2.
Recall that Stella is the pacesetter the 4:10
pace group of a marathon and is required to
finish within 2 minutes of the pace time.
Stella must run between
minutes and
meet the requirement.
minutes in order to

For a quadratic of the form px^2 + 40x + 16 to be a perfect square, it must be able to be written in the form (mx + n)^2 for some real numbers m and n.

Expanding (mx + n)^2 gives:

(mx + n)^2 = m^2x^2 + 2mnx + n^2

Comparing this to the given quadratic, we can see that:

m^2 = p

2mn = 40

n^2 = 16

Solving for m and n, we find that:

m = ±√p

n = ±4

Therefore, in order for the quadratic to be a perfect square, the square root of p must be rational, and the value of p must be one of the following:

p = 0, 1, 16

So the possible values of p that make the quadratic a perfect square are 0, 1, 16.

The element will be gone in approximately 10.9 minutes.

We can calculate this by using the formula:

Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))

Time = (log(300 / 110)) / (log(1 - 0.054))

Time = 10.9 (rounded to the nearest tenth of a minute)

Therefore, The element will be gone in approximately 10.9 minutes.

A logarithmic function is a mathematical function that relates the logarithm of a number to its argument. The logarithm of a number (base 10) is represented by the log symbol (log 10) and the number being used as the argument. The inverse of this function is an exponential function, which relates the exponential of a number to its argument. Logarithmic functions are often used in mathematics and science to simplify and solve equations involving large exponents. They are also commonly used in finance, engineering, and other fields that involve large numbers.

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Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))

Time = (log(300 / 110)) / (log(1 - 0.054))

Time = 10.9 (rounded to the nearest tenth of a minute)

The value for a in quadratic function a(x-1)²+3 is obtained as a = 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The vertex of the quadratic function is (1,3).

The line passes through the points (3,5).

The equation is in the form - a(x-1)²+3

It is known that the vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola.

So it can be written -

f(x) = a(x-1)² + 3

Substitute the value of (1,3).

f(1) = a(1-1)² + 3 = 3

And for the point (3,5) the equation will be -

f(3) = a(3-1)² + 3 = 5

Set up a system of equations -

a(1-1)² + 3 = 3

a(3-1)² + 3 = 5

Solving for a in these equations -

a = 2

Therefore, the value of a is obtained as 2.

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[tex]\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m[/tex]

You are a parabola with vertex at (x,y) = (-4,0) and a focus at (x,y) = (-4,3).

A parabola is a mathematical curve that is symmetrical in shape and is often described as an upside-down U. It is a two-dimensional, closed curve and is an important part of conic section geometry. A parabola has a single vertex, which is the highest or lowest point of the parabola. It can also be thought of as the focus of the parabola.

The zeros you have listed are the x-intercepts, which means that your equation is of the form y = ax^2 + bx + c, and your a value is negative because your parabola opens downwards. You can determine the other coefficients by looking at the vertex and focus coordinates.

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Using the given information, we can calculate the z-score as z = (56.4 - 67.6) / 3.5, which gives us a z-score of -2.3. This means that 2.3 standard deviations below the mean of adult men's heights is the doorway height of 56.4 inches. Since the area under the normal curve from -∞ to -2.3 is 16%, this means that 84% of adult men can fit through the door without bending.

Using the given information and the desired percentage, we can calculate the z-score as z = (x - 67.6) / 3.5, where x is the doorway height. Solving for x, we get x = 57.6 inches. Therefore, a doorway height of 57.6 inches would allow 40% of adult men to fit through without bending.

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For least integer function,

domain :  set of all real numbers

range : set of all integers

We know that the least integer function of any real number p is the least integer which is greater than or equal to the given number p.

The mathematical definition of ceiling function is :

f(x) = minimum { a ∈ Z ; a ≥ x }

where Z is the set of integers.

A least integer function is also known as the ceiling function.

The symbol to represent least integer function is ⌈ ⌉.

We can write least integer function for x as:

⌈x⌉ or ceil (x)

From above definition of ceiling function we can say that the domain of least integer function is the set of all real numbers whereas the range of  is the set of all integers.

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The balance after 9 years is $1139.94 rounded to the nearest cent.

The formula to use in this case is A = P(1 + r)^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.

