3 math questions for 50 points.

Dimensions of the area enclosed is l = 800 ,b = 800 and the maximum area = 6,40,000 square yards.

Given:

Liana has 3200 yards of fencing to enclose a rectangular area.

Let l and b be the length and breadth.

we know that:

perimeter of rectangle = 2(l+b)

2l + 2b = 3200

l+b = 1600

b = 1600 - l

Area of rectangle A = lb

= l*1600-l

= 1600 l - l^2

Apply derivative:

dA/dl = 1600 - 2l

1600 - 2l = 0

1600 = 2l

l = 1600/2

l = 800

l+b = 1600

b = 1600 - 800

= 800

Area = 800*800

= 6,40,000

Learn more about the length and breadth here:

https://brainly.com/question/19238180

#SPJ1

For the specified requirements, 105 sample size are required.

Given that,

Confidence Interval = 90

Margin of error (m) =0.08

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 90% confidence interval ,

Z* = 1.645 , m=0.08

Using equation we get

n = (1.645/0.08)²(0.5)( 1 - 0.5 )

By solving,

n =105.3 = 105

The necessary sample size is 105

Learn more about margin of error :

brainly.com/question/10501147

#SPJ4

Answer:

$180

Step-by-step explanation:

[tex]P\times{(1-0.20)}=144[/tex]

[tex]P\times{0.80}=144[/tex]

[tex]P=\frac{144}{0.80}[/tex]

[tex]P=180[/tex]

A store received shipment of 37 tvs valued at 625 each what is the total value of the shipment?

37 * $625 = $23,125

Answer: [tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]

Step-by-step explanation:

64+Ax+135x^2

135x^2+Ax+64=0

[tex]x_{1,\:2}=\frac{-A\pm \sqrt{A^2-4\cdot \:135\cdot \:64}}{2\cdot \:135}[/tex]

[tex]x_{1,\:2}=\frac{-A\pm \left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]

[tex]x_1=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135},\:x_2=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]

[tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]

The matrix

[tex]MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]

The given matrix is

[tex]M = \left[\begin{array}{ccc}1&0\\-4&3\\2&5\end{array}\right][/tex]

[tex]N = \left[\begin{array}{ccc}-2&1&0\\3&2&-1\\\end{array}\right][/tex]

The Order of M = (3×2)

The Order of N = (2×3)

Since the number of columns of M is equal to the number of rows, the multiplication of M and N is possible,

The order of the matrix formed is MN = ( 3 × 3 )

So,

[tex]MN = \left[\begin{array}{ccc}-2+0&1+0&0+0\\8+9&-4+6&0-3\\-4+15&2+10&0-5\end{array}\right] \\\\MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]

To read more about matrix, visit https://brainly.com/question/28180105

#SPJ1

The probability that Serena does not serve an ace or a double fault is 0.63..

Addition rule of probability applies to the calculation of probability for one or another event happen. These events are either mutually exclusive or not .

We have following information,

The probability of Serena serving an ace in tennis (p) = 0.15

Probability that she double faults(q) = 0.25

The probability of Serena not serving an ace in tennis = 1 -p = 1 - 0.15 = 0.85

let A and B be two events Serena not serving an ace and she double faults respectively.

Events A and B are not mutually exclusive events .

i.e, P(A ∩ B ) =/ 0

when Serna not serving an ace implies that either it is double faults or not and both have equally likely chance.

So, the probability of intersection of event A and B = 0.85/2 = 0.47

Adding Rule for probabilities is

P(A or B ) = P(A) + P(B) - P(A ∩ B)

The probability that Serena does not serve an ace or a double fault = 0.85 + 0.25 - 0.47

= 1.10 - 0.47 = 0.63...

Hence, the probability that Serena does not serve an ace or double fault is 0.63..

To learn more about Probability, refer:

https://brainly.com/question/13604758

#SPJ4

The value of the test statistic is 2.59.

A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.

Here, the percentage of residents favored construction is 34%.

[tex]p\leq 0.31\\p > 0.31[/tex]

The test statistics is given by,

[tex]Z=P-\frac{p}{\sqrt{p(1-p)n} }[/tex]

Here n=1600, P=0.34 and p=0.31,

Putting the values,

[tex]Z=0.34-\frac{0.31}{\sqrt{0.31(1-0.31)1600} }\\=2.59[/tex]

Test Statistics = 2.59

Therefore, the value of test statistics is 2.59.

To learn more about the Test Statistics visit here:

https://brainly.com/question/15110538

#SPJ4

The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.

The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.

Here, all the questions can be solved by using the BODMAS rule.

1) 7w + 2w - 6w

= (7w + 2w) - 6w

= 9w - 6w

= 3w.

2) 9x - 3x + 2x

= (9x + 2x) -3x

= 11x - 3x

= 8x.

