1. Considere as funções f e g, ambas com domínio Z, dadas por f(x) = x²- 2x e g(x) = x³-1. Associe as colunas e assinale a alternativa que apresenta a sequência correta: *
1 ponto
a) f (-2) ( )29
b) g(-2) ( )15/7
c) f(-1) + g(3) ( )8
d) f(5) : g(2) ( )-9

a) C, D, A, B
b) A, B, D, C
c) D, C, A, B
d) A, C, D, B



ajuuuuuda

Answer:

So the answer is the first one

Step-by-step explanation:

3 + 15 + 75 + 375 + 1,875

This is a geometric series.  The first term is 3, the common ratio is 5, and the number of terms is 5.

∑₁⁵ 3 (5)ⁿ⁻¹

∑₀⁴ 3 (5)ⁿ

3 + 12 + 48 + 192 + 768

This is a geometric series.  The first term is 3, the common ratio is 4, and the number of terms is 5.

∑₁⁵ 3 (4)ⁿ⁻¹

∑₀⁴ 3 (4)ⁿ

4 + 32 + 256 + 2048 + 16,384

This is a geometric series.  The first term is 4, the common ratio is 8, and the number of terms is 5.

∑₁⁵ 4 (8)ⁿ⁻¹

∑₀⁴ 4 (8)ⁿ

2 + 6 + 18 + 54 + 162

This is a geometric series.  The first term is 2, the common ratio is 3, and the number of terms is 5.

∑₁⁵ 2 (3)ⁿ⁻¹

∑₀⁴ 2 (3)ⁿ

Answer:

a) [tex] \mu_m -\mu_a [/tex]

[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning

[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon

[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning

[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon

[tex]n_{m}=49[/tex] sample size for the morning

[tex]n_{a}=54[/tex] sample size for the afternoon

b) Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]

Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]

c) [tex] t_{\alpha}= 1.66[/tex]

d) [tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]  

The p value would be:

[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]

e) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance

Step-by-step explanation:

Part a

[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning

[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon

[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning

[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon

[tex]n_{m}=49[/tex] sample size for the morning

[tex]n_{a}=54[/tex] sample size for the afternoon

t would represent the statistic

[tex]\alpha=0.05[/tex] significance level

The parameter of interest is:

[tex] \mu_m -\mu_a [/tex]

Part b

We want to verify if the people who exercise in the morning have a mean exercise time greater than those who work out in the afternoon or evening, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]

Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]

The statistic is given by:

[tex]t=\frac{\bar X_{m}-\bar X_{a}}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{a}}{n_{a}}}}[/tex] (1)

Part c

Based on the significance level[tex]\alpha=0.05[/tex] and the degrees of freedom given by:

[tex] df = 49+54-2= 101[/tex]

We can find the critical value in the t distribution iwth 101 degrees of freedom who accumuate 0.05 of the area in the right and we got:

[tex] t_{\alpha}= 1.66[/tex]

Part d

[tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]  

The p value would be:

[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]

Part e

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance

Answer:

Below.

Step-by-step explanation:

sin ((x))-(y)) / cos (x) sin (y)

    sin x cos y - cos x sin y

=  ----------------------------------

           cos x sin y

     sin x cos y

=    ----------------   -   1

     cos x sin y

But tan x = sin x / cos x  and cot y = cos y / sin y

So the above =  tan x cot y - 1.

Answer:

1,664 fluid ounces = 13 gallons

Step-by-step explanation:

Answer:

9x^3-21x^2+19x-6

Step-by-step explanation:

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6

9x^3-21x^2+19x-6

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6 is the answer to the question

Answer:

I think it changed from 36x to 48x

Depending on how you look at it, it could have changed from 3x to 4x or 36x to 48x.

If they said it was 18 feet instead of 18 inches, it would be 3x or 4x, but they had it as inches.

18 inches = 1.5 feet

72/1.5 = 48

54/1.5 = 36

So originally, it would have been a scale of 1 in : 36in , but it changed to 1 in : 48 in  

Sorry if this was confusing.

Answer:

One inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale. Otherwise known as D

I got 100% on my quiz.

Step-by-step explanation:

Answer:

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 22, \sigma = 5.1[/tex]

Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?

The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.

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

[tex]Z = \frac{24 - 22}{5.1}[/tex]

[tex]Z = 0.39[/tex]

[tex]Z = 0.39[/tex] has a pvalue of 0.6517

1 - 0.6517 = 0.3483

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Answer:

Cost of tools: $100

Cost for each chair: $25

Step-by-step explanation:

You can see that before 1 chair, the cost is at 100. This means that the cost of the tools is $100. Another way to determine this is to see that at 1 chair, the cost is $125. At 2, it's $150, and at 3 it's $175, etc. This tells you that the cost to produce each chair is $25, but it also tells you that the tools cost 100 dollars, since the total cost at 1 chair is $125, and each chair only costs $25.

Hope this helps!

Answer:

100,25

Step-by-step explanation:

Answer:

x= 13.7 (nearest tenth)

Step-by-step explanation:

Please see attached picture for full solution.

Since density is equal to mass per unit volume, mass is equal to density times volume. So we split up the lamina into tiny regions with "volume" (area) equal to dA, multiplied by the density, and integrated over the entirety of the lamina.

This is best done in polar coordinates:

[tex]\begin{cases}x=u\cos v\\y=u\sin v\end{cases}\implies\mathrm dA=\mathrm dx\,\mathrm dy=u\,\mathrm du\,\mathrm dv[/tex]

so that [tex]x^2+y^2=u^2\cos^2v+u^2\sin^2v=u^2[/tex].

The lamina is then the set of points

[tex]L=\left\{(u,v)\mid1\le u\le2\land0\le v\le\dfrac\pi2\right\}[/tex]

Now compute the integral: the mass of the lamina is

[tex]\displaystyle\iint_L(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^2u^3\,\mathrm du\,\mathrm dv=\frac\pi2\int_1^2u^3\,\mathrm du=\frac{15\pi}8[/tex]

Answer:

6m = b

Step-by-step explanation:

The area of triangle when angle and sides are given = 1/2* sin angle*ab

Area = 1/2 * sin 30 * 4*b

Area = 6m²

6 = 1/2 * sin 30 * 4*b

(6*2)/(sin 30 * 4)= b

12/(0.5*4) = b

12/2 = b

6m = b

Answer:

1 = D 75 inches

2 = A 27

Step-by-step explanation:

1 - 6.3 times 12 = 75.6

2 - 6 times 9 = 54

54/2 = 27

:)

Answer:

(-21a^5×b)/(2+4b)

Step by step explanation:

The question isn't complete and clear as we were not told what to determine from the expression.

Looking at the question, we can tell we are to simplify the expression.

[(-7a² × 9a³x³) :(-3ax³)] : [( 10a) -(-20a b) : (-5a²b)]

First we would work with expressions in each parenthesis (bracket).

Then we would work on the answer we derive after opening the parenthesis.

See attachment for detail

Answer:

1899

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 3234

Standard deviation = 871

Percentage of newborns who weighed between 1492 grams and 4976 grams:

1492 = 3234 - 2*871

So 1492 is two standard deviations below the mean.

4976 = 3234 + 2*871

So 4976 is two standard deviations above the mean.

By the Empirical Rule, 95% of newborns weighed between 1492 grams and 4976 grams.

Out of 1999:

0.95*1999 = 1899

So the answer is 1899

Answer:

  14 ft

Step-by-step explanation:

After the sides are folded up, the depth of the box is 2 ft, so the area of the square bottom is ...

  (200 ft^2)/(2 ft) = 100 ft^2

The edge dimension of the bottom is then ...

  √(100 ft^2) = 10 ft

Each side adds 2+2=4 ft to the bottom dimension in each direction, so the original square piece of metal was 14 ft square.

Answer:

6/5, or 1.2

Step-by-step explanation:

The right answer is 6/5

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

Given a negative square root √(-x);

From our knowledge of complex numbers, we know that

i^2 = -1 and vise versa

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.

If A × A = B

Then √B = A.

Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.

2 × 2 = -2 × -2 = 4

3 × 3 = -3 × - 3 = 9

And so on.

So, the square root of 4 = 2 or -2

The square root of 9 = 3 or -3

But if one of the numbers is positive while the other is negative, then the result is negative.

2 × -2 = -4

3 × -3 = -9

Clearly, √(-4) ≠ 2 ≠ -2

√(-9) ≠ 3 ≠ -3

It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.

Let i² = -1, then we have that

√(-1) = i.

This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.

-A = -1 × A

So, √(-A) = √(-1 × A)

= √(-1) × √A

= i × √A

= i√A

Example, to simplify √(-16)

√(-16) = √(-1 × 16)

= √(-1) × √16

= i × ±4

= ±4i

Answer:

The answer is c

Step-by-step explanation:

The statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.

The congruent triangles are:

Triangle MNO and Triangle NMO

The above means that:

Sides MN and NO or MN and MO are equal

So, the triangles are isosceles triangles

However, it is possible that sides NO and MO are congruent

Hence, the statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.

Read more about congruent triangles at:

https://brainly.com/question/1675117

Answer:

The approximate percentage of the Chipotle meals that have more than 471 calories is 95%.

Step-by-step explanation:

We are given that meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories.

Let X = Chipotle meals having calories

So, X ~ Normal([tex]\mu=1075, \sigma^{2} =302^{2}[/tex])

Now, the 68-95-99.7 rule states that;

So, the approximate percentage of the Chipotle meals that have more than 471 calories is given by;

                               [tex]\frac{X-\mu}{\sigma} = \frac{471-1075}{302}[/tex]

                                        =  -2

Since, it is stated above that 95% of the data values lies within two standard deviation points which means 95% values lies between -2 and 2 z score values.

SO, the approximate percentage of the Chipotle meals that have more than 471 calories is 95%.

Answer:

[tex]2mn[/tex]

Step-by-step explanation:

[tex]6m^3n,\:8mn^2[/tex]

Find the GCD of [tex]6,\:8[/tex]:

[tex]6[/tex]

[tex]=2\cdot \:3[/tex]

[tex]8[/tex]

[tex]=2\cdot \:4[/tex]

[tex]=2\cdot \:2\cdot \:2[/tex]

So the prime factor common to 6, 8 is:

[tex]2[/tex]

So the factor common to [tex]6m^3n,\:8mn^2[/tex]:

[tex]=2mn[/tex]

Answer:

Below.

Step-by-step explanation:

Yes - those are 2 semicircles so their combined area = πr^2

= 3^2π

= 9π.

Yes.. You can count it as full circle.

Answer:

3.9 squre inch

Step-by-step explanation:

Two semicircles are inscribed in a square of side 6 in. Both the semicircles if combined together will form a full circle.

Area of the yellow region would be half of the areas of the difference between area of square and area of two semicircles each with radius 3 inches.

Therefore,

Area of yellow region

[tex] = \frac{1}{2} (area \: of \: square - 2 \times area \: of \: semicircle) \\ \\ = \frac{1}{2} ( {6}^{2} - 2 \times \frac{1}{2} \pi {r}^{2} ) \\ \\ = \frac{1}{2} ( {6}^{2} - 3.14 \times {3}^{2} ) \\ \\ = \frac{1}{2} ( 36 - 3.14 \times 9 ) \\ \\ = \frac{1}{2} ( 36 - 28.26 ) \\ \\ = \frac{1}{2} \times 7.74 \\ \\ = 3.87 \: {in}^{2} \\ \\ = 3.9 \: {in}^{2}[/tex]

Step-by-step explanation:

Abby’s Expression:

Double m, giving 2m. She then takes 20% of the result, which we can write 0.2(2m). Finally she subtracts this from 2m, giving 2m−(0.2)2m

2m − (0.2)2m

Renato’s Expression:

Divide m by 5, giving m ÷ 5 = m/5, and then multiplies the result by 8, giving:

8(m/5)

Answer:

25 miles per gallon

Step-by-step explanation:

We want to find miles per gallon so take the miles and divide by the gallons

500 miles / 20 gallons

25 miles per gallon

Answer:

[tex]= 25 \: \: \: miles \: \: \: per \: \: \: gallon \\ [/tex]

Step-by-step explanation:

You have to find miles per gallon.