Given the information in the problem, we know that:

P = $800.00 (the principal or starting amount)

r = 0.04 (the interest rate as a decimal)

n = 1 (the interest is compounded annually)

t = 9 (the number of years)

Plugging these values into the formula, we get:

A = $800.00(1 + 0.04)^9

To solve for A, we need to calculate (1 + 0.04)^9

=1.04^9

=1.041.041.041.041.041.041.041.041.04

=1.424928

A = $800.00*1.424928

A = $1139.94

So the balance after 9 years is $1139.94 rounded to the nearest cent.

Therefore, The balance after 9 years is $1139.94 rounded to the nearest cent.

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A = $800.00(1 + 0.04)^9

To solve for A, we need to calculate (1 + 0.04)^9

=1.04^9

=1.041.041.041.041.041.041.041.041.04

=1.424928

A = $800.00*1.424928

A = $1139.94

The example of a linear equation in two variables in standard form is 3x + 2y = 6

A linear equation in two variables in standard form is of the form:

Ax + By = C

where A, B, and C are constants and x and y are variables.

An example of a linear equation in two variables in standard form is:

3x + 2y = 6

This equation can be written in standard form by first subtracting 6 from both sides,

3x + 2y -6 = 0

and then dividing both sides by the greatest common factor of the coefficients,

(3/1)x + (2/1)y = 6/1

This gives the standard form of the equation:

3x + 2y = 6.

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The length of BD and CD are 15 units and 20 units respectively

By the Angle Bisector Theorem, we have:

BD/DC = AC/BC = 21/28

We can use the Pythagorean Theorem to find AC:

AC² + BC² = AB²

21² + 28² = AB²

AB = 35 units

Now we can use the Angle Bisector Theorem to find BD:

BD/DC = 21/28

BD + DC = AB

BD = (21/49) × AB

BD = (21/49) × 35

BD = 15 units

To find CD, we can use the fact that BD + DC = AB:

CD = AB - BD

CD = 35 - 15

CD = 20 units

Therefore, the length are BD = 15 and CD = 20 units.

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Answer:

Step-by-step explanation:

How many kilometers he ran per hour?

Alex ran 6 kilometers per hour.

The ratio can be calculated as follows:

The first is to convert mixed fractions to improper fraction

4 [tex]\frac{1}{2}[/tex] km =  [tex]\frac{(4x2)+1}{2}[/tex] km

= [tex]\frac{8+1}{2}[/tex] km

= [tex]\frac{9}{2}[/tex] km

The next step is to compare worth comparison

[tex]\frac{a1}{b1}[/tex] = [tex]\frac{a2}{b2}[/tex]

[tex]a_{1}[/tex] = 4 [tex]\frac{1}{2}[/tex] km = [tex]\frac{9}{2}[/tex] km

[tex]a_{2}[/tex] = X

[tex]b_{1}[/tex] = [tex]\frac{3}{4}[/tex] hour

[tex]b_{2}[/tex] = 1 hour

So,

[tex]\frac{9/2}{3/4}[/tex] = [tex]\frac{X}{1}[/tex]

X = [tex]\frac{(9/2)x1}{3/4}[/tex]

X = [tex]\frac{9/2}{3/4}[/tex]

X = [tex]\frac{9}{2}[/tex] × [tex]\frac{4}{3}[/tex]

X = [tex]\frac{36}{6}[/tex] kilometers

X = 6 kilometers

Alex ran 6 kilometers per hour.

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Un equipo de cuatro personas participó en una carrera de relevo de 400 yardas, lo que significa que cada miembro del equipo corrió una distancia de 400 yardas. El equipo completo completó la carrera en 53.2 segundos. Para calcular el tiempo promedio que cada persona corrió, debemos dividir el tiempo total de la carrera entre el número de personas en el equipo. En este caso, se divide 53.2 segundos entre 4 personas, lo que da un tiempo promedio de 13.3 segundos por persona.

Set up a ratio: 150/100 = 210/x, or your investment gave you a return of 36% of the 150 you invested.

The investment's initial value is subtracted from its current value, which is then divided by the investment's original value to determine a simple rate of return.

The calculation is as follows in light of the facts above:

The entire sum should be

30 × 15

= $450

= 210 - 6

= $204

The total amount should be because it was sold for $210 plus a $6 commission.

Right now, rate of return is

= (204 - 450) ÷ 204×100

= 16.58%

You spent $150 to purchase 10 shares at a price of 15%, or 36%. You made 54$ after subtracting the commission of $6 and selling it for 210$.

Set up a ratio: 150/100 = 210/x, or your investment gave you a return of 36% of the 150 you invested.

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Answer:

Where is the statement?

Step-by-step explanation:

The 2 equations will have infinitely many solutions if k equals 10.

Here we have

10x + 5y − (k−5) = 0 and 20x + 10y − k = 0

Since these 2 are already in the standard form

a₁x + b₁y + c₁ = 0

and

a₂x + b₂y + c₂ = 0

we don't have to make any changes to them

According to the law, an equation has infinitely many solutions if

a₁/a₂ = b₁/b₂ = c₁/c₂

here,

a₁ = 10,  b₁ = 5, and c₁ = - k + 5

and,

a₂ = 20, b₂ = 10, and c₂ = - k

Hence, we get

10/20 = 5/10 = ( - k + 5)/(-k)

or, (k - 5)/k = 1/2

or, 2k - 10 = k

or, k = 10

Hence the 2 equations will have infinitely many solutions if k is equal to 10.

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Complete Question

For what value of k does the following pair of linear equations have infinitely many solutions?

10x + 5y − (k−5) = 0 and 20x + 10y − k = 0

Answer:50

Step-by-step explanation:

Answer:

A fruit bouquet artist charges $1.50 for each piece of fruit in a bouquet, x, plus an additional $17 for the basket and decorations. Customers receive free delivery when their order is over $40.

Step-by-step explanation:

$1.50 represents the cost of each piece of fruit, but we don't know how many fruits are included in the basket, so let x be the number of fruit. That total must be added to the cost of the basket.

If consumers receive free delivery for orders over $40, then 17+1.50x must be greater than $40.

Answer:

x=83

Step-by-step explanation:

All angles of a triangle add up to 180 so:

53+44=97

180-97=83

Answer:

[tex]\huge\boxed{\sf x = 83\°}[/tex]

Step-by-step explanation:

So,

x + 53 + 44 = 180

x + 97 = 180

x = 180 - 97

[tex]\rule[225]{225}{2}[/tex]

The following triangles are congurent

Yes SAS

The perimeter of the pentagon is 76 units. The solution is obtained using tangent to circle.

What is tangent to a circle?

A line that touches a circle only once is said to be tangent to it. A point to circle can only have one tangent.

In the figure, the circle is circumscribed by the pentagon.

We are given QZ = 10, YX = 9, WX = 9, UW = 17, and US = 10

VW = WX = 9   (tangent of circle)

So, VU = UW - VW

VU = 17-9= 8

Since, VU and UT are tangents of circle, therefore

UT = 8

US = UT + TS

⇒10 = 8 + TS

⇒TS = 2

Now, TS and SR being tangents, therefore

TS = SR = 2

Also, RQ and QZ are tangents, therefore

RQ = QZ = 10

Similarly, ZY and YX are tangents, therefore

ZY = YX= 9

Thus, Perimeter = SQ + QY + YW + WU + US

⇒Perimeter = SR+ RQ+ QZ+ ZY+ YX+ XW+ UW+ US

⇒Perimeter = 2+ 10+ 10+ 9+ 9+ 9+ 17+ 10

⇒Perimeter = 76 units

Hence, the perimeter of the pentagon is 76 units.

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The difference between the largest 8-digit number and the smallest 7-digit number is 98999999.

The aim is to find the smallest 7-digit and largest 8-digit numbers, and then we need to determine the difference between these two values.

Let's start by finding the smallest 7-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 therefore it  can be used in the highest place value.

Thus, we can create the required 7-digit smallest number with 0 and 1.

Hence, the smallest 7-digit number is 1000000.

Now, we will discover the largest 8-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 8-digit number with the digit 9.

Thus, the largest 8-digit number is 99999999.

Now, find the difference between these two values.

So, we can determine the difference between the smallest 7-digit and the largest 8-digit numbers by subtracting the smallest from the largest.

Thus, we get,

⇒99999999−1000000

⇒98999999

Hence, 98999999 is the difference between the smallest 7-digit and the largest 8-digit numbers.

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The four conditions of a binomial distribution are: independence, normality, symmetry, and rarity.