3) 8p + 3p - p

= (8p + 3p) - p

= 11p - p

= 10p.

4) 6b - 3b + 5b

= (6b +5b) - 3b

= 11b -3b

= 8b.

To know more about algebraic expressions:

https://brainly.com/question/19864285

Step-by-step explanation:

[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]

[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]

[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]

[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]

To cover 10000 steps the time taken will be 115 minutes and he will cover at 9:55 AM.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.

The time will be calculated as,

2000 steps ⇒ 23 minutes

1 Step ⇒ 23 / 2000 minutes

10000 steps ⇒ ( 23 x 10000) / 2000 minutes

10000 steps ⇒ 115 minutes

The time of covering 10000 steps will be at 9:55.

To know more about an expression follow

https://brainly.com/question/20411765

#SPJ1

The processing fee was = $36.96

acc to our question-

let the price of headphones be= x

Hence,The processing fee was = $36.96

learn more about unitary method click here:

https://brainly.com/question/24587372

#SPJ13

First Shaylee must substitute 6 for w. To simplify, Shaylee must divide

42 by 6.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

In this equation we have

42 ÷ w = 7

The question has already specified the value of w as 6

Hence we would have to remove w and replace it with the value six 6.

This is

42 ÷ 6

Next we have to find the value or the answer when we do this division. This can be easily done with a calculator

42 ÷ 6 = 7

Read more on division here: https://brainly.com/question/28119824

#SPJ1

Answer:

Step-by-step explanation:

1. Product means multiplying sign in math

23*39=897

2. Answer: 897

The angle C = 103.85° using the sine rule and rounded to the nearest hundredth.

In trigonometry, the sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Considering the ∆ABC, the sine rule states that;

(a/sinA) = (b/sinB) = (c/sinC)

so

25/sin120° = 20/sinB

sinB = (20 × sin120°)/25 {cross multiplication}

sinB = 0.6928

B = sin^(-1)[0.6928)] {sine inverse}

B = 43. 85°

Sum of interior angles in ∆ABC is 180° so;

C = 180° - (120° + 43.85°)

C = 180° - 76.15°

C = 103.85°

With the application of the sine rule, we can conclude that the value of the angle C is 103.85° rounded to the nearest hundredth.

Learn more about sine rule here: https://brainly.com/question/25852087

#SPJ1

Answer: 3

I used PEMDAS in this explanation: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Also known as the order of operations

Step-by-step explanation:

-5 + (5+3) :

First, add 5+3 =8

-5+8

When adding a negative to a positive, first, switch the -5 and 8 around like so.

8 + (-5)

then turn the -5 into it's opposite and subtract ---> 5

8-5=3

Unworded explanation:

-5 + (5+3) :

-5 + 8

8 + (-5)

8-5 = 3

The domain of the exponential function in this problem is given as follows:

0 ≤ n ≤ 5.

The exponential function in this problem is defined by the rule presented as follows:

g(n) = 10(1.02)^n.

In which the variables are listed as follows:

When the study was finished, the height of the flower was of 11.04 inches, hence the day at which the study was finished is obtained as follows:

10(1.02)^n = 11.04

(1.02)^n = 11.04/10

log[(1.02)^n] = log(11.04/10)

Applying the logarithm of power property, we have that:

nlog(1.02) = log(11.04/10)

n = log(11.04/10)/log(1.02)

n = 5.

The domain is the number of days for which the student was realized, hence:

0 ≤ n ≤ 5.

As the number of days cannot assume negative values.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The perpendicular bisector of the line segment with endpoints (6, -5) and (-2, -9) is 7x,2y = 6.

Therefore,

The coordinates of the end points:

(6, -5) and (-2, -9)

((6, -5) +(-2, -9))/2

= ((6,-9)/2, (-2, -5)/2)

= (1.5, 3.5)

The difference in endpoint coordinates will be;

(Δx, Δy) = (9-(-5), (-2)-6) = (14, 8)

Then the ratio of these values, so we need to divide both by the common factor of 2:

(Δx, Δy) = (7, 2)

A line perpendicular to this segment through the point (h, k) can be written as;

Δx·x +Δy·y = Δx·h +Δy·k

7x ,2y = 7(2) 2(4)

7x, 2y = 6 .

Hence the standard form equation for the perpendicular bisector will be;  7x ,2y = 6 .

To learn more about standard form equation, refer to:

https://brainly.com/question/1463202

#SPJ1

The number of books each classroom received = 185

In this question, we have been given two libraries donated books to a local school. One library donated 786 books and the other library donated 1,245 books. The school divided the books evenly among 11 classrooms.

We need to find the number of books each classroom received.

Total number of books received:

786 + 1245 = 2031

The school divided the books evenly among 11 classrooms.

Let x be the number of books each classroom received.

By unitary method,

x = 2031 /11

x ≈ 185

Therefore, the number of books each classroom received = 185

Learn more about Unitary Method here:

https://brainly.com/question/13163311

#SPJ1

Answer: -62.5

PLEASE GIVE BRAINLIEST THANK YOU!!!

Step-by-step explanation:

We know:

Equivalent equations are algebraic equations that have identical solutions.

We have the equation:

[tex]2x+\dfrac{1}{3}x=21[/tex]

multiply bot sides by 3

[tex]3\cdot2x+3\!\!\!\!\diagup\cdot\dfrac{1}{3\!\!\!\!\diagup}x=3\cdot21\\\\6x+x=63\\\\7x=63[/tex]

divide both sides by 7

[tex]\dfrac{7\!\!\!\!\diagup x }{7\!\!\!\!\diagup}=\dfrac{63}{7}\\\\\boxed{x=9}[/tex]

Answer:

x = 9

Step-by-step explanation:

Given equation,

→ 2x + (1/3)x = 21

Now the value of x will be,

→ 2x + (1/3)x = 21

→ (6/3)x + (1/3)x = 21

→ (7/3)x = 21

→ 7x = 21 × 3

→ 7x = 63

→ x = 63/7

→ [ x = 9 ]

Hence, the value of x is 9.

No, we cannot find a unique price for an apple and an orange

Let the price of an apple be $x and that of orange be $y.

Condition 1.

They need $10 for 4 apples and 4 oranges.

Then, 4x + 4y = 10

or, 2x + 2y = 5 .....(1)

Condition 2.

They need $12 for 6 apples and 6 oranges.

Then, 6x + 6y = 12

or, 2x + 2y = 5 .....(2)

Two identical linear equations have been discovered.

They do, however, create a system of dependent linear equations that reduces to:

2x + 2y = 5

There are infinite possible solutions to this linear equation.

Thus, we get the conclusion that an apple and an orange cannot have different prices.

Learn more about linear equations:

https://brainly.com/question/13738061

#SPJ4

Answer: 41.18% or 7/17

Step-by-step explanation:

7 + 4 + 6 = 17

7/17 (fraction)

41.18%

The coordinates of the midpoint M for the line segment AB are (-1/2, -2).

As per the stated values;

Th end points of the line segment AB are given as;

A(−5, 1) = (x1, y1)

B(4,−5) = (x2, y2)

The formula for the evaluation of the coordinates of the mid point is-

Mid point - M(x, y)

x = (x1 + x2)/ 2

x = (-5 + 4) /2

x = -1/2

y = (y1 + y2)/2

y = (1 - 5)/2

y = -2

Thus, the coordinates of the midpoint M for the line segment AB are (-1/2, -2).

To know more about the mid point of line segment, here

https://brainly.com/question/896396

#SPJ4

Answer:

Step-by-step explanation:

A formula is a method that has been proven to work when solving specific types of problems.

Let’s explore some of those familiar formulas by looking at rectangles, squares, area and perimeter.

The perimeter of a figure is the distance around the figure. Perimeter is the sum of all of the sides in a square or rectangle. Since a rectangle has two sets of parallel sides, the formula for determining perimeter  of a rectangle is:

and

Let’s look at an example.

[Figure 2]

The rectangle above shows its dimensions. Find the perimeter.

First, substitute the values for the width  and the length  into the perimeter formula.

Next, complete the multiplication and addition to find the perimeter.

The answer is 42.

The perimeter of the rectangle is 42 inches.

Area is the amount of square units inside the figure. Area is found by multiplying the . The formula for finding the area of a rectangle is:

You can use the dimensions from the rectangle above to find the area of this rectangle.

First, fill the values for  and  into the formula for area.

Next, solve for the area by multiplying.

The answer is 108.

The area of the rectangle is .

Notice that the unit of measurement for area is squared. That is because you multiplied a unit measure times itself: . Area is always written in square units.

You can also find the perimeter and area of a square. Remember that a square has four equal sides given the symbol . You can use the following formula for finding the perimeter of a square:

Let’s look at an example.

A rectangle has a length of 12 feet and a perimeter of 72 feet. Write and solve an equation to determine the width of the rectangle.

First, substitute the values for the perimeter  and the length  into the perimeter formula.

Next, complete the multiplication.

Then, subtract 24 from both sides to get your variable alone on the right side.

Then, multiply both sides by the reciprocal of 2 to isolate your variable.

The answer is 24.

The width of the rectangle is 24 feet.

Examples

Example 1

Earlier, you were given a problem about Raj and his garden fence.

He knows that the area of the land is 240 square feet, the length of one side is 15 feet, and needs to know the width of the land.

First, substitute the values for the area and the side length into the area formula.

Next, multiply both sides by the reciprocal of 15 in order to isolate the variable .

The answer is 16.

The width of Raj’s garden is 16 ft. Therefore the dimensions of the garden are 16 ft by 15 ft.

Example 2

A square has a perimeter of 196 inches. Determine the length of one side of the square.

First, substitute the value for the perimeter  into the perimeter formula.

Next, multiply both sides by the reciprocal of 4 to isolate your variable.

The answer is 49.

Example 3

Find the perimeter of the following square if the side length is 4.5 inches.

First, substitute the value for the side length into the perimeter formula.

Next, multiply by 4 to solve for the perimeter.

The answer is 18.

Example 4

Can you find the area of the square in Example 1?

First, substitute the value for the side length into the area formula.

Next, multiply to solve for the area.

The answer is 20.25.

The area of the square is .

Example 5

A square has an area of 144 sq. meters. What is the side length?

First, substitute the value for the area into the area formula.

Next, take the square root of the area to isolate . Remember that the opposite of square is square root.

The answer is 12.

Answer:

14.7

Step-by-step explanation:

Answer:

6[tex]\sqrt{6}[/tex]

or

≈14.7

Step-by-step explanation:

√6 x √6 x√6 can someone help​

√6 x √6 x√6 =

6[tex]\sqrt{6}[/tex]

or

≈14.7

The distance yet to be covered by Ashlee is 6.8 miles.

Ashlee is riding her bike to the beach. The beach is 17 miles from her home. She has already travelled 3/5 of the total distance. We need to find out how much farther she has to cycle.

Let the distance left to be covered by Ashlee be represented by the variable "D". The distance already covered by Ashlee on her cycle is calculated below.

d = (3/5)×17

d = 10.2

So she has already covered a distance of 10.2 miles. The distance yet to be covered is the difference between the total distance and the distance covered.

D = 17 - 10.2

D = 6.8

Hence, the distance yet to be covered by Ashlee is 6.8 miles.

To learn more about distance, visit :

https://brainly.com/question/15172156

#SPJ4

In accordance with algebra properties and relationship between logarithms and powers, the logarithm ㏒ₐ (108 / a³) is equal to the pseudolinear expression 2 · b + 3 · c - 3.

In this problem we must determine the base of a given set of logarithms by using algebra properties and relationships between powers and logarithms. Now we proceed to solve:

Step 1 - We get the following equations:

㏒ₐ 2 = b, ㏒ₐ 3 = c  

Step 2 - Now we add the other logarithm:

㏒ₐ (108 / a³)

Step 3 - By logarithm properties:

㏒ₐ 108 - ㏒ₐ a³

㏒ₐ (2² · 3³) - 3 · ㏒ₐ a

㏒ₐ 2² + ㏒ₐ 3³ - 3 · 1

2 · ㏒ₐ 2 + 3 · ㏒ₐ 3 - 3

Step 4 - By Step 1:

2 · b + 3 · c - 3

The logarithm ㏒ₐ (108 / a³) is equivalent to 2 · b + 3 · c - 3.

To learn more on logarithms: https://brainly.com/question/20785664

#SPJ1

The equation of given graph is y = |x - 3| + 5.

The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.

Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.

As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.

So, by putting the value of vertex in general equation we get the equation of the graph,

y = |x - 3| + 5

Therefore, the equation of given graph is y = |x - 3| + 5.

To learn more about the Absolute Function visit here:

https://brainly.com/question/25971887

#SPJ1

Answer:

  A, B, F

Step-by-step explanation:

You want to know the errors made in graphing y = -3x +2 by plotting the y-intercept of 2 and then plotting another point 3 down and 2 left of that.

The appropriate graph would be created by plotting the y-intercept at 2, then moving down 3 units and 1 unit right from there, because the slope is -3.

The y-intercept is correctly plotted at y=2.

The next point is incorrectly plotted down 3 units and 2 units left of the y-intercept. It should be plotted down 3 units and 1 unit right.

The slope is -3, or -3/1. For a negative slope, the rise or run, but not both, will be negative. We don't know the student's rationale for using 2 as the "run" in ...

  slope = rise/run

The best error descriptors seem to be ...

A)  The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −3/1 .

B)  The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.

F) After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −3/1, not −3/−2.

<95141404393>

The probability that the mean daily revenue for the next 30 days will exceed $7000 is 47.60%.

The formula for the z score is-

z = (x - μ)/σ

In which,

Put the value in formula

z = (7000 - 7200)/1200

z = - 0.16

Thus,

P(x > $7000) = P(z >  - 0.16)

See the p- value for obtained z from negative z score table.

P(x > $7000) = 0.4760

Thus, the probability that the mean daily revenue for the next 30 days will exceed $7000 is 47.60%.

To know more about the z score, here

https://brainly.com/question/25638875

#SPJ4