Julie will build a rectangular pen for her dog against a barn. A wall from the barn will form one side of the pen. She has 32 m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area.

What will be the dimensions of Julie's pen?

Answer: 299.5 cycles per second.

Step-by-step explanation:

An inverse variation can be written as:

y = k/x

Where, in this case:

y = frequency

x = length of the string

k = constant.

We know that 410 mm correspond to 515 cps.

then:

515cps = k/410mm

k = 515cps*410mm = 211,150 cps*mm

now, if we use x = 705mm we can find the frequency as:

y = ( 211,150 cps*mm)/705mm = 299.5 cycles per second.

Answer:

Step-by-step explanation:

In this problem we are going find the natural logarithmic of the numbers involved and solve for x

[tex]ln65-Ln x= 39\\[/tex]

from tables

[tex]4.17-ln x= 39\4.17-39= lnx\\-34.83=lnx\\[/tex]

taking the exponents of both sides we have

[tex]e^-^3^4^.^8^3= x\\x= 7.47[/tex]

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

Option A is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( 2 , 2 ) ------> ( x1 , y1 )

B ( 3 , 5 ) -------> ( x2 , y2)

Now, let's find the mid-point :

Midpoint = [tex] (\frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )[/tex]

plug the values

[tex] = ( \frac{2 + 3}{2} \: , \frac{2 + 5}{2} )[/tex]

Calculate the sum

[tex] = \: ( \frac{5}{2} \:, \frac{7}{2} )[/tex]

Hope this helps..

Best regards!!

Answer:

x = 4

Step-by-step explanation:

The midsegment ( median is equal to half the sum of the parallel bases, that is

[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values

[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2

7x - 2 = 26 ( add 2 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Answer:

(Choice B) B It decreases.

Step-by-step explanation:

According to the situation, the solution of the value of the expression is as follows

Let us assume

r         80 -2r

5        80 - 10 = 70

4        80 - 8 = 72

3        80 - 6 = 74

2        80 - 4 = 76

1         80 - 2 = 78

As we can from the above calculation that expression value risen if r value decreased

Therefore the correct option is B.

Answer:

It increases

Step-by-step explanation:

Answer:

There are 200 girls in that school

Step-by-step explanation:

The correct and complete question is as folly;

In a school 3/5 pupils are boys. One day 1/6 of the boys were absent when 250 boys were present. How many girls are in the school?

SOLUTION

Let the total number of students in the school be x students

Since 3/5 are boys , then the number of girls in the school would be 1-3/5 = 2/5

The number of boys are 3/5 * x = 3x/5

The number of girls are 2/5 * x = 2x/5

Now on a particular day, 1/6 of the boys were absent and 250 boys were present.

What this means is that the fraction of boys present is 1-1/6 = 5/6

Now, 5/6 of the total boys population were present.

Mathematically;

5/6 * 3x/5 = 250

3x/6 = 250

x/2 = 250

x = 2 * 250 = 500

So there are 590 students in the school.

The number of girls in the school is ;

2x/5 = 2/5 * 500 = 200 girls

Answer:

Bearing of R from S = S 45° E or 135°

The bearing of R from Q

= S 66.42° w or 246.42°

Step-by-step explanation:

Distance between R and S

RS²= RP²+PS²

RS²= 15²+15²

RS²=225+225

RS= √450

RS= 21.21

Angle at S

21.21= 15/sins

Sin s= 15/21.21

S= sin^-1 15/21.21.

S= 45°

90+45= 135°

Bearing of R from S = S 45° E or 135°

Distance between R and Q

RQ²= PQ²+PR²

RQ²= 35²+15²

RQ²=1225+225

RQ= √1450

RQ= 38.08

RQ= 15/sinQ

SinQ= 15/38.08

SinQ= 0.40

Q=23.58°

90-23.58 = 66.42°

66.42+180= 246.42°

The bearing of R from Q

= S 66.42° w or 246.42°

Answer:

Perimeter = 20cm ; area = 59.5cm

Step-by-step explanation:

Given the following :

Perimeter of entire figure = 42cm

Diameter of circle (d) = 7cm

Find the perimeter of the circle :

The perimeter (p) of a circle equals :

2πr

Where r = radius of circle

r = diameter /2 = 7/2 = 3.5cm

Therefore,

P = 2 * (22/7) * 3.5

P = 22 cm

Looking at the figure, we only take the semicircle :

