A dindercal container close at boat and have a radius 7cm and hight 6cm find total surface area of the container what is the volume of this container

1111 is the greatest common divisor of all numbers.

Lets simplify the problem,

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

After it , we get:

5555 _=_ 101 * 11  * 5

7777 = 101 * 11 * 7

9999 = 101 * 11 * 3 * 3

12221 = 101 * 11 * 11

14443 = 101 * 11 * 13

16665 = 101 * 11 * 3 * 5

abcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

Hence we get 1111 is the greatest common divisor.

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Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.                      

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex]       --->(1)

Given,[tex]\frac{dx}{dt}= 2feet/second[/tex]   at x=3

Put x=3 in Pythagoras theorem equation (1)

[tex](3)^{2} + y^{2} = 144[/tex]

         [tex]y^{2} = 144 - 9[/tex]

        [tex]y^{2}[/tex]  =  135

        y = 11.61

Derive equation (1) w.r.t to 't'

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]                ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]

12 + 23.22 [tex]\frac{dy}{dt}[/tex]  = 0

                  [tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]

                  [tex]\frac{dy}{dt} = -0.518[/tex]

Hence,  using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.  

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By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

It is given that  the total weight of your backpack and its contents is 13 3/8 pounds.

Also given , we want to carry no more than 15 pounds.

Let the number of bottles we can carry be x.

Each bottles weigh 3/4 pounds.

Total weight of the bottles = 3x/4 pounds.

Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .

Thus the statement equation formed is -

⇒ 107/8 + 3x/4 = 15

⇒ 3x/4 = 13/8

⇒ x = 13/6 = 2.166

∴  x ≈ 2

Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

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Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are given as follows:

[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]

Hence the lower and upper bound of the interval are given, respectively, by:

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Answer:

21

Step-by-step explanation:

(69.8-32)×(5/9)=21

The number of ways we can select 3 cracked and 2 good is 1200 ways.

Given there are 5 eggs in which 3 eggs are cracked and 2 eggs which are good.

We have to find the number of ways we can select 3 cracked and 2 good eggs from 5 eggs.

Number of ways can be found through permutations.

The factorial of n  equals the product of n with the smaller factorial..

Permutations is the technique of calculating  various ways in which objects from a set may be selected, generally without replacement, to form subsets.

n[tex]P_{r}[/tex]=n!/(n-r)!

So the number of ways will be 5[tex]P_{3}[/tex]*5[tex]P_{2}[/tex]

([tex]5P_{3}[/tex] for cracked eggs and [tex]5C_{2}[/tex] for good eggs)

=5!/(5-3)!*51/(5-2)!

=5*4*3*2!/2!*5*4*3!/3!

=5*4*3*5*4

=1200

Hence there are 1200 ways through which 3 cracked and 2 good eggs can be selected from 5 eggs.

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The weight of a 36-inch piece of PVC pipe is 0.20 pounds

The given parameters about the 36-inch piece of PVC pipe are

Height, h = 36 inches

Outside diameter, D = 0.82 inches

Inside diameter, d= 0.75 inches

The volume of the PVC pipe is then calculated as:

V = πh(D/2)^2 - πh(d/2)^2

Substitute the known parameters in the above equation

V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2

Evaluate the quotients

V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2

Evaluate the exponents

V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625

Evaluate the products

V = 19.002024 - 15.89625

Evaluate the difference

V = 3.105774 cubic inches

From the question, we have:

Weight =  0.063 pounds per cubic inch

So, the total weight is

Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch

Evaluate the product

Total weight = 0.195663762 pounds

Approximate

Total weight = 0.20 pounds

Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds

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Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

According to the question,

The customary units of capacity in Sava's are 1 fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

Customary units and its equivalent  

1 Fluid ounce = 2 Tablespoons

1 Cup = 8 fluid ounces

1 Pint = 2 cups

1 Quart = 2 pints

1 Gallon = 4 quarts

Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

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The correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression:

–3(2x – 5) < 5(2 – x)

Expand

-6x +15 < 10 - 5x

Collect the like terms

-6x+5x < 10 - 15

-x <-5

x > 5

Hence the correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Maximum value = 880/3.

Maximizing the objective function in the LP model means that the value occurs in an acceptable set of decisions. Linear programming refers to selecting the best alternative from the available alternatives that can represent the objective and constraint functions as linear mathematical functions.

As mentioned above, the equation is an example of a constraint. You can use this to think about what it means to solve equations and inequalities. For example, solving 3x + 4 = 10 yields x = 2. This is an easy way to express the same constraints.

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The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]

Hence,

[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

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Answer:

[tex]\dfrac{991}{40\sqrt{2}}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{72}-\dfrac{48}{\sqrt{50}}-\dfrac{45}{\sqrt{128}}+2\sqrt{98}[/tex]

Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:

[tex]\implies \sqrt{36 \cdot 2}-\dfrac{48}{\sqrt{25 \cdot 2}}-\dfrac{45}{\sqrt{64 \cdot 2}}+2\sqrt{49 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies \sqrt{36}\sqrt{2}-\dfrac{48}{\sqrt{25}\sqrt{2}}-\dfrac{45}{\sqrt{64}\sqrt{ 2}}+2\sqrt{49}\sqrt{2}[/tex]

Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:

[tex]\implies \sqrt{6^2}\sqrt{2}-\dfrac{48}{\sqrt{5^2}\sqrt{2}}-\dfrac{45}{\sqrt{8^2}\sqrt{ 2}}+2\sqrt{7^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+2\cdot 7\sqrt{2}[/tex]

Simplify:

[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+14\sqrt{2}[/tex]

Combine like terms:

[tex]\implies 20\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}[/tex]

Make the denominators of the two fractions the same:

[tex]\implies 20\sqrt{2}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

Rewrite 20√2 as a fraction with denominator 40√2:

[tex]\implies 20\sqrt{2}\cdot\dfrac{40\sqrt{2}}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

[tex]\implies \dfrac{1600}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

Combine fractions:

[tex]\implies \dfrac{991}{40\sqrt{2}}[/tex]

Answer:

1.

a.) 24in

b.)75.36in

c.)452.16in

Step-by-step explanation:

1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.

1b. the circumfrence of a circle is C (Circumfrence)=[tex]2\pi r[/tex] so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.

1c. Area=[tex]\pi r^{2}[/tex] so first do the radius by the second power, or [tex]r * r[/tex], susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in

Sorry I could not answer every question but hope this helps!

Answer:jio

Step-by-step explanation:

The causes of variation that can be identified and eliminated are called; Assignable Causes.

There are two primary causes of variation in the quality of a product or process. These two primary causes are called;

Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.

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Answer:

1540

Step-by-step explanation:

This is an arithmetic progression.

a = first term = 10

Common difference = d = second term - first term

                                         = 12 - 10

                                     d  = 2

Last term = l = 78

First we have to find how many terms are there in the sequence using the formula:  l = a + (n-1)*d

                   78 = 10 + (n -1) * 2

               78 -10 = (n -1)*2

                     68 = (n -1) *2

               68 ÷2 =  n -1

                      34 = n - 1

                 34 + 1 = n

                         n = 35

There are 35 terms.

  [tex]\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}}[/tex][tex]\sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}[/tex]

            [tex]\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540[/tex]

Step-by-step explanation:

This is an arithmetic progression.

a = first term = 10

Common difference = d = second term - first term

= 12 - 10

d = 2

Last term = l = 78

First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d

78 = 10 + (n -1) * 2

78 -10 = (n -1)*2

68 = (n -1) *2

68 ÷2 = n -1

34 = n - 1

34 + 1 = n

n = 35

There are 35 terms.

\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}} \sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}

Sum =

2

n

(a+l)

\begin{gathered}\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540\end{gathered}

=

2

35

(10+78)

=

2

35

∗88

=35∗44

=1540

Answer:

C

Step-by-step explanation:

Exponential functions have 2 things in common

-They increase infinitely once they approach a certain point

-They don't decrease anymore once they approach a certain point

Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12

The variation given in the first question is not a direct variation and there is no constant of variation.

y = k × x

when

y = -40 and x = -0.5

y = k × x

-40 = k × -0.5

-40 = -0.5k

k = -40/-0.5

k = 80

When y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8 / 2.5

k = 3.2

When y = 4 and x = -3

y = k × x

4 = k × -3

4 = -3k

k = -4/3

when y = 8 and x = -6

y = k × x

8 = k × -6

8 = -6k

k = 8/-6

k = -4/3

This is a direct variation and the constant of proportionality is -4/3

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The value of sample proportion is found to be 0.253.

The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.

Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.

Now, according to the question;

The 90% confidence interval for a proportion is found to be (0.22,0.28).

The confidence interval for the sample is given as-

Confidence interval = Sample proportion ± Margin of Error

Let [tex]\hat{p}[/tex] be the sample proportion.

The level of significance = 1 - 0.90

                                         = 0.10 (10%)

From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.

90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Thus,                       0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and

                               0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.

[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]

Take square root,

[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]

Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]

Therefore, the value of sample proportion is 0.253.

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Patrick has an absolute advantage in playing quarterback.

Given a table containing touchdowns and field goals by Partrik and Field goals as under:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

We are required to find a person who has an absolute advantage in playing quarterback.

Absolute advantage is the ability of an individual, company to produce greater advantage of good or service than the individual.

Total of touchdowns and field goals by Patrik=39+13=52

Total of touchdowns and field goals by Jimmy=25+5=30

We can see that total of touchdowns and field goals by Patrik is greater than total of touchdowns and field goals by Jimmy. So Patrik has an absolute advantage playing quarterback.

Hence Patrick has an absolute advantage in playing quarterback.

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Question is incomplete as it should include the following table:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

Answer:

1

Step-by-step explanation:

Points on a coordinate plane are written as (x,y) coordinates. The vertical axis is the y axis. If your point is "one unit up" its y-value is 1. (The horizontal axis is the x-axis. The x-value is 6.)

The z-test score is used for this hypothesis test to decide whether to reject or not to reject the null hypothesis. The z-test score for the given sample is 1.22.

The z-score for the hypothesis test is calculated by,

z-score = (X - μ)/(σ/√n)

Where X - sample mean, μ - population mean, σ - standard deviation, and n - sample size.

It is given  that,

Sample size n = 30

Population mean μ = 9.7

Sample mean X = 10.1

Standard deviation σ = 1.8

So, the z-score is

= (10.1 - 9.7)/(1.8/√30)

= 0.4/0.328

= 1.219 ≅ 1.22

Therefore, the p-value for this z-score is 0.22. This value decides whether to reject or not to reject the null hypothesis.

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Answer:

C.

Step-by-step explanation:

For any of the given functions, all of the first input values (x-values) in the relation are considered the domain values. On the other hand, the output values (y-values) are called the range values of the given equation.

The mapped relation is the domain (1, 2, 3). Since this is domain values (x-values), the correct answer will be the mapped with 1, 2, and 3 on the left side.

The correct answer is C.

Hope this helps!

x² ( 4x - 3)

Apply the multiplicative law of distribution.

Multiply the monomial

Multiply the monomial

Therefore, the correct option is "C".

Answer:

B

Step-by-step explanation:

[tex]\frac{x}{x-3}[/tex] × [tex]\frac{2x}{x+5}[/tex] ( no factors cancel on numerator / denominator )

= [tex]\frac{x(2x)}{(x-3)(x+5)}[/tex]

= [tex]\frac{2x^2}{x^2+2x-15}[/tex]

The probability of winning a lottery by selecting the correct six integers, are

[tex]\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}[/tex]

The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.

Part (a); positive integers not exceeding 30.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.

[tex]\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}[/tex]

Part (b); positive integers not exceeding 36.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.

[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}[/tex]

Part (c); positive integers not exceeding 42.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.

[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}[/tex]

Part (d); positive integers not exceeding 48.

To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.

[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}[/tex]

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The complete question is-

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.

Answer:

[tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]

Step-by-step explanation:

First, convert this into a quadratic, [tex]x^{2}+7x+8=0[/tex]. We can use the quadratic formula for this, [tex](-7[/tex]±[tex]\sqrt{7^{2}-4(1)(8)})[/tex][tex]/2(1)[/tex]. This becomes [tex](-7[/tex]±[tex]\sqrt{49-32})/2[/tex]. This is [tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]. This is your answer