A pair of inequalities joined by "and" or "or" is called a

x²+√2x+3  and x²+√2x+6  are expressions that are not polynomial. (Option a and Option b)

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.

For the algebraic expression to be called a  polynomial, the exponents in the algebraic expression should be non-negative integers. Also if an algebraic expression has a radical in it then it can not be called a polynomial.

a) x²+√2x+3. This expression is not a polynomial as the polynomial expression does not contain any radicals. √2 here is a radical root.

      ⇒   Hence, option a is not a polynomial expression.

b) x²+√2x+6.This expression is also not a polynomial expression as it has a radical √2 present in the expression.

      ⇒   Hence, option b is not a polynomial expression.

c) x³+3x²-3. This expression can be termed as a polynomial expression since all of the variables have positive integer exponents.

     ⇒    Hence, option c is a polynomial expression.

d) 6x+4​. This expression is also a polynomial expression as all of the variables have positive integer exponents.

      ⇒   Hence option d is a polynomial expression.

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The initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, an exponential function with rate of decay, h(t) = \(1250(0.865)^t\)

Here we need to identify the initial amount, rate and the value of function when t = 3

The general formula of exponential decay is given by,

A = P(1-r)ⁿ

Where A is final amount

P is initial amount

r = rate of decay

n = years or time

Comparing with general formula,

P = 1250

1-r = 0.865

r = 1-0.865

r = 0.135

r % = 13.5

h(3) = 1250(0.865)³

= 809

Hence, the initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809

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1. The x-intercepts are x = -1/2 and x = 3.

2. The solutions are x = 3 and x = -1/2.

3. The vertex is (5/4, 11/8).

4. The y-coordinate of the vertex is the same as the y-coordinate of these points.

To find the x-intercepts, we can use the quadratic formula:

\(x = (-b + \sqrt{(b^2 - 4ac)) / 2a}\)

Here, a = -2, b = 5, and c = 3, so substituting these values in the formula we get:

\(x = (-5 + \sqrt{(5^2 - 4(-2)(3))} ) / 2(-2)\\x = (-5 + \sqrt{(25 + 24)) / (-4)} \\x = (-5 + \sqrt{(49))} / (-4)\\x = (-5 + 7) / (-4)\)

An alternate method to find the x-intercepts would be to factor the quadratic equation as follows:

\(-2x^2 + 5x + 3 = 0\\-2x^2 + 6x - x + 3 = 0\\-2x(x - 3) - 1(x - 3) = 0\\(x - 3)(-2x - 1) = 0\)

Thus, the solutions are x = 3 and x = -1/2.

To find the vertex, we can use the formula x = -b/2a to find the x-coordinate of the vertex, and then substitute it into the equation to find the corresponding y-coordinate. Here, a = -2 and b = 5, so the x-coordinate of the vertex is x = -5 / 2(-2) = 5/4. Substituting this value into the equation, we get \(y = -2(5/4)^2 + 5(5/4) + 3 = 11/8.\) Therefore, the vertex is (5/4, 11/8).

Since the coefficient of the\(x^2\) term is negative, the parabola opens downwards and the vertex corresponds to a maximum value.

To graph the equation, we can start by plotting the vertex (5/4, 11/8). We can also plot the x-intercepts (-1/2, 0) and (3, 0). Since the parabola is symmetric around the vertical line passing through the vertex, we can use this line of symmetry to plot additional points. Specifically, we can evaluate the equation at a point one unit to the left of the vertex (3/4, 0.625) and a point one unit to the right of the vertex (7/4, 0.625), since the y-coordinate of the vertex is the same as the y-coordinate of these points. Finally, we can connect these points to obtain the graph of the parabola.

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The relationship between period and frequency is that they are inversely proportional to each other. In simpler terms, as the period of a wave or oscillation increases, its frequency decreases, and vice versa.

Mathematically, this relationship can be expressed using the formula: Frequency (f) = 1 / Period (T). Likewise, Period (T) = 1 / Frequency (f).To understand this relationship, let's first define the terms. Period (T) refers to the time it takes for one complete cycle of a wave or oscillation to occur. On the other hand, frequency (f) is the number of complete cycles that occur within a specific time interval, usually one second, and is measured in Hertz (Hz).

When a wave or oscillation has a longer period, it takes more time to complete one cycle, which means fewer cycles can occur within a given time frame. Consequently, the frequency is lower. Conversely, when the period is shorter, more cycles can fit within the same time frame, resulting in a higher frequency.

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Answer:

8

Step-by-step explanation:

40/5 = 8

56/7 = 8

64/8 = 8

Answer:

Step-by-step explanation:

x = -2

F(x)=1.5(2)^x=0.375 , G(x)=-3(1/4)^x=-48

x=0

F(x)=1.5(2)^x=3, G(x)=-3(1/4)^x=-3

x=1/2

F(x)=1.5(2)^x=1.06 , G(x)=-3(1/4)^x=-6

Answer:

B, C

Step-by-step explanation:

Plug in the x value for each x, and solve. Make sure that the two sides are equal to one another before verifying that it is true.

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Step-by-step explanation:

Vamos simplificar passo a passo.

k2-6k4-(3k4+k2+2)

Distribua o sinal negativo:

=k2-6k4+-1(3k4+k2+2)

=k2+-6k4+-1(3k4)+-1k2+(-1)(2)

=k2+-6k4+-3k4+-k2+-2

Combine os termos semelhantes:

=k2+-6k4+-3k4+-k2+-2

=(-6k4+-3k4)+(k2+-k2)+(-2)

=-9k4+-2

Responda:

=-9k4-2

Answer:

Ok, sabemos que:

Las medidas de cada mayólica tipo A son 45 cm x 45 cm.

Las mayólicas son cuadradas, y el área de un cuadrado de lado L es:

A = L^2.

Entonces el área de una mayólica tipo A es:

A = (45cm)^2 = 2,025cm^2.

Ahora, sabemos que en el patio 1 Víctor coloca 9 de estas en cada lado.

Entonces cada lado de este patio mide 9 veces 45cm

9*45cm = 405cm

El patio 1 es de 405cm x 405cm

el área es:

A1 = 164,025 cm^2

Ahora vamos al patio 2.

Acá usa mayólicas de tipo B, que son 30cm x 30cm

Y usa 12 en cada lado, entonces cada lado de este patio mide 12 veces 30 cm

12*30cm = 360cm

El patio dos es de 360cm x 360cm.

El área es:

A2 = 129,600 cm^2

Entonces:

Patio 1 tiene mayor área, y la diferencia entre las áreas es:

D = A1 - A2 = 164,025 cm^2 - 129,600 cm^2 = 34,425cm^2

Usando la fórmula para el área de un cuadrado, tiene-se que:

-----------------------

El área de un cuadrado de lado l es dado por:

\(A = l^2\)

-----------------------

\(A_{A} = 4.05^2 = 16.40 \text{m}^2\)

-----------------------

\(A_{B} = 3.6^2 = 12.96 \text{m}^2\)

-----------------------

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Answer:

Student 2 only

Step-by-step explanation:

Given that:

The written antiderivatives formulas by the students for k sin (kx), where  k > 1 are:

Student 1 : \(\int (k \ sin (kx)) \ dx= k^2 \ cos (kx) + C\)

Student 2: \(\int (k \ sin (kx) ) \ dx = - cos (kx) + C\)

The student that wrote the correct anti-derivate formula is Student 2 only.

This is because:

Suppose:

\(I = \int (k \sin (kx) ) \ dx\) where; k > 1

This implies that:

\(I = \int (k \sin (kx) ) \ dx\)

\(I =k \bigg ( \dfrac{-cos (kx)}{k} \bigg) + C\)   because \(\int sin (ax) \ dx = \dfrac{-cos (ax)}{a}+C\)

here;

C = constant of the integration

∴

I = - cos (kx) + C  which aligns with the answer given by student 2 only.

If the manufacturer's claim is correct, the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website is 0.033

We can use a one-sample t-test to test the manufacturer's claim. The null hypothesis is that the true mean deviation from perfect time is equal to 30 seconds per month, and the alternative hypothesis is that the true mean deviation from perfect time is greater than 30 seconds per month.

The test statistic for this one-sample t-test is calculated as follows

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the problem, we have

x = 34 seconds

μ = 30 seconds

s = 15 seconds

n = 40 clocks

t = (34 - 30) / (15 / √40) = 1.89

Using a t-distribution table with degrees of freedom (df) = n-1 = 39 and a significance level of α = 0.05 (one-tailed test), the critical value is 1.686.

Since our calculated t-value (1.89) is greater than the critical value (1.686), we reject the null hypothesis and conclude that the true mean deviation from perfect time is greater than 30 seconds per month.

To calculate the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website, we need to find the area under the t-distribution curve to the right of t = 1.89. Using a t-distribution calculator, we find this probability to be approximately 0.033

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Answer:

3 miles

Step-by-step explanation:

y(x) = total minutes

y = total miles

x = the time in minutes it take erica to run a mile

4x = 56

x = 56/4

x = 14

so it takes her 14 minutes to run one mile

plug 14 into x

y(14) = 42

42/14 = 3 miles

Minimal sedation is characterized by c) less than 50% N2O in the first stage of the continuum.

Minimal sedation is defined as a state in which the patient is able to respond normally to verbal commands, breathe on their own and maintain stable blood pressure and heart rate. It is achieved by administering a small dose of a sedative or anxiolytic medication.

Minimal sedation is a light form of sedation that allows the patient to remain conscious and responsive throughout the procedure, and it helps the patient to relax and reduce anxiety.

It is considered a safer option than deeper forms of sedation as the patient remains able to breathe on their own, which reduces the risk of complications. This level of sedation is often used in procedures such as dental work, minor skin procedures, and diagnostic tests.

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The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.

Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.

Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:

P(Democrat) = 60/100 = 0.6

Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:

P(Woman) = 60/100 = 0.6

Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:

P(Democrat and Woman) = 40/100 = 0.4

To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:

P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)

= 0.6 + 0.6 - 0.4

= 0.8

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Answer:

6

Step-by-step explanation:

f(x) = 2(x-5)

f(8) = 2(8-5)

f(8) = 6

Answer:

6

Step-by-step explanation:

Personally Took the quiz. this was the right answer

Using the definition of big o notation, t(n) = 32 * 4^n is O(f(n)) = 5^n with c = 26 and n0 = 1.

The definition of Big O notation states that a function t(n) is said to be O(f(n)) if there exist positive constants c and n0 such that |t(n)| <= c * |f(n)| for all n >= n0. In other words, t(n) grows no faster than f(n) as n becomes large.

To find the constants c and n0 that show that t(n) = 32 * 4^n is O(f(n)) = 5^n, we need to find a value of c and an n0 such that:

|32 * 4^n| <= c * |5^n|

for all n >= n0.

Let's start by finding a value for c that works for n = 1. We have:

|32 * 4^1| = 128 <= c * |5^1| = 5c

So, c >= 128 / 5 = 25.6.

Now let's try c = 26. We have:

|32 * 4^n| <= 26 * |5^n|

for all n >= 1.

Since 26 * |5^n| is an increasing function as n increases, we can conclude that:

t(n) = 32 * 4^n is O(f(n)) = 5^n

with c = 26 and n0 = 1.

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According to the information, it can be inferred that the bees must travel a distance of 4,803,620.82 km to complete the 30 kg of honey that a hive produces.

To calculate the distance that bees register to produce honey we must perform the following operation.

1. Calculate how many kilometers are equal to the circumference of the earth with the following formula 2*pi*R. In this case we replace the R, by the radius of the earth and we will obtain the distance of the circumference of the earth.

\(2\pi r\)

\(2\pi 6,371 km = 40,030.1736\)

2. Once we have identified the circumference of the earth, we must multiply it by four to know how much distance the bee will recover to produce one kg of honey.

40,030.1736 * 4 = 160,120.694

3. Finally we must multiply the distance it takes to produce 1kg by 30 to find the distance it takes to produce 30kg of honey.

160,120,694 * 30 = 4,803,620.82

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Events A and B are not mutually exclusive. Two events are mutually exclusive if they cannot occur at the same time. In other words, if event A occurs, then event B cannot occur, and vice versa.

The probability of two mutually exclusive events occurring together is 0. In this case, P(A) = 1/2, P(B) = 1/3, and P(A or B) = 2/3. Since P(A or B) is greater than P(A) + P(B), it follows that events A and B are not mutually exclusive.

To see this more clearly, let's consider the following possible outcomes:

Event A occurs: This happens with probability 1/2.

Event B occurs: This happens with probability 1/3.

Both events A and B occur: This happens with probability 2/3 - 1/2 - 1/3 = 0.

As we can see, it is possible for both events A and B to occur. Therefore, events A and B are not mutually exclusive.

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1 kilogram of soil fit into 5/6 of the container and hence fit into the container.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s.

Given that, 2/5 kilograms of soil fit into 1/3 of a container.

Let x be the volume of container taken to fit 1 kilogram of the soil.

Using the concept of proportion,

2/5 : 1 = 1/3 : x

This can also be written as,

(2/5) / 1 = (1/3) / x

Doing the cross multiplication,

2/5 x = 1/3

x = (1/3) × (5/2)

x = 5/6

So 1 kilogram of soil takes 5/6 of the container, so it can be fit.

Hence 1 kilogram of soil can be fit in to the container.

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Your question is incomplete. Probably the correct question is attached below.

The area enclosed by the two given curves can be found by calculating the definite integral of the difference between the upper curve and the lower curve.

In this case, the upper curve is y² = 1 - r and the lower curve is y² = x + 1. To find the points of intersection, we can set the two equations equal to each other:

1 - r = x + 1

Simplifying the equation, we get:

r = -x

Now we can set up the integral. Since the curves intersect at r = -x, we need to find the limits of integration in terms of r. We can rewrite the equations as:

r = -y² + 1

r = y² - 1

Setting them equal to each other:

-y² + 1 = y² - 1

2y² = 2

y² = 1

y = ±1

So the limits of integration for y are -1 to 1.

The area can be calculated as:

A = ∫[from -1 to 1] (1 - r) - (x + 1) dy

Simplifying and integrating, we get:

A = ∫[from -1 to 1] 2 - r - x dy

A = ∫[from -1 to 1] 2 - y² + 1 - x dy

A = ∫[from -1 to 1] 3 - y² - x dy

Integrating, we get:

A = [3y - (y³/3) - xy] [from -1 to 1]

A = 2 - (2/3) - 2x

So, the area enclosed by the two given curves is 2 - (2/3) - 2x.

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Answer:

34

4x+10=14

3x+7=10

10×+4

34

A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.

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Answer:

Step-by-step explanation:

l = (wh)/a(w+p)

wh = la(w+p)

w = (la(w+p))/h

It could be D but mathematically it's 3/6=1/2

The value of x is 5.

The length of ST is 16.

Collinear points are the points that lie on the same straight line or in a single line.

Given:

RS = 5x - 9 and RT = 3x + 17

As, R, S and T are collinear points.

so, we can write

RS = ST

and, RS + ST = RT

2ST = Rt

ST= RT/2

ST = (3x+ 17)/2

Now,

RS = ST

5x - 9 =  (3x+ 17)/2

10x - 18 = 3x+ 17

7x = 35

x=5

So, the value of x is 5.

Now, length of ST

= (3x+ 17)/2

=(3*5 + 17)/2

=32/2

=16

Thus, length of ST is 16 units

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Answer:

$8.75

Step-by-step explanation:

52.50/6=8.75

To make sure that is correct

8.75×6

Answer:

Her hourly rate is $8.75

Step-by-step explanation:

Answer:

\(L + W \leq 9\)

Step-by-step explanation:

Given

Represent lifeguarding cars with L

Represent washing cars with W

\(Hours = 9\ hours\) --- at most

Required

Express the scenario as an inequality

First, we need to determine the number of hours Lauren can work.

This is calculated as follows:

\(Total\ Hours = L + W\)

From the question, we understand that the total hours cannot exceed 9 hours.

This can be expressed as \(\leq 9\)

So, we have:

\(Total\ Hours \leq 9\)

Substitute L + W for Total Hours

\(L + W \leq 9\)

Answer:

x = 5

Step-by-step explanation:

6x - 3x = 3

7 + 8 = 15

15/3 = 5

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