Therefore perimeter of each semicircle =

22cm / 2 = 11cm

Therefore, perimeter of the red shaded region =

(42 - 22)cm = 20cm

Area of Circle = πr^2

(22/7) * 3.5^2 = 38.5 cm

Area of each semicircle = 38.5/2 = 19.25cm

Total area of semicircle = (19.25 +19.25) = 38.50cm

To find sides of rectangle :

Perimeter of the rectangle :

width = diameter of circle = 7cm

2(l + w) = 42

2(l + 7) = 42

2l + 14 = 42

2l = 42 - 14

2l = 28

l = 28/2

length (l) = 14cm

Therefore, area of rectangle :

Length * width

14 * 7 = 98cm

Area of red portion:

Area of rectangle - (area of the 2 semicircles)

98cm - 38.50cm

= 59.50cm

Answer:

120

Step-by-step explanation:

12 x 6 = 72

8x(12/2)=48

72+48 =120

Hey there! I'm happy to help!

There are 31 days in March, so there are 11 days left in March. We add this to the 20 days in April, giving us 31 total days this interest is compounded.

We could calculate the amount compounded each day for 31 total days, but that would take a long time. Instead, there is a formula we can use to calculate compound interest instead.

[tex]Total= P(1+i)^n\\\\P=Principal Amount\\i=interest rate\\\\n=number of times compounded[/tex]

So, let's plug in those numbers! Remember to convert the percent to a decimal so it works in the equation!

[tex]Total=1000(1+0.055)^3^1\\Total=1000(5.258068609)\\Total=5258.068609[/tex]

Now, we subtract the initial amount just to see how much interest was earned.

5258.068609-1000=4258.07 (rounded to nearest cent).

Therefore, the money will have earned $4,258.07 by April 20.

Have a wonderful day!

Answer:

1.5 rounded to the nearest tenth

Step-by-step explanation:

To find how much greater WBC are from RBC we do,

3.92 ÷ 2.6

= 1.50769230769

Which is 1.5 rounded to the nearest tenth.

Thus,

there are approximately 1.5 times WBC than RBC.

Hope this helps :)

The 1.5 times greater is the number of red blood cells than white blood cells

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Adult humans have approximately 2.6 red blood cells and 3.92 white blood cells.

To find the number of times greater is the number of red blood cells than white blood cells:

Use division operation,

3.92 / 2.6

= 1.5076

≈ 1.5 rounded to the nearest tenth.

Therefore, the required number is 1.5 times.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ5

Answer:

y = 110°

Step-by-step explanation:

The inscribed angle CHF is half the measure of its intercepted arc CDF

The 3 arcs in the circle = 360°, thus

arc CDF = 360° - 160° - 60° = 140°, so

∠ CHF = 0.5 × 140° = 70°

∠ CHF and ∠ y are adjacent angles and supplementary, thus

y = 180° - 70° = 110°

Answer:

138.37 gram

Step-by-step explanation:

Formula of density

density = mass/ volume

given

volume = 202 mL

density = 0.685g/mL

using these values in Formula of density

0.685g/mL = mass/ 202 mL

mass = 0.685g/mL * 202 mL = 138.37 gram

Thus, weight of liquid is  138.37 gram to the nearest hundredth.

Answer:

138.37 grams

Step-by-step explanation:

I'm taking the exam. Good luck on yours!

Answer: w=5

Step-by-step explanation:

Answer:

Slope = 3

Step-by-step explanation:

Slope is rise (vertical distance) over run (horizontal distance).

Our rise is equal to 3

Our run is equal to 1

So, slope = 3/1 = 3

Answer: -1

Step-by-step explanation:

[tex]5t-3=3t-5[/tex]

Add 3 to both sides.

[tex]5t=3t-2[/tex]

Subtract 3t from both sides.

[tex]2t=-2[/tex]

[tex]t=-1[/tex]

Hope this helps!

Answer: t=-1

Step-by-step explanation:

1) add 3 to both sides

2) subtract 3t from both sides

3) Divide both sides by 2

Answer:

The probability that a defective ball bearing was manufactured on a Friday is 0.375.

Step-by-step explanation:

The conditional probability of an events X given that another event A has already occurred is:

[tex]P(X|A)=\frac{P(A|X)P(X)}{P(A)}[/tex]

The information provided is as follows:

P (D|M) = 0.08

P (D|Tu) = 0.04

P (D|W) = 0.04

P (D|Th) = 0.04

P (D|F) = 0.12

It is provided that the Company manufactures an equal amount of ball bearings, 20% on each weekday, i.e.

P (M) = P (Tu) = P (W) = P (Th) = P (F) = 0.20

Compute the probability of manufacturing a defective ball bearing on any given day as follows:

[tex]P(D)=P(D|M)P(M)+P(D|Tu)P(Tu)+P(D|W)P(W)\\+P(D|Th)P(Th)+P(D|F)P(F)[/tex]

      [tex]=(0.08\times 0.20)+(0.04\times 0.20)+(0.04\times 0.20)+(0.04\times 0.20)+(0.12\times 0.20)\\\\=0.064[/tex]

Compute the probability that a defective ball bearing was manufactured on a Friday as follows:

[tex]P(F|D)=\frac{(D|F)P(F)}{P(D)}[/tex]

             [tex]=\frac{0.12\times 0.20}{0.064}\\\\=0.375[/tex]

Thus, the probability that a defective ball bearing was manufactured on a Friday is 0.375.

Answer:

Step-by-step explanation:

Given the surdic expression [tex]\frac{2}{3\sqrt{5} + 2\sqrt{11}}\\[/tex], to rationalize the expression, we will have to multiply the numerator and denominator of the expression by the conjugate of the denominator as shown;

[tex]= \frac{2}{3\sqrt{5} + 2\sqrt{11}} * \frac{3\sqrt{5} - 2\sqrt{11}}{3\sqrt{5} - 2\sqrt{11}}\\\\= \frac{2(3\sqrt{5} - 2\sqrt{11})}{(3\sqrt{5} + 2\sqrt{11})(3\sqrt{5} - 2\sqrt{11})}\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9\sqrt{25}+6\sqrt{55}- 6\sqrt{55}-4\sqrt{121} } \\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9(5)-4(11) }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{45-44 }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex]

Comparing the result [tex]\frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex] with the expression [tex]\frac{A\sqrt{B} + C\sqrt{D}}{E}[/tex], it can be seen that A = 6, B = 5, C = -4, D = 11 and E = 1

A+B+C+D+E = 6+5+(-4)+11+1

A+B+C+D+E = 11-4+12

A+B+C+D+E = 19

Hence the value of A+B+C+D+E is 19

Answer:

15, 16, 17, 18

Step-by-step explanation:

29-14=15

15, 16, 17, 18 are less than or equal to 18

Answer:

x = 1

Step-by-step explanation:

Using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

3[tex]log_{2}[/tex] (2x) = 3

[tex]log_{2}[/tex] (2x)³ = 3

(2x)³ = 2³

8x³ = 8 ( divide both sides by 8 )

x³ = 1 ( take the cube root of both sides )

x = 1

Answer:

x=1 is the correct answer

Step-by-step explanation:

got it right on edge!!!!

Answer:

The expression is equal to 3,120 when x = -5 and y = 25.

Step-by-step explanation:

In order to obtain the output of the expression when x = -5 and y = 25, we need to apply these numbers in its correct places as shown below. We need to pay close attention to [tex]|x|[/tex] which is the absolute value of "x", this means that if x is positive, then [tex]|x|[/tex] will also be positive, but if x is negative then the result will still be positive.

[tex]\frac{5|x| - y^3}{x}[/tex]

[tex]\frac{5*|-5| - (25)^3}{-5}\\\frac{5*5 - 15625}{-5}\\\frac{25 - 15625}{-5}\\\frac{-15600}{-5} = 3,120[/tex]

The expression is equal to 3,120 when x = -5 and y = 25.

Answer:

A).300763=+ 67

b) 704969= +87

c)( - 226981)= -61

Step-by-step explanation:

The values of the cube root iyf the given numbers above will be looked up in a calculator and the estimated value will be returned back.

Going through the numbers

A).for 300763

The value of the cube root = +67

B). For 704969

The value of the cube root = +89

C). For ( - 226981)

The value of the cube root= -61

Answer:

Hey there!

Angles in a quadrilateral add to 360 degrees, so we have 56+78+90+x=360

Solving, we see that the missing angle, x, is 136 degrees.

