(t) / [P(t) - 1] = 7/12 * 3^(t/2)

Multiplying numerator and denominator by 3^(-t/2),

we get

P(t) / [P(t) - 1] = 7/12 * 3^(t/2) * 3^(-t/2) / (3^(-t/2) - 1)

P(t) / [P(t) - 1] = 7/12 * 3^(t/2) / (1 - 3^(-t/2))

Multiplying numerator and denominator by -1, we get

P(t) / [1 - P(t)] = 7/12 * [1 / (3^(-t/2) - 1)] - 1S

imilarly, using P(0) = 7,

we get

P(0) / [1 - P(0)] = 7/12 * [1 / (3^(0/2) - 1)] - 1 => P(0) = 7

Using the differential equation we can write,

P'(t) = kP(t)(1 - P(t))P'(t) = kP(t) - kP^2(t)P'(t) + kP(t) = kP(t) - kP^2(t) + kP(1 - P(t))U

sing P(t) = 7,

we have

P'(t) = k * 7 * (1 - 7) = -42k

Using P(t) = 4, we have

P'(t) = k * 4 * (1 - 4) = -12k

Therefore, the solution to the initial value problem is,

P(t) = [7e^(ln 6/14 * t)] / [7/6 + e^(ln 6/14 * t)]

Given, P(0) = 7,

we have

P(0) = [7e^(ln 6/14 * 0)] / [7/6 + e^(ln 6/14 * 0)] => 7 = 7/13

Solving for t, we have

4 = [7e^(ln 6/14 * 2)] / [7/6 + e^(ln 6/14 * 2)]

Multiplying numerator and denominator by e^(-ln 6/14 * 2), we get

4 = [7e^(-ln 6/14 * 2)] / [7e^(-ln 6/14 * 2)/6 + 1]24 + 7e^(-ln 6/14 * 2) = 42e^(-ln 6/14 * 2)31e^(ln 6/14 * 2) = 24e^(ln 6/14 * 2)e^(ln 6/14 * 2) = 24/31

Solving for t, we have;

\(t=\frac{2\ln (\frac{24}{31})}{\ln(\frac{6}{14})}\approx 6.69\)

Therefore, the solution to the initial value problem is P(6.69) = 4.

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Answer:

f(x) ≥ 0 over the interval [5, ∞).

( option A )

A valid prediction about the continuous function f(x) is the values of f(x) for x ≥ 5 are greater than or equal to zero. The correct answer is option A.

A function is continuous if its graph has no gaps or jumps. A function f(x) is said to be continuous at a point x=a if the limit of f(x) as x approaches a exists and equals f(a). A function on an interval is continuous if it is continuous at every point in that interval.

The table is given in the question as follows:

x: -5, -3, -1, 1, 3, 5, 7

f(x): 8, 4, 0, -2, -2, 0,4

Using the given values of x and f(x), we can make some observations about the behavior of the function f(x) over the given intervals:

Over the interval [5, ∞), f(x) is positive for all x, since all the values of f(x) for x ≥ 5 are greater than or equal to zero.

Therefore, option A is a valid prediction.

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The missing table is attached below.

Answer:

1/2 dozen of one score is 30%.

Step-by-step explanation:

As we know that 1 dozen = 12 units.

1/2 dozen = 1/2 times 12=6 units

1 score = 20 units.

By using this conversion, we get

6/2 times 100=30%

So 1/2 dozen of one score is 30%

The percentile score of 71 on test score is 27 and the score of victor is 71.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula

\(R_{100} =\frac{100(N < )+\frac{1}{2} }{N}\)

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60th percentile.

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

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Answer:

the C(X) pattern is +4? i need more context but i can give u that much

Step-by-step explanation:

Answer:

y - 7 = 6(x - 2)

Step-by-step explanation:

1. Since we're given one point and the slope of a line, we can use the point slope form: \(y-y_1=m(x-x_1)\)

2. (Plugging in values)

Therefore, one equation of the line is y - 7 = 6(x - 2).

Answer:

m = -11 + h

Step-by-step explanation:

we don't know if h is bigger than 11 or smaller

so we couldn't put directly like h-11

Answer: M=h-11

Step-by-step explanation:

In order to solve this linear equation, we need to group all the variable terms on one side, and all the constant terms on the other side of the equation.

In our example,

- term 11, will be moved to the left side.

Notice that a term changes sign when it 'moves' from one side of the equation to the other.

The x and y intercepts of each of the following is (a) x intercepts are 3 and -5, y intercept is 16. (b) x intercepts are 1 and 2.5, y intercept is -2.5. (c) x intercept is 8 and the y intercept is -16.

x intercept is the x coordinate of the point on the line where it touches the X axis. The y coordinate will be 0 there.

y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.

(a) We have the points from the table.

(3, 0) and (-5, 0)

y coordinate is 0. So x intercepts are 3 and -5.

We also have (0, 16).

y intercept is 16.

(b) We have the points (1, 0) and (2.5, 0).

x intercepts are 1 and 2.5.

We also have (0, -2.5).

y intercept is -2.5.

(c) We have (8, 0) and (0, -16).

x intercept is 8 and the y intercept is -16.

Hence the x and y intercepts are found.

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Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

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(a) at least 4 people born in the same month,

(b) In order to ensure that at least two persons were born on the same day,

(a)

we have 37 people.

we want to know at least how many were born in the same month.

