Na figura abaixo estão representadas cinco ruas do bairro onde moram João, Marcos, Pedro, Vitor e Samuel. A localização da casa de cada menino é identificada pela inicial de seu nome. Na esquina das ruas A e D fica a escola onde todos estudam. Sabe-se que as ruas A, B e C são paralelas e que todos os meninos vão a pé para a escola, sempre pelo caminho mais curto. Se Samuel caminha 100 m até a escola, Vitor caminha 260 m, João caminha 180 m e Marcos, 270 m, qual é a distância, em metros, que Pedro percorre de sua casa até a escola?


280m
300m
340m
460m
320m

Answer:

[tex]g^{-1}(x)=\frac{x-1}{6}[/tex]

Answer:

4z + 2 - 5/2z

Step-by-step explanation:

8z^2 + 4z -5

divided by 2z

8z^2 /2z = 4z

4z/2z =2

5/2z = 5/2z

Putting them back together

4z + 2 - 5/2z

Answer:

A   4z + 2 - 5/2z

Step-by-step explanation:

Answer:

(x+4)^2+(y+6)^2 = 25

Step-by-step explanation:

The radius squared is equal to the distance between the center and the point

3^2 + 4^2 = 25

We can shift the center like this

(x+4)^2+(y+6)^2 = 25

Answer:

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Step-by-step explanation:

(–2x³y² + 4x²y³ – 3xy⁴) – (6x⁴y – 5x²y³ – y⁵)=

–2x³y² + 4x²y³ – 3xy⁴ – 6x⁴y + 5x²y³ + y⁵=

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Answer:

shift B

Step-by-step explanation:

shift a is 78.6 repeating

shift b is 79.3 repeating

mean is when you add them all then divide it by the numbers it has

Answer:

shift B

Step-by-step explanation:

To calculate the mean for a set of data, add all the numbers in that set, then divide by the number of data points in the set.

Answer:

(a)No. The probability of drawing a specific second card depends on the identity of the first card.

(b)4/663

(c) 4/663

(d) 8/663

Step-by-step explanation:

(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.

(b) P(ace on 1st card and jack on 2nd).

[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]

(c)P(jack on 1st card and ace on 2nd)

[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]

(d)Probability of drawing an ace and a jack in either order.

We can either draw an ace first, jack second or jack first, ace second.

Therefore:

P(drawing an ace and a jack in either order) =P(AJ)+(JA)

From parts (b) and (c) above:

[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]

Answer:

n2-6n-16

Step-by-step explanation:

n(n+2)-8(n+2)

n2+2n-8n-16=

n2-6n-16

Answer: n 2 + 6n - 16

Step-by-step explanation:

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]

Compute the probability that on a randomly selected day she will have five messages as follows:

[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]

               [tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Answer:

False

Step-by-step explanation:

The greatest sum of two consecutive even integers would be 200 + 198, or 398

Answer:

its true

Step-by-step explanation:

Answer:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Step-by-step explanation:

For this case we can use the following function to model the population of protzoa:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Answer:

Step-by-step explanation:

Hello!

I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values

When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.

In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.

The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.

Watching the example, the median is 33

I hope this helps!

Answer: D

Step-by-step explanation:

Answer:

360 miles

Step-by-step explanation:

Answer:

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

 B. F(x) = 2(x+3)^2 + 3

 D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

75

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

3

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.

Answer:

D

Step-by-step explanation:

It's a football ....=> So ... A sphere !!

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.

The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.

We would set up the hypothesis.

a) The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

For disk shaped,

Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8

Standard deviation = √(summation(x - mean)²/n

n1 = 6

Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54

Standard deviation, s1 = √(337.54/6) = 7.5

For oval shaped,

Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375

n2 = 8

Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875

Standard deviation, s2 = √(991.75875/8) = 11.1

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

Therefore,

t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)

t = - 3

c) The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46

df = 12

We would determine the probability value from the t test calculator. It becomes

p value = 0.011

d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes

Answer:

The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following:

To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:

[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]

First, solve [tex]0>20x+2[/tex]

[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]

Next, solve [tex]20x+2>-32[/tex]

[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]

Finally, combine the intervals

[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]

The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:

Answer:

Step-by-step explanation:

Answer:

height = 5

Step-by-step explanation:

The volume of a prism is V = l*w*h

You are not given any information about the exact values of l and w.

You do know however that L and w when multiplied together = 20, so you can put that in for l*w. Then the formula becomes

V = 20*h

You are told that the volume is 100. Now the problem is simplified. You get

100 = 20 * h               Divide both sides by 20

100/20 = 20*h/20     Combine like terms.