Hope this helps :)

Answer:

Hey.... Ans is 154°

The mate who ans before me HAVE TO FIND x TOO

Step-by-step explanation:

For example take a quadrilateral ABCD (refer to the pic)

Then solution is...

In quadrilateral ABCD

            Sum of all sides of a quadrilateral= 360°

           =angle A + angle B+ angle C+ angle D=

Given,

          Angle A= 56° + angle B=78° + angle C=90° + angle D=x

        =56° + 78° + 90° + x.            (add all the numbers)

         x+226=360°                           (56+78+90=226)

         x=360° - 226°

         x=154°

Therefore the largest angle = x = 154°

Hope it helped u!!

Answer:

x=3

Step-by-step explanation:

-2x-3=-9

Add 3 to each side

-2x-3+3=-9+3

-2x = -6

Divide by -2

-2x/-2 = -6/-2

x = 3

Answer:

x =3

Step-by-step explanation:

[tex]-2x-3=-9. \\ - 2x = - 9 + 3 \\ - 2x - 6 \\ \frac{ - 2x}{ - 2} = \frac{ - 6}{ - 2} [/tex]

[tex]x = 3[/tex]

Answer:

Slope = -6/7

Step-by-step explanation:

You need to use the formula m = y2 - y1 ÷ x2 - x1

The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1

So,

m = 2 - 5 ÷ 3/2 - (-2)

m = -3 ÷ 7/2

m = -6/7

Hope this helps :)

Answer:

[tex]4 \frac{1}{4} [/tex] hours

Step-by-step explanation:

Given,

Time spent in studies : [tex]1 \frac{3}{4} [/tex] hours

Time spent in playing cricket : [tex]2 \frac{1}{2} [/tex] hours

Now, let's find the time that he spent in all:

[tex]1 \frac{3}{4} + 2 \frac{1}{2} [/tex]

Add the whole number and fractional parts of the mixed numbers separately

[tex](1 + 2)( \frac{3}{4} + \frac{1}{2} )[/tex]

Add the numbers

[tex]3 +( \frac{3}{4} + \frac{1}{2} )[/tex]

Add the fractions

[tex]3 + ( \frac{3 + 1 \times 2}{4} )[/tex]

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

[tex]3 + \frac{5}{4} [/tex]

Convert the improper fraction into mixed number

[tex] 3 + 1\frac{1}{4} [/tex]

Write the mixed number as a sum of the whole number and the fractional part

[tex]3 + 1 + \frac{1}{4} [/tex]

Add the numbers

[tex]4 + \frac{1}{4} [/tex]

Write the sum of whole number and the fraction as a mixed number

[tex]4 \frac{1}{4} [/tex] hours

Hope this helps..

Best regards!!

Answer:

4 1/4 hours.

Step-by-step explanation:

1 3/4 + 2 1/2

= 1 + 2 + 3/4 + 1/2

= 3 + 3/4 + 1/2   The LCM of 2 and 4 is 4 so 1/2 = 2/4. and so we have:

3 + 3/4 + 2/4

= 3 + 5/4

= 3 + 1 1/4

= 4 1/4 hours.

Answer:

4c

Step-by-step explanation:

We can say that the maximum number of cars can be represented as:

Maximum number of cars = Total of rows × Number of cars per row

In this particular case, we have 4 rows and the number of cars per row is c, thus, the expression above becomes:

Maximum number of cars = 4c

Answer:

Answer c): write the function in standard form

Step-by-step explanation:

To start with, it is important to write the polynomial in standard form, so as to have the two terms with the dependence in x together:

[tex]6x^2-42\,x+5[/tex]

then you extract 6 as a common factor of just the terms with the variable x:

[tex]6(x^2-7x)+5[/tex]

Then proceed to complete the square in the expression inside the parenthesis:

[tex]6(x^2-7x+\frac{49}{4} -\frac{49}{4})+5[/tex]

[tex]6\,((x-\frac{7}{2} )^2-\frac{49}{4} )+5\\6\,(x-\frac{7}{2} )^2-\frac{147}{2}+5\\6\,(x-\frac{7}{2} )^2-\frac{137}{2}[/tex]

Then, the function can be finally be written as:

[tex]f(x)=6\,(x-\frac{7}{2} )^2-\frac{137}{2}[/tex]

in vertex form

Answer:

C.) Write the function in standard form

Step-by-step explanation: