HELP ME PLEASE PLEASE PLEASE

The amount of heavy-duty fencing to be used is 2000 ft for $9000 and the amount of standard fencing to be used is 3000 ft for $9000 in order to make a total cost of $18000.

The area of the rectangular plot is denoted by the length multiplied by the width.

Let us assume that the length = x and the width = y.

Then, for two opposite with heavy fencing for $4.50 a foot and the standard fencing for $3 a foot, we have:

2x (4.50) + 2y(3) = 18000  ---- (1)

⇒ 9x + 6y = 18000

Make (y) the subject, we have:

[tex]\mathbf{y = \dfrac{18000-9x}{6}}[/tex]

Replace the value of y with the area of the rectangle, and we get:

[tex]\mathbf{Area =x(\dfrac{18000 - 9x}{6})}[/tex]

Area = x(3000 - 1.5x)

Area = 3000x - 1.5x²

For the area to be maximum, we take the differentiation of the Area:

dA/dx = 0

dA/dx = 3000 - 3x

x = 3000/3

x = 1000 ft

From equation (1)

2x (4.50) + 2y(3) = 18000  

x (4.50) + y(3) = 9000  

1000(4.50) + 3y = 9000

3y = 9000 -4500

y = 4500/3

y = 1500 ft

So, there are (1000× 2)ft = 2000ft heavy duty fencing for $9000, and (1500 ×2)ft = 3000ft standard fencing for $9000 to make a cost of $18000.

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Answer:

No solutions

Step-by-step explanation:

Hello!

To solve for x, we should expand the parenthesis and isolate the variable x.

The are no solutions for x, as 6 does not equal to 5.

Based on the fact that the snake was placing the mice one - by - one into a jar, this is A. Combining sets.

When sets are combined, it means that numbers from a certain set of variables are combined with those from another set.

The snake had captured the mice separately which means they were in different sets. Putting them into one jar means they are being combined so this is combining sets.

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Critical value z_{0.05}=-1.645

Decision Rule, Reject H if z< -1.645

We do not reject the null hypothesis.

Generally, the equation for the hypothesis  is  mathematically given as

H P=0.3

H2:P<0.13

Therefore

[tex]z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\z=\frac{0.11-0.13 }{\sqrt{\frac{0.13(1-0.13)}{76}}}[/tex]

z=-0.52

In conclusion, from the table

Critical value z_{0.05}=-1.645

Decision Rule, Reject H if z< -1.645

In conclusion, we do not reject the null hypothesis.

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Answer:

Again, this would be 2444.

Step-by-step explanation:

Because of the previous answers 1963 and 481, we can add them together to make 2444.

The person who ran farther is Hayley.

Average speed is the total distance travelled per time.

Average speed = total distance / total time

Tyler's average speed =  1 / 8.30 seconds = 0.12 miles per minute

The distance covered by Tyler in 10 minutes = 0.12 x 10 = 1.2 miles

Distance covered by Hayley in 10 minutes : 10 = 8x

x = 10 / 8 = 1.25 miles

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Answer:

  72 guests

Step-by-step explanation:

We can add up the numbers of bottles per guest, then use that total to find the number of guests from the number of bottles.

Let g represent the number of guests at the party. Then there are ...

The total number of bottles is ...

  g(1/3 +1/6 +1/4) = 54

Multiplying by the inverse of the coefficient of g, we find its value to be ...

  g(4/12 +2/12 +3/12) = g(9/12) = 54

  g = 54(12/9) = 72

There are 72 guests at the party.

The integers are 12,14 and 16

Consecutive even integers are represented as:

x, x + 2 and x + 4

So, the statement is represented as:

7 * (x + x + 2 + x +4) = 140 + 11 * (x + 2)

Evaluate the like terms

7 * (3x + 6) = 140 + 11 * (x + 2)

Open the brackets

21x + 42 = 140 + 11x + 22

Collect the like terms

21x -11x =

Evaluate

10x = 120

Divide by 10

x = 12

So, we have

x + 2 = 14

x + 4 = 16

Hence, the integers are 12,14 and 16

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Answer:

16

Step-by-step explanation:

A fraction that is divided by a number is just multiplication with the denominator. So with that 8(2)=16

Answer:

Graph D (look in the attached picture)

The way you do this is use the quadratic formula to solve for the x intercepts which are [tex](\frac{1+\sqrt{2} }{2} )[/tex] and [tex](\frac{1-\sqrt{2} }{2})[/tex]

The numbers are:

What is number system?

A number system is defined as a system of writing to express numbers.

First, the number between 8,500 and 8,800.

So, the thousands place digit is 8.

Second, When multiplied by 8, the result is a whole number.

So, multiplying by 8, the decimal has to end in 5.

Because there is no zeroes in the decimal place..

options are:

8 times 0.5

8 times 0.25

8 times 0.125

Now, The digit in the hundredths place is 200% of the digit in the tenths place

considering digit in the hundreds place is ¾ the digit in the thousands place.

So, choose 0.125.

Now, The digit in the hundreds place is 3/4 the digit in the thousandths place.

Digit in Thousandth Place = 5

Digit in Hundreds place=3/4*2=6

Our number now is:86_ _.125

As, The sum of all the numbers is 26

8+6+1+2+5=22

26-22=4

The possible numbers are:

8,640.125

8,604.125

8,622.125

8,613.12

8,631.125

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Step-by-step explanation:

2A and 2B are scalar multiplications : every item in the matrix has to be multiplied by that factor.

the subtraction then of 2A - 2B is simply to subtract every positive in B from the corresponding same position in A.

that is all.

2A =

4 0

-6 2

2B =

0 2

-4 6

2A - 2B =

4-0 0-2

-6--4 2-6

=

4 -2

-2 -4

Answer:

the distance is 10

Step-by-step explanation:

since the slope is the same you know they're parallel, but just find the difference from the two y intercepts (the +3/-7) the difference is 10, so 10.

n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.

Since these are solutions

x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.

We have (x-2)(x-5i)(x+5i) = 0

Now,

f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.

f(-1) = (-3)(26) = -78.

But -78 x -2 = 156, so our polynomial becomes

Y= -2x (x - 2 ) x (x to the power of 2 + 25) = 0

Answer:

[tex]f(x)=2x^4-12x^3+50x^2-56x-120[/tex]

Step-by-step explanation:

Complex Conjugate Theorem

For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs.  So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.

Given zeros:

-1, 3, and (2 + 4i)

As one of the given zeros is a complex number, (2 - 4i) is also a zero.

Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:

[tex]\begin{aligned}f(x) & =a(x+1)(x-3)(x-(2+4i))(x-(2-4i))\\& = a(x+1)(x-3)(x-2-4i)(x-2+4i)\\& = a(x+1)(x-3)(x^2-2x+4ix-2x+4-8i-4ix+8i-16i^2)\\& = a(x+1)(x-3)(x^2-4x+4-16i^2)\end{aligned}[/tex]

Remember that [tex]i^2=-1[/tex], therefore:

[tex]\begin{aligned}f(x)&=a(x+1)(x-3)(x^2-4x+4-16(-1))\\&=a(x+1)(x-3)(x^2-4x+4+16)\\&=a(x+1)(x-3)(x^2-4x+20)\end{aligned}[/tex]

To find the value of the leading coefficient (a), use the given [tex]f(1)=-136[/tex] :

[tex]\begin{aligned}f(1) & = -136\\\implies a(1+1)(1-3)(1^2-4(1)+20) & = -136\\a(2)(-2)(17) & = -136\\-68a & = -136\\\implies a & = 2\end{aligned}[/tex]

Therefore, the polynomial in factored form is:

[tex]f(x)=2(x+1)(x-3)(x^2-4x+20)[/tex]

Finally, expand the brackets:

[tex]\begin{aligned}f(x) & =2(x+1)(x-3)(x^2-4x+20)\\& =2(x^2-2x-3)(x^2-4x+20)\\& =2(x^4-4x^3+20x^2-2x^3+8x^2-40x-3x^2+12x-60)\\& =2(x^4-4x^3-2x^3+20x^2+8x^2-3x^2-40x+12x-60)\\& =2(x^4-6x^3+25x^2-28x-60)\\& =2x^4-12x^3+50x^2-56x-120\end{aligned}[/tex]

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Answer:

C.

Step-by-step explanation:

The algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

The number that is x more than 2x+1

x is the number.

x > 2x + 1

After simplification:

2x - x < -1

x < -1

x ∈ (-∞, -1)

Thus, the algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1

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Step-by-step explanation:

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Answer:

y ≤ 2.5x-3

Step-by-step explanation:

we know two points: (2 , 2 ) and ( 0 , -3)

[tex]Grad = \frac{2--3}{2-0} =\frac{5}{2} =2.5\\[/tex]

we also know the y intercept is -3

therefore equation in question is : [tex]y = 2.5x-3[/tex]

we take any point either above the line or below the line and substitute in the equation above. Let us try point (0,0) which is above the line and in the unwanted(shaded region):

y = 2.5x-3

0=2.5(0)-3

0=-3

Normally 0 can  never be equal to -3 but is ≥ -3.

Since the point taken was not in the wanted region we reverse ≥  to ≤  to show the wanted region. The inequality in question becomes :

y ≤ 2.5x-3

Step-by-step explanation:

if I understand your comment correctly, then you need the mean value of the lifetime of these light bulbs.

1. get the midpoint of each interval.

2. multiply each frequency with its midpoint.

3. sum all frequencies.

4. sum all multiplication results if 2. (of frequencies and midpoints).

5. divide 4. by 3.

lifetime midpoints :

(25 + 50)/2 = 75/2 = 37.5

(50 + 100)/2 = 150/2 = 75

(100 + 150)/2 = 250/2 = 125

(150 + 200)/2 = 350/2 = 175

(200 + 250)/2 = 450/2 = 225

(250 + 300)/2 = 550/2 = 275

(300 + 350)/2 = 650/2 = 325

multiply frequencies with their midpoints :

37.5 × 47 = 1762.5

75 × 86 = 6450

125 × 45 = 5625

175 × 36 = 6300

225 × 0 = 0

275 × 37 = 10175

325 × 50 = 16250

sum all frequencies

47+86+45+36+0+37+50 = 301

sum all multiplication results of 2.

1762.5+6450+5625+6300+0+10175+16250 = 46,562.5

divide 4. by 3.

the mean value is

46,562.5 / 301 = 154.692691... hours ≈

≈ 154.69 hours

Answer:

Step-by-step explanation:

n = the number

n = 5m - 3

the astronaut would weigh 1 pound above the Earth.

Given that;

Gravitational force = Gm/r^2

M1 = 196 pounds

M2 = unknown

R1 = 4000 miles

R2 = 300 miles

We can deduce that;

[tex]\frac{m1}{r^21} = \frac{m2}{r^22}[/tex]

Let's substitute the values

[tex]\frac{196}{4000^2} = \frac{x}{300^2}[/tex]

[tex]\frac{196}{1.6 *10^7} = \frac{x}{9 *10^4}[/tex]

Cross multiply

196 × 9 ×10^4 = x × 1.6 ×10^7

1.76 × 10^7 = x × 1.6 ×10^7

Make 'x' the subject of formula

x = [tex]\frac{1.76* 10^7}{1.6*10^7}[/tex]

x = 1.1

x = 1 pound

Thus, the astronaut would weigh 1 pound above the Earth.

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Answer:

19/24

Step-by-step explanation:

3/8=36/96

5/12=40/96

36/96+40/96=76/96

76/96=19/24

Answer:

B. 13

Explanation:

[tex]\sf\:Given\:expression: log(\dfrac{x^2 y^3}{z} )[/tex]

Logarithm rules:

[tex]\sf (i) \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \ log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)[/tex]

Breakdown of the expression:

[tex]\rightarrow \sf log\left(\dfrac{x^2y^3}{z}\right)[/tex]

[tex]\rightarrow \sf log\left(x^2\right) + log\left(y^3\right) - log(z)[/tex]

[tex]\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)[/tex]

insert given values

[tex]\rightarrow \sf 2(3)+3(2)-(-1)[/tex]

[tex]\rightarrow \sf 13[/tex]

The value of the equation is A = 12p , where p is the number of packages of batteries

Equations are mathematical statements with two algebraic expressions on either side of the equals (=) sign.

It depicts how the expressions on the left and right sides are linked together.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are all parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of packages be represented as p

Let the number of batteries in one package = 12 batteries

So , the total number of batteries in p packages A = number of packages x number of batteries in one package

The total number of batteries in p packages A = 12p

Hence , the equation is A = 12p

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Answer:

y=2x-11

Step-by-step explanation:

arralel lines have same gradient

since gradient of the known line is 2( the coefficient of x), it therefore follows that the gradient of the second line we want to find is also 2

So we know the gradient of the second line is 2, and we have one known point (7,3). We can therefore apply the formula for finding gradient to come up with the line

[tex]2=\frac{y-3}{x-7} \\\\y-3=2(x-7)\\\\y-3=2x-14\\\\y=2x-14+3\\\\y=2x-11[/tex]

[tex]\huge\boxed{L^\prime(0, -1)}[/tex]

To rotate a point around the origin by 180 degrees, multiply both parts of the coordinate point by [tex]-1[/tex]. (This means you go from [tex](x, y)[/tex] to [tex](-x, -y)[/tex].)

[tex]L(0, 1)[/tex]

[tex]L^\prime(0*(-1), 1*(-1))\\\boxed{L^\prime(0, -1)}[/tex]

Answer: -2, 1, all real numbers, all real numbers

Step-by-step explanation:

g o f(n) is basically g(f(n))

Using the question as an example we can get that f(0) = 1 so

g(f(0)) = g(1) = -2

f(1) = 0 so g(f(1)) = g(0) = 1

The domain of f(x) is all real numbers and the range of g(x) is all real numbers

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationships between sides of a right triangle and trig functions of the acute angles. It tells you ...

The given triangle shows values of an acute angle and its opposite side. You are to find the other two sides in the triangle, as well as the other acute angle.

X is the side adjacent to the given angle, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(25°) = (4 ft)/X

Solving for X gives ...

  X = (4 ft)/tan(25°) . . . . . . . . multiply by X/tan(25°)

  X ≈ 8.58 ft

Y is the hypotenuse, so the relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(25°) = (4 ft)/Y

  Y = (4 ft)/sin(25°) . . . . . . multiply by Y/sin(25°)

  Y ≈ 9.46 ft

The sum of angles in a triangle is 180°, so if one of them is 90°, the sum of the other two is 90°.

  Z = 90° -25°

  Z = 65°

In this scenario, children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.

Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment such as direct comparison.

In this scenario, we can infer and logically deduce that the children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.

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Domain: [-4, ∞)

Range: (-∞, 0]

*Domain are all x-values listed. Here you can see the graph going the right (positive) of -4 (Doesn't go to the left)

*Range are all y-values listed. Here you can see the graph starts from zero and goes down (negative)

Hope it helps!