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Aleks04 [339]
3 years ago
13

Mr. Drew wants to build a square sandbox with an area of 289 square feet. What is the total length of wood Mr. Drew needs to mak

e the sides of the​ sandbox?
Mathematics
1 answer:
alisha [4.7K]3 years ago
5 0

Answer:

  68 feet

Step-by-step explanation:

A square with area 289 ft² has sides √289 = 17 ft long. There are 4 of them so the perimeter is 4×17 ft = 68 feet.

Mr. Drew needs 68 feet of wood for the sides of the sandbox.

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Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB?
insens350 [35]

Answer:

Option C) y + 4 = x

Step-by-step explanation:

We are given the following information in the question:

Line AB goes through the points A (0, –4) and B (6, 2).

We can use the two-point form of equation of straight line.

The equation of line is given by:

(y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)

where, (x_1,y_1), (x_2.y_2) is the point through which the line passes.

The equation of line is:

(y+4) = \displaystyle\frac{2+4}{6-0}(x-0)\\\\(y+4)= x\\y = x-4

Thus, the equation of line AB is given by Option C) y + 4 = x

7 0
3 years ago
Read 2 more answers
For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.
nordsb [41]

Answer:

<h3>For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.</h3>

By De morgan's law

(A\cap B)^{c}=A^{c}\cup B^{c}\\\\P((A\cap B)^{c})=P(A^{c}\cup B^{c})\leq P(A^{c})+P(B^{c}) \\\\1-P(A\cap B)\leq  P(A^{c})+P(B^{c}) \\\\1-P(A\cap B)\leq  1-P(A)+1-P(B)\\\\-P(A\cap B)\leq  1-P(A)-P(B)\\\\P(A\cap B)\geq P(A)+P(B)-1

which is Bonferroni’s inequality

<h3>Result 1: P (Ac) = 1 − P(A)</h3>

Proof

If S is universal set then

A\cup A^{c}=S\\\\P(A\cup A^{c})=P(S)\\\\P(A)+P(A^{c})=1\\\\P(A^{c})=1-P(A)

<h3>Result 2 : For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B) and P(A) ≥ P(B)</h3>

Proof:

If S is a universal set then:

A\cup(B\cap A^{c})=(A\cup B) \cap (A\cup A^{c})\\=(A\cup B) \cap S\\A\cup(B\cap A^{c})=(A\cup B)

Which show A∪B can be expressed as union of two disjoint sets.

If A and (B∩Ac) are two disjoint sets then

P(A\cup B) =P(A) + P(B\cap A^{c})---(1)\\

B can be  expressed as:

B=B\cap(A\cup A^{c})\\

If B is intersection of two disjoint sets then

P(B)=P(B\cap(A)+P(B\cup A^{c})\\P(B\cup A^{c}=P(B)-P(B\cap A)

Then (1) becomes

P(A\cup B) =P(A) +P(B)-P(A\cap B)\\

<h3>Result 3: For any two events A and B, P(A) = P(A ∩ B) + P (A ∩ Bc)</h3>

Proof:

If A and B are two disjoint sets then

A=A\cap(B\cup B^{c})\\A=(A\cap B) \cup (A\cap B^{c})\\P(A)=P(A\cap B) + P(A\cap B^{c})\\

<h3>Result 4: If B ⊂ A, then A∩B = B. Therefore P (A)−P (B) = P (A ∩ Bc) </h3>

Proof:

If B is subset of A then all elements of B lie in A so A ∩ B =B

A =(A \cap B)\cup (A\cap B^{c}) = B \cup ( A\cap B^{c})

where A and A ∩ Bc  are disjoint.

P(A)=P(B\cup ( A\cap B^{c}))\\\\P(A)=P(B)+P( A\cap B^{c})

From axiom P(E)≥0

P( A\cap B^{c})\geq 0\\\\P(A)-P(B)=P( A\cap B^{c})\\P(A)=P(B)+P(A\cap B^{c})\geq P(B)

Therefore,

P(A)≥P(B)

8 0
3 years ago
Expand the following: 6(x – 4y)
Lemur [1.5K]

Answer:

6(x-4y) = 6x - 24y

Step-by-step explanation:

Here, we want to expand the given expression

We can do this using the distributive approach

We have this as;

(6 * x) - (6 * 4y)

= 6x - 24y

3 0
3 years ago
To finance her community college​ education, Sarah takes out a loan for ​$4300. After a year Sarah decides to pay off the​ inter
VashaNatasha [74]

Answer:

301

Step-by-step explanation:

4300*.07=301

8 0
3 years ago
Read 2 more answers
Joe and grace are baking cookies.they need a total of 2 cups of sugar for the recipe. Joe has 11/10 cups of sugar and grace has3
labwork [276]
No, Joe and Grace don’t have enough together because 11/10 is only 1.1 and 3/4 is .75 and u add that together u get 1.85 which is less 2.

Grace needs 12 cups of sugar to make the cookies because 1 cups of sugar makes 6 cookies and each person is getting 3 that’s only enough for 2 people , so multiple every by 12 to get 24 people, 12 cups of sugar, and 72 cookies .
6 0
3 years ago
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