You have $9000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure

Answer:

The margin of error is approximately 0.39.

Step-by-step explanation:

Formular for the margin of error is

Margin of error = z* (sd/√n)

Where z* is 95% confidence level = 1.96, sd is 1.8 and n is 81

Margin of error = 1.96 (1.8/√81)

= 1.96(1.8/9)

= 1.96*0.2

= 0.392

Answer:

x=81 or 1/3

Step-by-step explanation:

[tex]x^\log_3(x)} =81x^3\\\log_3(x^{\log_3(x)})=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^{-1}=1/3[/tex]

Answer:

Answer B) (2 times )

Step-by-step explanation:

Let's start with the person that shook hands more (Dora), so we already know how four of this connections took place See attached image.

step 1:

D is connected to A, B, C, and E

Step 2:

Now proceed with the connections for the second greatest (C who shook hands with 3 people). Notice that C is already connected with D, and can connect with B and with E, but NOT with A (since this person shook hands only once - with D. So C is connected to B, D, and E completing the three handshakes.

step 3: Now just corroborate that B is already connected to two people (C and D).  So just count the number of connections that E is left with: 2 handshakes.

Answer:

( E ) 0

Step-by-step explanation:

Solution:-

- There can be two ways in solving this question. Either we lay-out a map of every person ( Alan, Bella, Claire, Dora, and Erik ) shaking hands with each other.

- We will use an intuitive way of tackling this problem.

- We have a total of 5 people who greeted each other at the party.

- Each of the 5 people shook hands exactly " once "! We can give this a technical term of " shaking hands - without replacement ".

- We will define our event as shaking hands. It takes 2 people to shake hands.

- We will try to determine the total number of unique "combinations" that would result in each person shaking hands exactly one time.

- We have a total of 5 people and we will make unique combinations of 2 people shaking hands. This can be written as:

                            5C2 = 10 possible ways.

- So there are a total of 10 possible ways for 5 people to greet each other exactly once at the party.

- We are already given the data for how many handshakes were made by each person as follows:

                      Name                 Number of handshakes

                       Alan                                   1

                       Bella                                  2

                       Claire                                 3

                       Dora                                   4

               =======================================

                      Total                                  10

               =======================================

- So from the data given. 10 unique hand-shakes were already done by the time it was " Eriks " turn to go and greet someone. This also means that Erik has already met all 4 people in that party. So he doesn't have to approach anyone to shake hands and know someone. He is already been introduced to rest of 4 people in the group.

Answer: Erik does not need to shake hands with anyone! He is known and greeted rest of the 4 people on the group.

Answer:isosceles is the correct

Step-by-step explanation:

According to the given conditions the triangle ABC is an isosceles triangle.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles  ADB and CBD congruent by SAS rule,

So, the proof is as follows,

AD = CD [definition of median]

∠ ADB = ∠ CDB [definition of altitude]

BD = BD [reflexive property]

∴ Δ ADB ≅ Δ CBD by SAS rule

AB = BC by CPCT

According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.

Hence, according to the given conditions the triangle ABC is an isosceles triangle.

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Answer: B

Step-by-step explanation:

The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The numbers are given below.

3 and 8/11

The sum of the numbers is calculated as,

⇒ 3 + 8/11

⇒ (33 + 8) / 11

⇒ 41 / 11

⇒ 3.7272

The quotient of the numbers is calculated as,

⇒ 3 / (8/11)

⇒ 3 x 11 / 8

⇒ 4.125

The product of the numbers is calculated as,

⇒ (3) x (8 / 11)

⇒ 24 / 11

⇒ 2.1818

The difference between the numbers is calculated as,

⇒ 3 - 8/11

⇒ (33 - 8) / 11

⇒ 25 / 11

⇒ 2.2727

The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.

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Answer:

[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]

Step-by-step explanation:

According to the Parallelogram definition, every Parallelogram have a pair of congruent sides.  In this case, Namely [tex]\overline{RS} \cong \overline{TQ}[/tex]  and [tex]\overline{QR} \cong \overline{TS}[/tex]

(not listed as an option)

And the opposite angles are congruent too.

So

[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]

∠R≅∠T relationship is true for the RSTQ parallelogram

A quadrilateral is a polygon having four sides, four angles, and four vertices.

A parallelogram is a quadrilateral with four sides.

a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

In parallelogram the opposite sides have equal length.

The opposite sides are congruent and the opposite angles are also congruent.

SR=TQ

ST=RQ

These sides are equal and

∠R≅∠T

∠S≅∠Q

In the given options only ∠R≅∠T is given, so we can consider this.

Hence ∠R≅∠T relationship is true for the RSTQ parallelogram

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Answer:D

Step-by-step explanation:

Additive property big brain

This step works because of the addition of property equality.