5 = h

Answer:

4a

Step-by-step explanation:

The mean is found by adding all of the data set together and then dividing by the amount of individual pieces of data in the set.

(2+3+3+8) = 16

16/4=4

The answer is 4a.

Answer:

The volume of the crystal is [tex]V=125 \:cm^3[/tex].

Step-by-step explanation:

The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.

To find the volume of a cube recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself three times. Or as a formula

                                                         [tex]V=s^3[/tex]

where:

s is the length of any edge of the cube.

From the information given we know that the crystal has edge lengths of 5 centimeters. Therefore, the volume of the crystal is

[tex]V=5^3=125 \:cm^3[/tex].

Answer:

6

Step-by-step explanation:

Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.

x = 8 *3/4 = 6

Answer:

x= y^2+4y+4

Step-by-step explanation:

x= (y+2)(y+2)

x= y^2+2y+2y+4

x= y^2+4y+4

Answer:

X = y^2 + 4y + 4

Y= (√X) -2

Step-by-step explanation:

X = (Y+2)^2

X = (Y+2)(Y+2)

X = Y^2 + 4y + 4

X = (Y+2)^2

√X = √(Y+2)^2             (taking the root of both sides cancels the exponent)

√X = Y+2

-2        -2

(√X) - 2 = Y

or

Y = (√X) - 2

Answer:

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $79.20

Standard deviation r = $10.41

Number of samples n = 14

Confidence interval = 90%

Using the z table;

The critical value that should be used in constructing the confidence interval.

z(α=0.05) = 1.645

Critical value at 90% confidence z = 1.645

Substituting the values we have;

$79.20+/-1.645($10.42/√14)

$79.20+/-1.645($2.782189528308)

$79.20+/-$4.576701774067

$79.20+/-$4.577

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

In the given point(-4,b) -4 is the x value.

Locate -4 on the graph and find the y value where the line is located. The y value would be b.

B = 1

Answer:

h ≈ 77 cm

Step-by-step explanation:

Let us convert the liters to cm³.

Smaller barrel

0.001 litres = 1 cm³

100 litres = 100000  cm³

Larger barrel

0.001 litres = 1 cm³

160 litres = 160000  cm³

For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.

This means

h³/90³ = 100000/160000

cube root both sides

h/90 =  ∛100000 / ∛160000

h/90 = 46.4158883/54.2883523

cross multiply

54.2883523h = 46.4158883 × 90

54.2883523h = 4177.429947

divide both side by  54.2883523

h = 4177.429947/54.2883523

h = 76.9489175858

h ≈ 77 cm

Answer:

e. the gender of the students in a class

Step-by-step explanation:

Quantitative data is measured is numbers. For example 1, 2, 3.5,...

Qualitative data are labels, that is, tall, short, male, female, Brazilian, Colombian,...

In this question:

The only data that is not measured in numbers is the gender of the studens in class, which can be male or female, they do not assume any numeric value. So the answer is e.

The quantitive data example does not include option e. the gender of the students in a class.

learn more about the data here: https://brainly.com/question/20296761

Answer:

33084

Step-by-step explanation:

22056 divided by 2 =11028

altogether (on sunday and monday) the total amount would be..

22056+11028=33084

Answer:

33084

Step-by-step explanation:

If 22056 people came to the game on Sunday and Half as many people came on Monday, you do

22056 divided by 2. this is how many people cam on monday

Add this answer to 22056 and this is how many people came on both days.

Answer:

C = 20 + 0.001x

C = $20 + $0.001x

Step-by-step explanation:

Let x represent the number of minutes spent talking on the phone.

Given;

Fixed monthly charge F = $20

Charge per 10 minutes V = $0.01

Charge per minute = V/10 = $0.01/10 = $0.001

The equation to model the cost of a monthly cell phone bill;

Total cost = fixed cost + variable cost

C = F + (V/10)x

Substituting the values;

C = 20 + 0.001x

Answer:

14

Step-by-step explanation:

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

Answer:

  (0, 3/2)

Step-by-step explanation:

The equation can be put in the form ...

  x^2 = 4py

where p = 3/2.

In this form, the focus is distance "p" from the vertex in the direction the parabola opens.

The vertex is at (0, 0); the parabola opens upward. So, the focus is 3/2 units above the vertex, at ...

  focus = (0, 3/2) . . . . . matches choice A

the correct answer is 59.

Answer:

59

Step-by-step explanation: