1. The perimeter of a rectangular field is 180 feet. Let x be the length of the field (in feet) and let y be the width (in feet). Write an equation to model the perimeter of the rectangular field. 

Also this question so there's 2 questions


2. Tyrone is designing a rectangular sandbox. He wants the sandbox to be 15 feet long and have a perimeter of 46 feet. How wide does Tyrone’s sandbox need to be? ​

Answer:

2

Step-by-step explanation:

Here, we have a mean of 50 and a standard deviation of 25, we now need to find out in terms of standard deviation how 0 is far from 50.

Firstly, we subtract 0 from 50

That gives 50. Now, we need to divide this difference by the standard deviation

That will be 50/25 and that makes it 2

So 0 is two deviations away from 50

Answer:

0.6 + 0.08

Step-by-step explanation:

Answer:

120 ways

Step-by-step explanation:

To solve the question above, we use combination formula:

Where ;

nCr = n! / (n-r)! r!

10C7 = 10! / (10 - 7)! 7!

10C7 = 10! / 3! 7!

10C7 = (10 * 9 * 8) / 3 * 2 * 1

10C7 = 720 / 6

= 120 ways

Answer:

[tex]\theta = 56[/tex]

Step-by-step explanation:

Represent the angles with [tex]\theta[/tex] and [tex]\alpha[/tex]

Such that:

[tex]\theta = 22 + \alpha[/tex]

Since both angles are complementary, we have:

[tex]\theta + \alpha = 90[/tex]

Substitute [tex]\theta = 22 + \alpha[/tex]

[tex]22 + \alpha + \alpha = 90[/tex]

[tex]22 + 2\alpha = 90[/tex]

Collect Like Terms

[tex]2\alpha = 90 - 22[/tex]

[tex]2\alpha = 68[/tex]

[tex]\alpha = 68/2[/tex]

[tex]\alpha = 34[/tex]

Recall that:

[tex]\theta = 22 + \alpha[/tex]

[tex]\theta = 22 + 34[/tex]

[tex]\theta = 56[/tex]

Hence:

The larger angle is 56

Answer:

38.5

Step-by-step explanation:

17-19= -2

-2+156=154

154 divided by 4= 38.5

it should be 17 - 19 + 154 then divided by 4

so 38.5 cookies

Answer:

3

Step-by-step explanation:

Answer:

y=5

x=10 and

z=2

Step-by-step explanation:

since they are equivalance then,

for

triangle ABC and triangle DFE

AB=DF,BC=FE and AC= DE

So, AB=DF

8y-20= 4y

or, y=5

Then, BC= FE

2x+5=x+15

or, x=10

and

AC=DE

3z+9=10z-5

or, z= 2

hope u got ut.

The triangles are parallel thus their sides are equal to each other peer to peer.

So ;

[tex]x + 15 = 2x + 5[/tex]

Subtract sides -5

[tex]x + 15 - 5 = 2x + 5 - 5[/tex]

[tex]x + 10 = 2x[/tex]

Subtract sides -x

[tex]x - x + 10 = 2x - x[/tex]

[tex]x = 10[/tex]

_________________________________

[tex]4y = 8y - 20[/tex]

Subtract sides -8y

[tex]4y - 8y = 8y - 8y - 20[/tex]

[tex] - 4y = - 20[/tex]

Negatives simplifies

[tex]4y = 20[/tex]

Divided sides by 4

[tex] \frac{4}{4}y = \frac{20}{4} \\ [/tex]

[tex]y = 5[/tex]

_________________________________

[tex]10z - 5 = 3z + 9[/tex]

Plus sides 5

[tex]10z - 5 + 5 = 3z + 9 + 5[/tex]

[tex]10z = 3z + 14[/tex]

Subtract sides -3z

[tex]10z - 3z = 3z - 3z + 14[/tex]

[tex]7z = 14[/tex]

Divided sides by 7

[tex] \frac{7}{7}z = \frac{14}{7} \\ [/tex]

[tex]z = 2[/tex]

_________________________________

And we're done....♥️♥️♥️♥️♥️

Part (a)

Plug in y = 0 and solve for x. Use the zero product property

y = x(x+3)(x-2)

0 = x(x+3)(x-2)

x(x+3)(x-2) = 0

x = 0 or x+3 = 0 or x-2 = 0 .... zero product property

x = 0 or x = -3 or x = 2

The three roots or zeros are x = 0 or x = -3 or x = 2

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

Part (b)

The roots of the graph are: x = -2, x = 1, x = 3. Each root is where the graph crosses or touches the horizontal x axis.

Note how x = 0 is found in part (a), but not found here. This is one example where the graphs don't match. Another would be x = -3 is in part (a), but not here.

So that's why the graph does not match with the function in part (a)

Answer:

23/3

Step-by-step explanation:

x=-4

plug x into equation

4(-4)+3y = 7  

-16+3y = 7

3y=23

y=23/3

Answer:

Step-by-step explanation:

To write the value of three hundred and eighty two thousandths in words, we can follow the steps below:

Split the expression based on the place values

The statement is expressed as:

[tex]\frac{382}{1000}[/tex] = 0.382

three hundred thousandth = 0.300 (thousandth)

eighty thousandth= 0.080

two thousandth = 0.002

Add the values gotten

= 0.300 + 0.080 + 0.002

= (3*10⁻¹) + (8*10⁻²) + (2*10⁻³)

= 0.382

Answer: The heaviest 19% of fruits weigh more than 753grams.

Step-by-step explanation:

Let X = fruit's weights that are normally distributed.

Given: [tex]\mu=720,\ \ \ \sigma=38[/tex]

To find : x such that P(X>x)=19%

i.e. P(X<x) = 81%  [100%-19%=81%]

i.e. P(X<x) = 0.81

[tex]P(\dfrac{X-\mu}{\sigma}<\dfrac{x-720}{38})=0.81[/tex]

Since, [tex]Z=\dfrac{X-\mu}{\sigma}[/tex] and from z-table the z value for p-value of 0.81 (one -tailed) = 0.8779

[tex]\dfrac{x-720}{38}=0.8779\\\\\Rightarrow\ x-720 =38\times0.8779\\\\\Rightarrow\ x-720 =33.36\\\\\Rightarrow\ x = 33.36+720=753.36\approx753[/tex]

Hence, the heaviest 19% of fruits weigh more than 753grams.

Answer:

Negation: The product of any irrational number and any nonzero rational number is not irrational.

Step-by-step explanation:

(a)

Given statement: The product of any irrational number and any nonzero rational number is irrational.

Negation: The product of any irrational number and any nonzero rational number is not irrational.

(b)

Let if possible the product of any irrational number and any nonzero rational number is not irrational that is rational.

Let [tex]x[/tex] be an irrational number and [tex]y\neq 0[/tex] be a rational number.

[tex]xy=z[/tex] where [tex]z[/tex] is rational.

So,

[tex]xy=z\\x=\frac{z}{y}[/tex]

As quotient of two rational numbers is also rational, [tex]x[/tex] must be rational which is a contradiction to the fact that [tex]x[/tex] is irrational.

Answer:

[tex]\displaystyle \frac{\sqrt{2}}{x^2}[/tex]

Step-by-step explanation:

Dividing Radicals

Given the division of radicals:

[tex]\displaystyle \frac{\sqrt{Z}}{\sqrt{Y}}[/tex]

We can join both arguments of the radicals into one simple radical as follows:

[tex]\displaystyle \sqrt{\frac{Z}{Y}}[/tex]

We are given the expression:

[tex]\displaystyle 2\frac{\sqrt{24}}{\sqrt{48x^4}}[/tex]

Joining them in a single radical:

[tex]\displaystyle 2\frac{\sqrt{24}}{\sqrt{48x^4}}=2\sqrt{\frac{24}{48x^4}}[/tex]

Simplifying the fraction:

[tex]\displaystyle 2\sqrt{\frac{24}{48x^4}}=2\sqrt{\frac{1}{2x^4}}[/tex]

Multiplying by 2 in numerator and denominator:

[tex]\displaystyle 2\sqrt{\frac{1}{2x^4}}=2\sqrt{\frac{2}{4x^4}}[/tex]

The denominator is a perfect square:

[tex]\displaystyle 2\sqrt{\frac{2}{4x^4}}=2\frac{\sqrt{2}}{2x^2}[/tex]

Simplifying by 2:

[tex]\boxed{\displaystyle \frac{\sqrt{2}}{x^2}}[/tex]

You would need 3/4 cups of water.

The measurement of ∠KNL   is 102°

First, you must set up an equation to find x.

[tex]5x+2=[3(x+14)[/tex]

Then, you must simplify both sides of the equation.

[tex]5x+2=3x+42[/tex]

Next, subtract 3x on both sides.

[tex]2x+2=42[/tex]

Then, subtract 2 on each side.

[tex]2x=40[/tex]

Next, divide 2 on each side.

[tex]x=20[/tex]

Now that we have the value of x, we can substitute it in for angle KNL.

[tex][3(20+14)][/tex]

[tex][3(34)][/tex]

[tex]102[/tex]

[tex]102[/tex]°

Answer:

-7

Step-by-step explanation:

(-12)-(-5)

negative and negative make a positive

-12+5

= -7

Answer:

-7

Step-by-step explanation:

The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.

Here,

Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:

f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57

Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:

f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57

Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).

Mathematically, we want to find P(Y > X + 0.11).

Let's set up the integral to calculate this probability:

P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy

We integrate with respect to x first and then with respect to y:

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy

P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy

P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57

P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]

P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]

P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]

P(Y > X + 0.11) = 3.0805 * [0.84895]

P(Y > X + 0.11) ≈ 2.6092

Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.

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Answer:

4, 2.75, 1.5, 0.25, –1, . . .

Step-by-step explanation:

edge2020

Answer:

6

Step-by-step explanation:

I solved the equation, but you can't simplify 6.

Answer:

yes the last person is correct

Step-by-step explanation:

Answer:

NOM and POR

(so so sorry if it's wrong, I tried my best to help you but I had to look up an image of a angle like that but i hope you have a wonderful day, sorry again if i am wrong, i hope i help in a way, in i did not, sorry)

Answer:

im just here for the points sorry

Step-by-step explanation:

Answer/Step-by-step explanation:

Part A: In the table given above, every input value has exactly one output value. No input value gives two different output value. Therefore, the data in the table represents a function.

Part B: in the table given, when x = 4, y = 9. That is, f(4) = 9.

Given the relation f(x) = 2x - 8, to find what value it would give us, when x = 4, substitute x = 4 into the relation.

f(4) = 2(4) - 8 = 8 - 8

f(4) = 0

Therefore, the relation in the table has a greater value when x = 4.

Part C: using, f(x) = 2x - 8, when f(x) = 34, value of x would be calculated as shown below:

34 = 2x - 8

Add 8 to both sides

34 + 8 = 2x

42 = 2x

Divide both sides by 2

42/2 = x

21 = x

x = 21

Answer: 54

Step-by-step explanation:

Answer:

i will

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Given data:

Area of smaller flower bed = 25/4

Area of bigger flower bed = 75/4.

Solution:

75/4 = 25/4

Divide both sides 5

15/4 = 5/4

= 15/4 / 5/4

= 15/4 / 4/5

= 3

Answer:

The larger flower bed has 3 square ft of space for every square foot of the smaller flower bed

Step-by-step explanation:

In other words in this question, we are asked to calculate how many of the smaller flower bed is contained in the larger one.

Mathematically, that would be 25/4 squares ft divided by 75/4 squared feet

Thus will be 75/4 divided by 25/4

Hence 75/4 * 4/25 = 3

Answer:

Question 19: 45 Question 20: 130

Step-by-step explanation:

Answer:

45 and 130

Step-by-step explanation:

Convert your percentage into decimals first then multiply.

150% is the same as 1.5

40% is the same as 0.4

So you multiply 1.5 times 30 and get 45

multiply 0.4 times 325 and get 130

Answer:

6

Step-by-step explanation:

51 divided by 8.5

Answer:

a = -6

Cov (2X+Y, 3X-4Z) = 30

Step-by-step explanation:

Key points:

Cov(2X, -3Y+2) = a⋅Cov (X,Y)

Cov (2X, -3Y) + Cov (2X, 2) = a⋅Cov (X,Y)

(2)⋅(-3)⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

-6⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

⇒ a = -6.

(c)

Suppose that X, Y, and Z are independent, with a common variance of 5, i.e. V (X) = V (Y) = V (Z) = 5

Cov (2X+Y, 3X-4Z) = Cov (2X, 3X) + Cov (2X, -4Z) + Cov (Y, 3X) + Cov (Y, -4Z)

                               = 6⋅Cov (X, X) - 8⋅Cov (X, Z) + 3⋅Cov (Y, X) - 4⋅Cov (Y, Z)

                               = (6 × 5) - 0 + 0 - 0

                               = 30

Thus, the value of Cov (2X+Y, 3X-4Z) is 30.

The value of a = -6. And, Cov (2X+Y, 3X-4Z) = 30.

Since

Cov (aX, bY) = a·b·Cov (X, Y)

Cov (X, X) = V (X)

Cov (X, a) = 0

In the case when X and Y are independent so Cov (X, Y) = 0.

Now

Cov(2X, -3Y+2) = a⋅Cov (X,Y)

Cov (2X, -3Y) + Cov (2X, 2) = a⋅Cov (X,Y)

(2)⋅(-3)⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

-6⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

a = -6.

(c)

here

Suppose that X, Y, and Z are independent, with a common variance of 5, i.e.

V (X) = V (Y) = V (Z) = 5

So,

Cov (2X+Y, 3X-4Z) = Cov (2X, 3X) + Cov (2X, -4Z) + Cov (Y, 3X) + Cov (Y, -4Z)

= 6⋅Cov (X, X) - 8⋅Cov (X, Z) + 3⋅Cov (Y, X) - 4⋅Cov (Y, Z)

= (6 × 5) - 0 + 0 - 0

= 30

Thus, the value of Cov (2X+Y, 3X-4Z) is 30.

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