The addition property of equality tells us that adding the identical wide variety to each facet of an equation offers us an equal equation. If a−b=c, then a−b+b=c+b,or a=c+b. The same goes with the subtraction belongings of equality

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Answer:

Mean = 16.5

Variance = 35.55

Step-by-step explanation:

           x      P(x)        x. P(x)     x²            x². P(x)

          6      0.10          0.6      36            3.6

         12     0.35          4.2       144           50.4

        18     0.25           4.5       324            81

        24     0.30          7.2        576         172.8

                  ∑x P (x)  16.5         ∑x² P (x) 307.8

The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.

Mean is given by  E(X)=  ∑x P (x) =  16.5

Similarly the variance is also calculated using the expected value of X and X².

Variance is given= E(X)²-  [E(X)]²= 307.8- (16.5)²=  307.8-272.25 = 35.55

for labor. Joni paid $85 less per hour for labor. explanation:

The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.

It refers to the total amount of the expenditure done on a product in manufacturing or procuring.

It refers to the expenditure done on procuring labor for the work.

In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,

labor cost Shannon Paid=339.50-112

=$227.50

labor cost per hour=227.50/3.5

=$6.5 per hour

Joni paid total $455 in which the cost of spare parts is $310 and rest is labor

labor cost paid by Joni=455-310

=$145

labor cost per hour=145/2.5

=$58 per hour

So by doing comparing we found that Shannon had paid $6 per hour extra for labor.

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Answer:

120°

Step-by-step explanation:

Given that an angle = 240 less than 6 × its own supplement,

Let x = be the angle

Its supplement = (180 - x)

If the angle (x) is 240 less than 6 times its own supplement, (180 - x), we will have the following expression:

[tex] x = 6*(180 - x) - 240 [/tex]

Simplify the expression to solve for x

[tex] x = 1080 - 6x - 240 [/tex]

[tex] x = 1080 - 240 - 6x [/tex]

[tex] x = 840 - 6x [/tex]

Add 6x to both sides

[tex] x + 6x = 840 - 6x + 6x [/tex]

[tex] 7x = 840 [/tex]

Divide both sides by 7 to solve for x

[tex] \frac{7x}{7} = \frac{840}{7} [/tex]

[tex] x = 120 [/tex]

I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.

The only function there is the last one. (Right bottom)

Answer:

62.12% to 77.88%

Step-by-step explanation:

We proceed as follows mathematically;

From the question

n=130

Estimate for sample proportion=70% = 70/100 = 0.7 = p

Level of significance is =1-0.95=0.05

Z critical value(using Z table)=1.96

Confidence interval formula is ;

p ± Z * √(p(1-p)/n

= 0.70 ± √(0.7(1-0.7)/130

=(0.6212,0.7788)

Lower confidence interval limit =0.6212

Upper confidence interval limit =0.7788

In percentages , we simply multiply by 100 in both cases =

62.12 % to 77.88%

Answer:

97

Step-by-step explanation:

ez

Answer:

(c) 97

Step-by-step explanation:

97 is the largest prime number because 97 has no other multiples other than 1 and itself. 99 is divisible by 3, 9, 11, 33, 99.

91 is a prime number but it is not the greatest.

93 is a composite.

99 is a composite as well.

Answer:

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

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Step-by-step explanation:

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

d≤7

Step-by-step explanation:

-10d≥-70

d≤7

Answer:

It should be 10 for the first box, 1000 for the second box and 100 for the third box.

Step-by-step explanation:

Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths

Answer:

A = 0.507 or 29 degrees

Step-by-step explanation:

5 = tanA * 9

inv tan = 5/9

angle A = 0.507

angle A = 29 degrees

Answer:  4

Step-by-step explanation:

Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.

The attachment shows the graph rotated 1-turn to the left (90°).

Notice it is in the exact same position as #4.

Answer:

0.40

Step-by-step explanation:

The computation of the probability for the second student be sophomore and the first is a freshman is shown below:

Let us assume

Sophomore = S

Freshman = F

Based on this assumption, the probability is as follows

So,

[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]

= 0.40

Hence, the probability for the second student be sophomore and the first student be freshman is 0.40

Answer:

-1

Step-by-step explanation:

If a line is parallel on a graph, then that means that they will descend/climb at the same rate. Therefore, the slope of this line is also -1.

Hope this helped!

Answer:If they are parallel,

Then their slope will be same...

Step-by-step explanation:

Answer: E(X) = 4

              V(X) = [tex]\frac{16}{3}[/tex]

Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:

f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]  

The mean or expectation of an unifrom distribution is:

E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]

For the density function in interval [0,8], expectation value is:

E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]

E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]

E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]

E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]

E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]

E(X) = 4

Variance of a probability distribution can be written as:

V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]

For uniform distribution in interval [0,8]:

V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]

V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]

V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{64}{3}[/tex] - 16

V(X) = [tex]\frac{16}{3}[/tex]

The mean and variance are 4 and 16/3, respectively

Answer:

1). [tex]\frac{2}{(x+1)}[/tex]

2). [tex]\frac{x^2}{2(x+1)}[/tex]

Step-by-step explanation:

For multiplication of the rational expressions,

[tex]\frac{x}{(x+1)}\times \frac{2}{x}[/tex]

= [tex]\frac{2x}{x(x+1)}[/tex]

= [tex]\frac{2}{(x+1)}[/tex]

For division of the rational expressions,

[tex]\frac{x}{(x+1)}\div \frac{2}{x}[/tex]

= [tex]\frac{x}{(x+1)}\times \frac{x}{2}[/tex]

= [tex]\frac{x^2}{2(x+1)}[/tex]

[When the divisor is a rational expression or a rational number, we change the sign from division to multiplication and reciprocate or flip the fraction.

This is applicable for division of the rational expressions only].

Answer:

The error that might occur is [tex]\±0.123cm^3[/tex]

Step-by-step explanation:

Given

[tex]V = \frac{4}{3}\pi r^3[/tex]

[tex]Radius,\ r = 1.4cm[/tex]

[tex]Error = 0.005cm[/tex]

Required

Determine the error that might occur in the volume of the tumor

Given that there's an error in measurement, this question will be solved using the concept of differentiation;

First, we'll rewrite the given parameters in differentiation notations;

[tex]r = 1.4[/tex] --- Radius

[tex]dV = \±0.005[/tex] --- Change in measurement

[tex]V(r) = \frac{4}{3}\pi r^3[/tex] --- Volume as a function of radius

The relationship between the above parameters is as follows;

[tex]\frac{dV}{dr} = V'(r)[/tex]

This can be rewritten as

[tex]\frac{dV}{dr} = (V(r))'[/tex]

Substitute [tex]\frac{4}{3}\pi r^3[/tex] for [tex]V(r)[/tex]

[tex]\frac{dV}{dr} = (\frac{4}{3}\pi r^3)'[/tex]

Multiply both sides by dr

[tex]dr * \frac{dV}{dr} = (\frac{4}{3}\pi r^3)' * dr[/tex]

[tex]dV = (\frac{4}{3}\pi r^3)' * dr[/tex]

[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]

Differentiate

[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]

[tex]dV = \frac{4}{3}\pi* 3r^2\ dr[/tex]

[tex]dV = 4\pi* r^2\ dr[/tex]

Substitute the values of r, dr and take [tex]\pi[/tex] as 3.142

[tex]dV = 4 * 3.142* 1.4^2 * \±0.005[/tex]

[tex]dV = \±0.1231664[/tex]

[tex]dV = \±0.123[/tex] (Approximated)

Hence, the error that might occur is ±0.123

Answer:

[tex]75[/tex]

Step-by-step explanation:

[tex]\frac{d}{dx}\left(x^3\right)[/tex]

[tex]=3x^{3-1}[/tex]

[tex]=3x^2[/tex]

[tex]3\left(5\right)^2[/tex]

[tex]=3\cdot \:25[/tex]

[tex]=75[/tex]

Answer:

The correct option is (D).

Step-by-step explanation:

In this case, we need to test whether the  mean pulse rate (in beats per minute) of students in a large math class is greater than 71.

The hypothesis can be defined as follows:

H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.

Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.

It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.

The sample mean is not very different from the population mean.

So, it cannot be said in confidence that the sample is unusual.

Thus, the correct option is (D).

"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."

Answer:

[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]

Step-by-step explanation:

The expression, [tex] -6(4\frac{2}{3}) [/tex] , can be understood or interpreted as negative six multiplied by four and two-third.

Thus, it could be evaluated using distributive property of multiplication, as shown below:

[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]

[tex](-6)(4) + (-6)(\frac{2}{3}) \\(-24) + (-2)(2)\\-24 + (-4)\\-24 - 4\\= -28[/tex]

Answer:

76°

Interior angle of a rhombus =360

104° +104° +76° +X =360

X= 360 - 284

X= 76°

We know that the value of ∠x in the given rhombus is 76°.

So, get the ∠x as follows:

Then,

Therefore, we know that the value of ∠x in the given rhombus is 76°.

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Answer:

Step-by-step explanation:

The formula for calculating the standard error of the mean is expressed as shown below;

Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

[tex]\sigma[/tex] is the standard deviation and n is the sample size.

Given [tex]\sigma[/tex] = 14 and n = 100

Substituting this values into the formula fr calculating the standard error of the mean;

[tex]SE = \frac{14}{\sqrt{100} } \\\\SE = \frac{14}{10} \\\\SE = 1.4[/tex]

Hence, standard error of the mean is 1.4

Answer:

Discount : $34.25 off. Percent of the discount : 25%

Step-by-step explanation:

137 - 102.75 = 34.25.

34.25/137 x 100 = 25%