So to solve that you have to divide miles by gallon.

[tex] \frac{500}{20} \\ = 25 \: \: \: miles \: \: \: per \: \: \: gallon[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Explanation:

The equation for the total cost of the clothes is 4×80+25+c=430, where c is the cost of the coat.

320 + 25 + c = 430

         345 + c = 430

345 - 345 + c = 430 - 345

c = 85

The cost of the coat was $85.

Answer:

$85 for the coat

Step-by-step explanation:

1 dress = $80

4 dress =$80×4

=$320

sweater=$25

coat=?

4 dresses plus the sweater cost :

$320+$25=$345

The cost of all the item $430

cost of the coat :

$430-$345=$85

Answer:

Step-by-step explanation:

The sum of 7 and 10 is 17. So 123 / 17 = 7.235 (roughly)

7.235 x 10 (for Adriana's aunt's age) equals 72.35

And to double check: We can find adriana's age by doing. 7.235 x 7 = 50.645. If we add 50.645 and 72.35 we get 122.995 which is roughly 123 and the reason why it is not 123 on the dot is because 123 / 17 is roughly 7.235 the full expanded one is: 7.23529411765

You may try checking with the full number without estimating but i am sure of my answer

Answer:

(-5,13)

Step-by-step explanation:

because t=3

[tex]x = 1 - 2 \times 3 = - 5 \\ y = 4 \times 3 + 1 = 13[/tex]

Answer:

1st one is 2. 2nd one is 5. 3rd one is less than. 4th one is, is smaller

Step-by-step explanation:

Answer:

2x(2x - 1)(x + 3)

Step-by-step explanation:

4x^3 + 10x^2 - 6x =

Factor out the common factor 2x.

= 2x(2x^2 + 5x - 3)

Factor the trinominal.

= 2x(2x - 1)(x + 3)

Answer:

[tex]=2x\left(2x-1\right)\left(x+3\right)[/tex]

Step-by-step explanation:

[tex]4x^3+10x^2-6x\\\mathrm{Factor\:out\:common\:term\:}2x:\quad 2x\left(2x^2+5x-3\right)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\x^3=x^2x\\=4x^2x+10xx-6x\\\mathrm{Rewrite\:}6\mathrm{\:as\:}2\cdot \:3\\\mathrm{Rewrite\:}10\mathrm{\:as\:}2\cdot \:5\\\mathrm{Rewrite\:}4\mathrm{\:as\:}2\cdot \:2\\=2\cdot \:2x^2x+2\cdot \:5xx-2\cdot \:3x\\\mathrm{Factor\:out\:common\:term\:}2x\\=2x\left(2x^2+5x-3\right)\\\mathrm{Factor}\:2x^2+5x-3:\quad \left(2x-1\right)\left(x+3\right)[/tex]

[tex]2x^2+5x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(2x^2-x\right)+\left(6x-3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-x\mathrm{:\quad }x\left(2x-1\right)\\2x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=2xx-x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(2x-1\right)\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}6x-3\mathrm{:\quad }3\left(2x-1\right)\\6x-3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=3\cdot \:2x-3[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}3\\=3\left(2x-1\right)\\=x\left(2x-1\right)+3\left(2x-1\right)\\\mathrm{Factor\:out\:common\:term\:}2x-1\\=\left(2x-1\right)\left(x+3\right)\\=2x\left(2x-1\right)\left(x+3\right)[/tex]