Simplify this problem. Leave answer in exponents.

Using the normal distribution, we have that:

a) There is a 0.0548 = 5.48% probability that an individual distance is greater than 218.00 cm.

b) There is a 0.7967 = 79.67% probability that the mean for 25 randomly selected distances is greater than 204.20 cm.

c) Since the underlying distribution is normal, the central limit theorem can be applied.

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]

For this problem, the parameters are:

[tex]\mu = 205.5, \sigma = 7.8, n = 25, s = \frac{7.8}{\sqrt{25}} = 1.56[/tex]

Item a:

The probability is one subtracted by the p-value of Z when X = 218, hence:

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

[tex]Z = \frac{218 - 205.5}{7.8}[/tex]

Z = 1.6

Z = 1.6 has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

There is a 0.0548 = 5.48% probability that an individual distance is greater than 218.00 cm.

Items b and c:

Since the underlying distribution is normal, the central limit theorem can be applied, hence the probability is one subtracted by the p-value of Z when X = 204.2.

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

By the Central Limit Theorem:

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

[tex]Z = \frac{204.2 - 205.5}{1.56}[/tex]

Z = -0.83

Z = -0.83 has a p-value of 0.2033.

1 - 0.2033 = 0.7967.

There is a 0.7967 = 79.67% probability that the mean for 25 randomly selected distances is greater than 204.20 cm.

More can be learned about the normal distribution at https://brainly.com/question/4079902

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Answer:

To make a box and whisker plot, you need to draw a number line that would be able to represent all the values in the data (look at your lowest and highest numbers).

You will need to graph the following 5 points on your number line (median, lower quartile, lower extreme, upper quartile, and upper extreme).

Create a box around the quartiles and extend the lines to the extremes.

See the picture I have attached for the box and whisker box for this data set.

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

Suppose there are 7 males so there will be 1 female according to the question.

So there is 1 female out of a total of 8 students. So the answer is 1/8.

Because the female is 1 out of the 8 people.

What is the header for this page?

Header means the text written at the top of the page. The word written at the top of our page is The slope. Hence, it is the header for the page...~

Answer:

180 burritos

Step-by-step explanation:

15 burritos = 5 mins

x burritos = 60 mins

cross multiply

5x = 60 ×15

5x = 900

x = 900/5

therefore x = 180 burritos

Answer:

28

Step-by-step explanation:

So first you need to add up the time they played yesterday which means add up the times for each drill(22+35+27) which equals 84. Now you need to divide 84 by 3 because there are 3 drills(84÷3) which equals 28 and you will get your answer

22 + 35 + 27 = 84 ÷ 3 = 28

Hope this helps

Please mark brainliest.

This is the Answer really

Answer:

2286

Step-by-step explanation:

If you take 14 percent of a number and get 320, then what is that number? In other words, you know that 14 percent of a number is 320 and you want to know what that initial number is.

To solve this problem you multiply 320 by 100 and then divide the total by 14 as follows: (320 x 100) / 14

When we put that into our calculator, we get the following answer:

2285.71

can't have a portion of someone to you round it to the nearest whole number.

Answer:

The town’s population is 2286 (approximately)

Step-by-step explanation:

Let x be the number of the town’s residents :

We can translate the statement “14% of the town’s population is over the age of 65 and there are 320 residents over the age of 65” mathematically like this :

[tex]\frac{14}{100} x=320[/tex]

[tex]\Longrightarrow 14x=320\times 100\\\\\Longrightarrow 14x=32000[/tex]

[tex]\Longrightarrow x=\frac{32000}{14}[/tex]

[tex]\Longrightarrow x=2285.71428571429[/tex]

The addition of the new dog will change the median. The correct answers may be A and D.

The Median is the middlemost value of the numbers arranged in ascending order. If the number of the data is an odd number so the median will be a middle number if the number of the data is even then the median is the mean of the middle two numbers.

In light of the fact that the average weight of 15 dogs in a pet shop is 12 pounds. The median will shift as a result of the new dog. The right responses could be A and D.

To know more about the median follow

https://brainly.com/question/26151333

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Step-by-step explanation:

The answer is 3950 $

First we will calculate the two profits the dealership earned.

1. Profit on purchase.

18000 x 15% = 18000 x 0.15

=2700 $

2. Profit on Sale:

5000 x 25% = 5000 x 0.25

= 1250$

3. Adding both profits:

Total profit = 2700 + 1250 = 3950 $

Answer:

[tex]\huge\boxed{\sf d = 14.39\ cm}[/tex]

Step-by-step explanation:

Given:

Circumference = c = 45.1846 cm

π = 3.14

Required:

Diameter = d = ?

Formula:

C = πd

Solution:

Rearrange formula

d = C / π

d = 45.1846 / 3.14

d = 14.39 cm

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

The larger the negative number gets, the farther from zero it becomes. -9.8 is closer to zero- therefore "larger" than -11.3.

Have a nice day/night :)

~pinetree

Answer:

[tex]y=-3x+5[/tex]

Step-by-step explanation:

The equation for slope is:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We can substitute the given coordinates into the equation:

[tex]Slope=\frac{3-0}{\frac{2}{3}-\frac{5}{3}}=\frac{3}{\frac{2-5}{3}}=\frac{3}{\frac{-3}{3}}=\frac{3}{-1}=-3[/tex]

The slope is -3

The equation for a line is:

[tex]y=mx+b[/tex]

m: slope

b: y-intercept

x, y: (x, y) coordinate pair

Now, plug in the slope and one of the (x, y) coordinate pairs to solve for the y-intercept.

[tex]y=mx+b\\y=-3x+b\\0=-3(\frac{5}{3})+b\\0=\frac{-15}{3}+b\\0=-5+b\\$Add 5 to both sides\\b=5[/tex]

Therefore the equation is:

[tex]y=-3x+5[/tex]

Answer:

let x yd be the height of the rectangular prism.

4/5x = 35/15

      x= 2 11/12 yd

Step-by-step explanation:

since the formula for the volume of cuboids is base area times height, we can use that equation to find out! :D

Answer:

area of shaded region: 21.07 ft²

Given for semi circle:

Given for rectangle:

Find area of rectangle:

Length * Width

14 * 7

98 ft²

Find the area of semi circle:

1/2 * π * r²

1/2 * 3.14 * (7)²

76.93 ft²

Area of shaded region:

area of rectangle - area of semi-circle

98 ft² - 76.93 ft²

21.07 ft²

Answer:

Jason's original position is 70.02 yards, or 70 yards

Step-by-step explanation:

These types of questions are understood better when drawn out.

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, we will use the concept of integration and algebric identities

We have,

[tex]\bold{\displaystyle\int}{\bold{\dfrac{ cos^{2}x}{1 + sinx}}}{\bold{dx}}[/tex]

By using trigonometric identity,

[tex]\sf{\displaystyle\int}{\sf{\dfrac{ 1 -sin^{2}x }{1 + sinx}}}{\sf{dx}}[/tex]

By using algebraic identity :-

[tex]\sf{\displaystyle\int}{\sf{\dfrac{ (1 + sinx) (1 - sinx) }{1 + sinx}}}{\sf{dx}}[/tex]

[tex]\sf{\displaystyle\int}{\sf{( 1 - Sinx)dx}}[/tex]

[tex]\sf{ {\displaystyle\int} dx - {\displaystyle\int}sinxdx}[/tex]

We know that,

[tex]\sf{ x - (-cosx) + c}[/tex]

[tex]\bold{ x + cosx + c}[/tex]

Hence, The answer is x + Cosx + c.

We are given with an integral and need to solve the integral , so let's start ;

[tex]{:\implies \quad \displaystyle \int \sf \dfrac{\cos^{2}(x)}{1+\sin (x)}dx}[/tex]

As we know that sin²(x) + cos²(x) = 1 , using this

[tex]{:\implies \quad \displaystyle \int \sf \dfrac{1-\sin^{2}(x)}{1+\sin (x)}dx}[/tex]

Can be further written as

[tex]{:\implies \quad \displaystyle \int \sf \dfrac{1^{2}-\sin^{2}(x)}{1+\sin (x)}dx}[/tex]

[tex]{:\implies \quad \displaystyle \int \sf \dfrac{\cancel{\{1+\sin (x)\}}\{1-\sin (x)\}}{\cancel{\{1+\sin (x)\}}}dx\quad \qquad \{\because a^{2}-b^{2}=(a+b)(a-b)\}}[/tex]

[tex]{:\implies \quad \displaystyle \int \sf \{1-\sin (x)\}dx}[/tex]

Now , as integrals follow distributive property , so ;

[tex]{:\implies \quad \displaystyle \int \sf 1\: dx-\int \sin (x)dx}[/tex]

Now , as antiderivative (Integration) of sin(x) is -cos(x) + C and that of dx is x + C So ;

[tex]{:\implies \quad \displaystyle \bf \therefore \underline{\underline{\int \bf \dfrac{\cos^{2}(x)}{1+\sin (x)}=x+\cos (x)+C}}}[/tex]

This is the Required answer

Answer:

C) glossary

Step-by-step explanation:

It is the one given in the picture.

Answer:

the answer is 6+x=24

Step-by-step explanation:

awesome

Answer:

6 + x = 24

Step-by-step explanation:

This is an equation because it has an EQUAL SIGN "=". an expression with an equal sign makes an equation.

It's in the name "EQUATION" (EQUAL)

A representation " = "

Answer:

d

Step-by-step explanation:

the length of the third side should be less than the sum of other two sides, that is  5+ 11 = 16 and it should be greater than the 5

6 < x < 16

Answer:

I learned how to multiply

Step-by-step explanation:

8×8=64

8 times the number you are multiplying

like this look

IIIIIIII there are Eight sticks each one has a value of 8

so you go 8,16,24,32,40,48,56,64. more

Answer:

Step-by-step explanation:

The sort of sequence it is can be determined by looking at the differences of n-values and the differences of t(n)-values. When the n-value differences are constant, the nature of the relation between the t(n)-values can tell you the kind of sequence.

Here, the n-values all differ by 1. The t(n)-value differences double with each increase in n. That is, they are 5 and 10. We notice also that the t(n) values double with each increase in n. We can fill the rest of the table using that relationship:

  t(n) = t(n-1) × 2 . . . . . each term is double the previous term

  t(4) = t(3) × 2 = 20 × 2 = 40

  t(5) = t(4) × 2 = 40 × 2 = 80

When the terms of the sequence have a common ratio, the sequence is geometric, and the function describing the sequence is an exponential function.

__

The general term of a geometric sequence is ...

  t(n) = t(1) × r^(n-1)

The table tells us the first term is ...

  t(1) = 5

And our observation above tells us the common ratio is r = 10/5 = 2. Then the equation of the sequence is ...

  t(n) = 5 × 2^(n-1)

__

See the attachment for a graph.

Answer:

a)   (4, 40) and (5, 80)

b)  [tex]t(n)=2.5 \cdot2^n[/tex]

c)  see attached

Step-by-step explanation:

As the value of t(n) doubles each time, we can conclude that this is an exponential function.

Therefore, the missing ordered pairs are (4, 40) and (5, 80)

General form of an exponential function:  [tex]y=ab^x[/tex]

where:

If [tex]b > 1[/tex] then it is an increasing function

If [tex]0 < b < 1[/tex] then it is a decreasing function

Given:

Substitute these ordered pairs into the general form of the exponential function:

Equation 1:   [tex]ab^2=10[/tex]

Equation 2:   [tex]ab^3=20[/tex]

Divide Equation 2 by Equation 1 to find [tex]b[/tex]:

[tex]\implies \dfrac{ab^3}{ab^2}=\dfrac{20}{10}[/tex]

[tex]\implies b=2[/tex]

Now substitute the found value of [tex]b[/tex] into one of the equations and solve for [tex]a[/tex]:

[tex]\implies ab^2=10[/tex]

[tex]\implies a\cdot 2^2=10[/tex]

[tex]\implies a=\dfrac{10}{4}[/tex]

[tex]\implies a=2.5[/tex]

So the final exponential equation is:  [tex]t(n)=2.5 \cdot2^n[/tex]

Graphing

Plot the points from the table

To find the y-intercept:

Substitute [tex]n = 0[/tex] into the equation:

[tex]\implies t(0)=2.5 \cdot2^0[/tex]

[tex]\implies t(0)=2.5[/tex]

Therefore, the y-intercept is at (0, 2.5)

Asymptote:  [tex]t(n) = 0[/tex]

Answer:

3s

Step-by-step explanation:

the answer is 3 seconds

Solution:

Perimeter is the sum of the figure's sides.

Note that:

Simplify the expression:

I have attached the labelled diagram, Let's find the perimeter now..

Length of all sides:

Now, Let's add these values

[tex] \sf: \implies \: 10 + 10 + 10 + 10 + 10 + 4 + 4 + 30[/tex]

[tex] \sf: \implies \: 50+ 4 + 4 + 30[/tex]

[tex] \sf: \implies \: 50+ 8+ 30[/tex]

[tex] \sf: \implies \: 58+ 30[/tex]

[tex] \boxed{ \tt: \multimap \: 88}[/tex]

Thus, The perimeter of the given figure is 88 cm...~

Answer:

False

Step-by-step explanation:

3^5=234

234x2=486

486=64

The numbers dont match.

Hence, the equation is false

Answer:

Not true

Step-by-step explanation:

= 3⁵ x 2

= 3 x 3 x 3 x 3 x 3 x 2

= 9 x 9 x 6

= 81 x 6

= 486

486 ≠ 64

Not true

Answer:

216

Step-by-step explanation:

9*(2*12)

9*(24)

9*24

216 ans

Answer:

costo total = c

costo del artículo = x

impuesto = 8,25 % = 0,0825 {cambiar el porcentaje a decimal moviendo el punto decimal dos a la izquierda}

Para encontrar impuestos:

- multiplique el costo del artículo por el porcentaje de impuestos (como decimal)

= .0825x

Para encontrar el costo total:

- agregue el costo del artículo más impuestos

= x + .0825x

c = x + .0825x {costo del artículo más impuestos}

Step-by-step explanation: