Which of the following statements is true?

Answer:

9.1

Step-by-step explanation:

3(9.1)=27.3

27.3÷3=×

×=9.1

Answer:

Define different tipes of discontuinity of a function .also,write the condition for increasing, decreasing and concave of function

thomas age:44

huilan age: 29

Step-by-step explanation:

h = t + 15

t + t + 15 = 73

2t = 73 - 15

2t = 58

t = 29

Answer:

Zeros: 0, 1, and 7

Step-by-step explanation:

Given function: f(x) = 3x(x - 1)²(x - 7)²

To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.

1. Substitute f(x) = 0:

[tex]\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2[/tex]

2. Divide both sides by 3:

[tex]\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2[/tex]

3. Separate into possible cases:

[tex]\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0[/tex]

4. Simplify:

[tex]\sf a)\ x = 0\ \textsf{[ already simplified ]}[/tex]

[tex]\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1[/tex]

[tex]\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7[/tex]

Therefore, the zeros of this function are: 0, 1, and 7.

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

Graph of the given equation is a opening up parabola passing through origin (0,0) and (2,0) and having vertex (1,-1)

Step-by-step explanation:

parabola - it is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

vertex - The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.

the given equation can be resolved as:

[tex]g(x)=(x-1)^2-1\\g(x) = x^2 -2x +1 -1\\g(x) = x^2 - 2x[/tex]

now substituting x = 0,

[tex]g(x) = x^2 - 2x\\g(x) = (0)^2- 2(0)\\g(x) = 0[/tex]

therefore the equation satisfies the point (0,0)that is origin.

now putting g(x) = 0,

[tex]g(x) = x^2 - 2x\\0 = x^2- 2x\\2x = x^2\\2=x[/tex]

so when y coordinate is 0 x coordinate is 2,

therefore the equation also satisfies the (2,0)

general equation of a parabola is

[tex]f(x) = ax^2 + bx + c[/tex]

and the vertex of the parabola is given by  [tex]\frac{-b}{2a}{,}{f{(}\frac{-b}{2a}{)}}[/tex]

given equation of parabola [tex]g(x) = x^2 - 2x[/tex]

here a = 1 and b= -2

substituting in the vertex formula,

vertex of the parabola is [tex]{(}{1}{,}{f{(}{1}{)}}{)}[/tex]

[tex]f(1) = 1 - 2 = -1[/tex]

therefore the vertex is (1,-1).

so the parabola is passing through origin(0,0) and (2,0) with vertex (1,-1).

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The quotient is -27m/ 55.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

(9mn²)(−3m*6n)÷33m*10n³

=9mn² *(-18mn) / 330mn³

= -162m²n³/ 330mn³

= -27m/ 55

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let :

C = number of cats

D = number of dogs

Raul's pet store has a play area that can fit up to 30 cats and dogs.

C + D = 30

The pet store never has more than 8 cats in the play areas.

(there can never be 9 or more cats)

As or the number of dogs :

C + D = 30

C = 30 - D

Since we know that C < 9. To get the number of dogs allowed, we just plug in 30 - D for C.

30 - D < 9

30 - 9 < D

or

(dogs have to be 22 or more)

Answer:

C. 261

Step-by-step explanation:

45 times 7= 315

326-315=11

125 times 2=250

250+11=261

so the answer is C. $261

Answer:

Yes.

Step-by-step explanation:

In mathematics, a number line ends in arrows on both sides, signifying it going infinite in the positive and negative directions.

Answer:

Yes.

Step-by-step explanation:

A number line is infinite in both directions it faces. This means left or right there is a infinite amount of numbers.

The average time taken to travel to Toronto by  the swarm of Rasberry Crazy Ants  is 12,947 Years

To arrive at the solution above, we need to look at the information given and the information assumed.

Step 1 - Information given:

Step 2 - Information assumed:

The swarm are travelling to the location of the student which is assumed to be Toronto.

Hence,

Time taken for the swam to get to Toronto (TTS) =

Distance between Austin, Texas and Toronto (DBTT) / Average distance covered per day by the Rasberry Ants. (ADC)

Estimated distance between Austin Texas and Toronto = 2592.6 Kilometers

Time travelled per day by the ants (In Km) = 0.00054864

Thus,

TTS  = DBTT/ADC

= 2592.6 /0.00054864

≈ 4,725,503.06 days or

≈ 12,947 Years

The answer to both questions is NO.

The average life expectancy in Toronto (as at 2022) is 80 years. Assuming I was born today, it is expected that the time between now and when my last grand child will die is about:

80 x 3 = 240 years.

Given that the ants have to travel 12,947  to get to Toronto, the possibility of my grand children seeing them is zero.

Besides, even if they by chance got to Toronto and infested my grandchildren's residence, they would have nothing to worry about because Rasberry Crazy Ants are 100% harmless.

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Answer:

y = 21x + 413

Step-by-step explanation:

Use y = mx + b

m represents the slope which in this case is 21.

b represents the y - intercept which in this case is 413.

Now, just fill in the variables.

y = 21x + 413

Hope this helps!

Because both lines have the same slope but different y-intercepts, we conclude that the lines are parallel.

Here we have the two lines:

6x - 2y = -2

y = 3x + 12

If we write both of these in the slope-intercept form, we get:

y = (-2 - 6x)/-2  = 3x + 1

y = 3x + 12

So, as you can see, both lines have the same slope but different y-intercepts. That means that the two lines are parallel, so they never do intercept.

Then we can conclude that the correct option is parallel.

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Answer:

1/2(6-8), 1/2(-3+7)=-1,2

Answer: C - (-1, 2)

Step-by-step explanation:

Considering that the mean of the normal distribution is the same as the median, the median is of 88%.

It states that, for a normally distributed random variable:

For the normal distribution, the median is the same of the mean, that is, the median is of 88%.

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Answer:

The number in the green box should be 3.

Step-by-step explanation:

[tex]c + 4 {c}^{2} - 2 + 2c - {c}^{2} + 5 = 3 {c}^{2} + 3c + 3[/tex]

Answer:

D -6, 15

Step-by-step explanation:

Because 3,11 is the middle, and 12,7 is the other end, you can do

12 - 3 = 9

3 - 9 = 6

then

11 - 7 = 4

11 + 4 = 15

so

6 is you x and 15 is your y

Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.

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Answer

(0,3)

Step-by-step explanation:

Answer is B.

Step-by-step explanation:

Since we know that in 30-60-90 triangle, the side corresponding to angle 90 degrees is two times the length of side corresponding to 30 degree angle. The length of side corresponding to 60 degree angle is  times the length corresponding to 30 degree angle.

We can see from our given choices that the side corresponding to 30 degree angle is 5 units.  

Therefore, the side lengths of a 30-60-90 triangle will be  and option B is the correct choice.  

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0.072 is the margin of error.

The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation.

According to the question,

In a random sample of 250 students,

p= 0.98 (or 98%) were in favor of longer hours at the school library.

The standard error of p(the sample proportion) is (approximately)

The standard error of p =   [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

p = 0.98

1 - p = 1 - 0.98 = 0.02

Here,

n = 250

The standard error of p =   [tex]\sqrt{ \frac{0.98 (0.02) }{250}[/tex]

The standard error of p ≈   0.072

Therefore,

The margin of error is 0.072.

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The number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a number line shown in the picture.

As we can see each unit is represented by 1.

So after 2 there will be 3 and after 4 there will be 5 and so on.

So after 8, there will be 9 which is represented by the arrow.

Thus, the number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.

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Answer: 9

Step-by-step explanation:

The number line going from - 4 to + 12 represents the range of possible values for the dividend of the division expression. The arrow going from 0 to 9 indicates the actual value of the dividend. Therefore, the number represented by the arrow is 9.

Using the normal distribution, it is found that 7.64% of of sample means are greater than 8.8 hours.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 8.4, \sigma = 1.77, n = 40, s = \frac{1.77}{\sqrt{40}} = 0.2799[/tex]

The proportion of sample means greater than 8.8 hours is one subtracted by the p-value of Z when X = 8.8, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{8.8 - 8.4}{0.2799}[/tex]

Z = 1.43

Z = 1.43 has a p-value of 0.9236.

1 - 0.9236 = 0.0764.

7.64% of of sample means are greater than 8.8 hours.

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Answer:

Step-by-step explanation:

We know that, 252 = 625

And, 262 = 676

Now, 676 - 625 = 51

So, there are 51 - 1 = 50 numbers lying between 252 and 262

The area of the sector, to 4 decimal places, is: 78.6794 cm².

Area of sector = ∅/360 × πr².

Given the following:

Area of sector = 46/360 × π(14²)

Area of sector ≈ 78.6794 cm²

The area of the sector is approximately 78.6794 cm².

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[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]

23 is a prime number, therefore there are two possibilities:

[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]

or

[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]

[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]

Now, we check if any of these solutions is also a solution to the second equation:

[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]

Therefore, 3 is not a solution.

[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]

Therefore, 4 is a solution.

[tex]\text{II.}[/tex]

[tex](x-3)!=23[/tex]

We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.

So, the only solution is [tex]x=4[/tex].

Answer:

The formula is: y = y•e^(-k•x)

In this specific case the function is: 512•e^(-x/1.44)

The number of players in the round 7 is 4

El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.

En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.

Entonces el costo por 2 pares es:

C = ($90 + $90)*(1 - 25%/100%)

Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:

C = ($180)*(0.75) = $135.

En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.

C = $90 + $90*(1 - 40%/100%) =

C = $90 + $90*(0.6) = $144

Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.

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Answer:

From what my calculations said its 20%