Independence: Each trial in a binomial distribution is independent of the other trials, meaning that the outcome of one trial does not affect the outcome of any other trial.

Normality: The distribution of the data follows a normal distribution, meaning that it is bell-shaped and symmetrical.

Symmetry: The binomial distribution is symmetrical around the mean, meaning that the probability of the outcome being above the mean is the same as the probability of the outcome being below the mean.

Rarity: The binomial distribution is characterized by rare events, meaning that the probability of an event occurring is relatively low. This is because the outcomes of each trial are determined by a random process.

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The expression 2x2 3x 9 area of the garden is a quadratic polynomial.

2x2 contains a power value and 3x contains the constant x and 9 is the integer so this is the Quadratic Polynomial. When a variable term in the polynomial expression has a highest power of 2, the polynomial is said to be quadratic.

Only the exponent of the variable is taken into account when determining a polynomial's degree. It is not taken into account how strong a coefficient or constant term is.

A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the name given to the solutions of such an equation.

The capability to derive a number of significant inferences from the analysis of the discriminant is an additional advantage of this approach.

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Full Question: What is the type of polynomial 2x^2-3x-9 expressing area of the garden?

(a) linear polynomial

(b)Quadratic polynomial

(c) cubic polynomial

(d) constant polynomial​

1. She can look at similar job postings online to compare the salary range offered.

2. She can contact the average employer and ask directly what salary range they offer for the job.

There are two ways Bruna can compare the pay for advertised jobs. First, she can research the salary range of similar job postings. This can be done through job search websites, social networks, and other online resources. She can look at the salary range offered for similar jobs to get an idea of the pay she can expect from an employer.

The second way she can find out the best paying job for her is to ask the employer directly about the salary range. She can contact the employer and ask directly what salary range they offer for the job. This will give her an accurate picture of the salary range that the employer is offering, so she can make an informed decision on which job to apply for. By using these two methods, Bruna can compare the pay for advertised jobs and find the one that offers the best salary.

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You can solve 2 equations with 2 variables using calculator in equation mode.

To solve a system of two equations with two variables using a scientific calculator, you can use the following steps (based on CASIO fx-991ES PLUS):

First press the 'mode' button and then press '5' corresponding to equations.

Now press '1' corresponding to a linear equation in two variables of format anX + bnY = cn. Now a matrix appears, each row correspond to each equation. The first column represent the coefficient of X, second column represent the coefficient of Y and third column, the coefficient. Note that the equation should be of the format mentioned before.

Now press '=' to get the solution. On the first press you get X and on second press, you get the value of 'Y'.

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Order of addends has no bearing on the amount according to the commutative property of addition. 6 added value.

The machine below produces a different number when a number is entered. 9 is produced if 3 is inserted. If 6 is put in, 12 will come out. If 7 is put in, 13 will come out. ​

Order of addends has no bearing on the amount according to the commutative property of addition.

Changing the addends' order does not alter the amount, according to the commutative property of addition.

Every output number, as we can see, adds a value of 6 to the corresponding input number.

3 + 6 = 9.

6 + 6 = 12.

7 + 6 = 13.

The Complete Question.

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The equation states the ratio of two numbers, where the numerator and denominator can be changed to obtain an equivalent equation. To solve for the meaning term, the numbers in the numerator and denominator must be manipulated to get the same ratio and the value of the meaning term can be found.

1)2:3=N:21

N=21*2/3

N=14

2)5:2=20:N

N=20*5/2

N=50

3)2:7=12:N

N=12*2/7

N=4.57

4)6:7=30:N

N=30*7/6

N=35

5)N:10=15:55

N=15*10/55

N=2.73

The equation states the ratio of two numbers, where the numerator and denominator can be changed to obtain an equivalent equation. To solve for the meaning term, the numbers in the numerator and denominator must be manipulated to get the same ratio. To do this, the numerator and denominator of the first equation can be multiplied or divided by the same number to get the same ratio as the second equation. When the ratio is the same, the meaning term can be found by dividing the numerator of the second equation by the denominator of the first equation. For example, the equation 2:3 = N:21 can be solved by multiplying 3 and 21 by 2, giving 6:42 = N:42, which has the same ratio. The meaning term is then found by dividing 42 by 3, giving N = 14. This process can be applied to all equations to find the meaning term.

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