I would think that at least 4 people had to be born in the same month.

here's why.12 months in a year.

if every 12 people were born in a different month, then out of 37 people, at least 3 people were born in the same month.

first 12 people        1   2  3  4   5  6  7  8  9  10  11   12

second 12 people  1   2  3  4  5   6  7  8   9    10  11  12

third 12 people       1   2  3  4  5  6  7  8  9  10  11  12

remaining 1 person 1

we could have minimum 4 people that were born in the same month,

Hence,  at least 4 people born in the same month,

(b)

 Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?

there are 365 days in the year.

You could have 365 people where no two persons were born on the same day, assuming that everyone was born on a different day.

However, the 366th individual would have to share the same birthday as another member of the group.

In order to ensure that at least two persons were born on the same day, the group's minimum size would consequently need to be 366.

The complete question is -

(a) Among 37 people at least how many were born in the same month?

(b) Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?

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The relation between polar and cartesian coordinates is given by:

In this case, we have:

Using the formulas above and the values of x, y and r, we have:

1) sin θ

2) cos θ

3) tan θ

4) csc θ

5) sec θ

6) cot θ

The required expression that represents the total number of boxes sold for the season if s = the number of weeks Stephanie sold cookies

Stephanie and Kelandria are in the Girl Scouts. They both sell 27 boxes of cookies each week.

Stephanie sold an additional five boxes one week. We are required to write an expression that represents the total number of boxes sold for the season if s = the number of weeks Stephanie sold cookies and k = the number of weeks Kelandria sold cookies.

Stephanie sold cookies for s weeks, and she sold an additional 5 boxes one week. Therefore, she sold 27 + 5 = 32 boxes that week.

so the total number of boxes she sold would be:K = 27kThus, the total number of boxes sold by Stephanie and Kelandria would be:

S + K = 27s + 32 + 27kS + K = 27(s + k) + 32

The above expression represents the total number of boxes sold by Stephanie and Kelandria for the season.

Therefore, the required expression that represents the total number of boxes sold for the season if s = the number of weeks Stephanie sold cookies and k = the number of weeks Kelandria sold cookies is:

S + K = 27s + 32 + 27k.

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Answer:

5/2

Step-by-step explanation:

(18/15)*(25/12)=(18*25)/(15*12)=450/180=5/2

when we add negative number to the positive number we just subtract the smaller number from the larger number and put the sign or the larger number after words

examples:- First

\(5 + ( - 2) = 5 - 2 = 3\)

like here we put + in front of 3 as larger number 5 is positive

\( - 7 + 5 = - 2\)

we put negative because 7 is larger then 5 and 7 is negative

Answer:

milk to oil - correctly shows ratio 3:1

Answer:

B 2/7 <3/1

Step-by-step explanation:

Answer:

8.9x+1.66

Step-by-step explanation:

1.)5.3x − 8.14 + 3.6x + 9.8

2.)group the numbers on one side and the x's on the other

3.)5.3x + 3.6x - 8.14 + 9.8

solve

= 8.9x +  1.66

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The given expression can be expressed as a single trigonometric function known as the tangent function.

Let's consider the given expression, which we aim to express as a single trigonometric function. Without the specific expression, it is challenging to provide a detailed explanation. However, I can offer a general approach to solving such problems.

To express an expression as a single trigonometric function, we often use trigonometric identities and algebraic manipulation. We simplify the expression using identities like Pythagorean identities, reciprocal identities, and double-angle identities. By applying these identities and rearranging the terms, we can often transform the expression into a single trigonometric function.

For example, if the given expression involves sine and cosine terms, we can use the identity tan(x) = sin(x) / cos(x) to express the expression solely in terms of the tangent function.

It is important to note that the specific steps and identities used to simplify the expression depend on the given expression itself. Therefore, to provide a more detailed explanation, it would be helpful to know the specific expression you are referring to.

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Answer:

A is 85 degrees

Answer:

B.

Step-by-step explanation:

We can start by dividing 3.5 and 0.75.

3.5/0.75 is 4.67.

Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.

1*4.67 is 4.67.

The Tukey method calculates the range of differences between each pair of means and compares it to a critical value called the Honestly Significant Difference (HSD).

The Tukey method is used to perform multiple comparisons between the four levels of treatments.

It is done at the 0.01 significance level.

This method helps identify significant differences among the treatments, while controlling the overall Type I error rate.

The Tukey method calculates the range of differences between each pair of means and compares it to a critical value called the Honestly Significant Difference (HSD).

If the range of differences is greater than the HSD, then the means are considered significantly different from each other.

This process is repeated for all possible pairs of means.

The Tukey method is commonly used in analysis of variance (ANOVA) to determine which treatments have statistically significant differences.

It provides a useful way to compare multiple treatment levels simultaneously and make accurate conclusions about their differences.

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Answer:

42.1 cm

Step-by-step explanation:

θ = 265°

Radius (r) = 9.1 cm

Arc length of major arc GH = θ/360 × 2πr

Plug in the values into the equation

Length of arc GH = 265/360 × 2 × π × 9.1

= 42.0886149

= 42.1 cm (nearest tenth)

The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

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Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

To solve the exponential equation 23^x = 6, take the logarithm base 23 of both sides to get x = log base 23 of 6.

Angie, to solve the exponential equation 23^x = 6, you need to find the value of x such that when you raise 23 to the power of x, you get 6. To do this, you can use logarithms.

In particular, you can use the logarithmic function log_23. The log_23 of a number y is the exponent x such that 23^x = y. So, to solve the equation 23^x = 6, you can take the log_23 of both sides:

log_23(23^x) = log_23(6)

x = log_23(6)

The right side of this equation can be evaluated using a calculator or logarithmic tables. Once you have the value of x, you will have solved the exponential equation.

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