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Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
5
,
about the
y
-axis.

V
=

Answer:

[tex]{ \tt{5x + 3 \geqslant 48}} \\ { \tt{5x \geqslant 45}} \\ { \tt{x \geqslant 9}}[/tex]

Answer:

x[tex]\geq[/tex]9

Step-by-step explanation:

5x+3[tex]\geq \\[/tex]48  /-3

5x[tex]\geq[/tex]45   //5

x[tex]\geq[/tex]9

Hello!

The answer is a.

Good luck! :)

Answer:

This is a Categorical variable and the measurement scale is ordinal scale.

Step-by-step explanation:

The measurement scale that is being used to classify sleep is the ordinal measurement. In this question, the variable that is called sleep quality is a categorical variable. categorical variables are variables that have the data representing groups. sleep quality has been given this categorical order extremely low very low low and extreme high.

The ordinal scale is a scale that denotes order it has all variables in a specific order.

Answer:

x-intercept(s):(3,0)

y-intercept(s):(0,9)

Step-by-step explanation:

Answer:

3x-3

Step-by-step explanation:

3x has a variable attach, because no other numbers have a variable attached leave it alone.

2+(-5) are like terms so combine these two. 2+(-5)=-3

now put back in the equation

3x-3

Answer:

36 introverts

Step-by-step explanation:

Total number of adults in the survey = 120

Ratio of introverts to extroverts = 3:7

Number of introverts = ratio number of introverts / ratio total × 120

Ratio number of introverts = 3

Ratio total = 3 + 7 = 10

Number of introverts = 3/10 × 120

= 36

Given:

The numbers are [tex]\dfrac{3}{5},2,0,1,-0.45, 1.44[/tex].

To find:

All the values that cannot be probabilities.

Solution:

We know that,

[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

The minimum value of favorable outcomes is 0 and the maximum value is equal to the total outcomes. So, the value of probability lies between 0 and 1, inclusive. It other words, the probability lies in the interval [0,1].

[tex]0\leq \text{Probability}\leq 1[/tex]

From the given values only [tex]\dfrac{3}{5}, 0, 1[/tex] lie in the interval [0,1]. So, these values can be probabilities.

The values [tex]2,-0.45, 1.44[/tex] does not lie in the interval [0,1]. So, these values cannot be probabilities.

Therefore, the correct values are [tex]2,-0.45, 1.44[/tex].

Answer:

6x

Step-by-step explanation:

If x is the length of one side, and each side is the same length, you will multiply it by 6 times (there are 6 sides in a hexagon).

So, you will add it up 6 times, but you can say 6x for short.

Answer:

Step-by-step explanation:

P(answers correctly)=1/5

P(answers incorrectly)=1-1/5=4/5

P( answers correctly second question)=4/5 ×1/5=4/25

Lauren will get 2/25 because the coin only lands on heads or tail

Answer:

0.96784

Step-by-step explanation:

17-13.3/2

=1.85

p(x<1.85)

=0.96784

The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.

Mean [tex]\mu[/tex]=13.3 minutes

Standard deviation[tex]\sigma[/tex]=2 minutes

The value of the z-score tells you how many standard deviations you are away from the mean.

So, the z-score of the above data

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{17-13.3}{2}[/tex]

[tex]z=1.85[/tex]

From the standard normal table, the p-value corresponding to z=1.85

Or, p(x<1.85)=0.9678 or 96.78%

Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.

To get more about the z-score visit:

https://brainly.com/question/25638875

Answer:

4yz^2

Step-by-step Explanation:

Answer:

a AND ~c

Step-by-step explanation:

you can find the full explanation in wikipedia:

https://en.m.wikipedia.org/wiki/Material_conditional

under "Negated conditionals"

Hello,

[tex]if\ n=1\ then\ 1^2=1\ and\ \dfrac{1}{6}*1*2*3=1:\ true\ for\ n=1\\[/tex]

We suppose the property true for n:

1²+2²+...+n²=n(n+1)(2n+1) / 6

and we are going to demonstrate that the property is true for n+1:

1²+2²+..+(n+1)²=(n+1)*(n+2)*(2n+3)/6

[tex]1^2+2^2+...+n^2+(n+1)^2\\\\=n*(n+1)*(2n+1)/6+(n+1)^2\\\\=(n+1)/6*[n(2n+1)+6n+6]\\\\=(n+1)/6*(2n^2+7n+6)\\\\=(n+1)(n+2)(2n+3)/6\\[/tex]

Answer:

2）=2

4）=3

5）=5

8）=-1

Step-by-step explanation:

just divide the number by the number with variable

Answer:

157,476 people

Step-by-step explanation:

the formula :

P(x) = 86700. (1+ 0.089)^r

for r = 7

=> P(x) = 86700 × (1+ 0.089)^7

= 86700 × (1.089)^7

= 86700 × 1.8163

= 157,476 people

Kindly find complete question attached below

Answer:

Kindly check explanation

Step-by-step explanation:

Given a normal distribution with ;

Mean = 36

Standard deviation = 4

According to the empirical rule :

68% of the distribution is within 1 standard deviation of the mean ;

That is ; mean ± 1(standard deviation)

68% of subjects :

36 ± 1(4) :

36 - 4 or 36 + 4

Between 32 and 40

2.)

95% of the distribution is within 2 standard deviations of the mean ;

That is ; mean ± 2(standard deviation)

95% of subjects :

36 ± 2(4) :

36 - 8 or 36 + 8

Between 28 and 44

3.)

99% is about 3 standard deviations of the mean :

That is ; mean ± 3(standard deviation)

99% of subjects :

36 ± 3(4) :

36 - 12 or 36 + 12

Between 24 and 48

Answer:

Standard deviation, means, skewness and kurtosis.

Step-by-step explanation:

Two normal curves may be same but they have different means, standard deviation and skewness. There can be different standard deviation for two curves and there is difference in skewness.

Answer:

0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean number of miles between services is 4959 miles, with a standard deviation of 448 miles

This means that [tex]\mu = 4959, \sigma = 448[/tex]

Sample of 43:

This means that [tex]n = 43, s = \frac{448}{\sqrt{43}}[/tex]

What is the probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles?

p-value of Z when X = 4959 + 111 = 5070 subtracted by the p-value of Z when X = 4959 - 111 = 4848, that is, probability the sample mean is between these two values.

X = 5070

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

By the Central Limit Theorem

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

[tex]Z = \frac{5070 - 4959}{\frac{448}{\sqrt{43}}}[/tex]

[tex]Z = 1.62[/tex]

[tex]Z = 1.62[/tex] has a p-value of 0.9474

X = 4848

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

[tex]Z = \frac{4848 - 4959}{\frac{448}{\sqrt{43}}}[/tex]

[tex]Z = -1.62[/tex]

[tex]Z = -1.62[/tex] has a p-value of 0.0526

0.9474 - 0.0526 = 0.8948

0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles

Answer:

There are 256 pairs in all.

Answer:

[tex]x=6\\y=4[/tex]

Step-by-step explanation:

Elimination method:

[tex]x+5y=26[/tex]

[tex]-x+7y=22[/tex]

Add these equations to eliminate x:

[tex]12y=48[/tex]

Then solve [tex]12y=48[/tex] for y:

[tex]12y=48[/tex]

[tex]y=48/12[/tex]

[tex]y=4[/tex]

Write down an original equation:

[tex]x+5y=26[/tex]

Substitute 4 for y in [tex]x+5y=26[/tex]:

[tex]x+5(4)=26[/tex]

[tex]x+20=26[/tex]

[tex]x=26-20[/tex]

[tex]x=6[/tex]

{ [tex]x=6[/tex] and [tex]y=4[/tex] }    ⇒ [tex](6,4)[/tex]

hope this helps...

Answer:

x = 6, y = 4

Step-by-step explanation:

x + 5y = 26

- x + 7y = 22

_________

0 + 12y = 48

12y = 48

y = 48 / 12

y = 4

Substitute y = 4 in eq. x + 5y = 26,

x + 5 ( 4 ) = 26

x + 20 = 26

x = 26 - 20

x = 6

Answer:

Slope is undefined. Line parallel to y-axis.

Step-by-step explanation:

By Analytic Geometry, we can determine the slope of a line by knowing two distinct lines and using the definition of secant line:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)

Where:

[tex](x_{1}, y_{1})[/tex] - Coordinates of the initial point.

[tex](x_{2}, y_{2})[/tex] - Coordinates of the final point.

[tex]m[/tex] - Slope.

If we know that [tex](x_{1}, y_{1}) = (17, -13)[/tex] and [tex](x_{2}, y_{2}) = (17, 8)[/tex], then the slope of the line is:

[tex]m = \frac{8-(-13)}{17-17}[/tex]

[tex]m = \frac{21}{0}[/tex]

The slope is undefined, which means that line is parallel to y-axis.

Answer:

[tex]\sum_{n = 1}^{7} -2 -2n[/tex]

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference of consecutive terms is always the same, called common difference.

The nth term of a sequence is given by:

[tex]a_{n} = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term and d is the common difference.

Sigma notation to represent the sum of the first seven terms

Sum going from the index starting at 1 and finishing at 7, that is:

[tex]\sum_{n = 1}^{7} f(n)[/tex]

Now we have to fund the function, which is given by an arithmetic sequence.

−4, −6, −8,

First term -4, common difference - 6 - (-4) = -6 + 4 = -2, so [tex]a_1 = -4, d = -2[/tex]

Then

[tex]f(n) = a_{n} = a_1 + (n-1)d[/tex]

[tex]f(n) = -4 + (n-1)(-2)[/tex]

[tex]f(n) = -4 - 2n + 2 = -2 - 2n[/tex]

Sigma notation:

Replacing f(n)

[tex]\sum_{n = 1}^{7} -2 -2n[/tex]

Answer:

C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]

D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]

Step-by-step explanation:

We are given that

n=18

Mean, [tex]\mu=6.75[/tex]

Standard deviation, [tex]\sigma=2.28[/tex]

c.

[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]

[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]

[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]

Using the formula

[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]

[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]

[tex]P(7.0039<x<7.8026)=0.1334[/tex]

D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]

Answer:

Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).

Remember that the general Taylor expansion is:

[tex]f(x) = f(a) + f'(a)*(x - a) + \frac{1}{2!}*f''(a)(x -a)^2 + ...[/tex]

for our function we have:

f'(x) =  1/x

f''(x) = -1/x^2

f'''(x) =  (1/2)*(1/x^3)

this is enough, now just let's write the series:

[tex]f(x) = ln(a) + \frac{1}{a} *(x - a) - \frac{1}{2!} *\frac{1}{a^2} *(x - a)^2 + \frac{1}{3!} *\frac{1}{2*a^3} *(x - a)^3 + ....[/tex]

This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.

Answer:

The correct one is 3 over b equals 7 over a

Answer:

3/b = 7/a

Step-by-step explanation:

I took it on Edge

Answer:

1-x^2/x^3 - 1 = 1/x

Step-by-step explanation:

First rewrite x^3 as x^2 * x cancel x^2  in both numerator and denominator.

   Write below

1 - 1/x - 1

Subtract

   1 - 1 = 0

now simplify

1 -1 /x - 1 = 1/x

1/x  = Answer

Can you Understand

Hi there!

[tex]\large\boxed{(-\infty, 9)}[/tex]

We can find the range using completing the square:

y = -x² - 2x + 8

Factor out a -1:

y = -(x² + 2x) + 8

Use the first two terms. Take the second term's coefficient, divide by 2, and square:

y = -(x² + 2x + 1) + 8  

Remember to add by 1 because we cannot randomly add an additional number into the equation:

y = -(x² + 2x + 1) + 8 + 1

Simplify:

y = -(x + 1)² + 9

Since the graph opens downward (negative coefficient), the range is (-∞, 9)

A photograph having length of 24 inches which is proportionate to another photograph having dimensions 3 × 4 inches, has width of 18 inches.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

Let the width of the photograph be x inches.

The length of the photograph is 24 inches.

A similar proportion photograph has width as 3 inches.

A similar proportion photograph has length as 4 inches.

The equation to find the width of photograph is -

x / 24 = 3 / 4

Simplify the equation -

x = (24 × 3) / 4

x = 72 / 4

x = 18

Therefore, the width value is 18 inches.

To learn more about proportion from the given link

https://brainly.com/question/19994681

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