The surface area of an open-top box with length L, width W, and height H can be found using the
formula:
A = 2LH + 2WH + LW
Find the surface area of an open-top box with length 9 cm, width 6 cm, and height 4 cm.

Answer:

the unit rate for eggs per hen = 60/10 = 6

1 week 1 hen will lay 6 eggs

Step-by-step explanation:

A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

Answer:

its proportionality

Step-by-step explanation:

Answer:

We know that 37% of all college students were enrolled part time. If 5.9 millions college students were enrolled part time that year, we can use this information to find the total number of college students.

We know that the part-time enrollment percentage is represented by the ratio:

part-time students / total students = 37%

We can set up the equation:

5.9 million / x = 37/100

Where x represents the total number of students

To find the total number of students, we can cross-multiply and divide:

5.9 million * 100 = 37 * x

x = 5.9 million * 100 / 37

The total number of college students that year was:

x = 16,081,081

So the total number of college students that year was 16,081,081

I think its Y = x+ 3

Answer:

I think around 43.3%

Step-by-step explanation:

215-150

150

65

150          x 100

=43.3333333333333

Answer:

I think around 43.3%

Step-by-step explanation:

Given: The equation of a parabola below

To Determine: The vertex, focus, and directrix of the parabola

Let us re-write the given equation

The general equation of the parabola with vertex (h, k) is of this form

Let us compare the general equation with the given equation

Therefore

Hence,

Vertex = (1, -4)

Focus = (1, -1)

Directrix, y = -7

Answer:

Plan B: 5n > 8

Plan A: 3n + 8 < 5n

Answer:

x=10

Step-by-step explanation:

Answer:

x = - 5/3

Step-by-step explanation:

Calculate the product

4x/5 = 2x + 4/2

Reduce the faction with 2

4x/5 = 2x + 2

Multiply both sides of the equation by 5

4x = 10x + 10

Move variable to the left-hand side and change its sign

4x - 10x = 10

Collect like terms

-6x = 10

Divide both sides of the equation by -6

x = - 5/3

Solution

x = -5/3

Alternate form

x = -1 2/3, x = -1.6

Step-by-step explanation:

\(M= ( b, d, h) \\ F= (d, e, j) \\ M \: u \: F \: = \: ( b\: , d,h,e,j \: )\)

Union of two set is the joining together o the two sets

\(M n F. = (d \: )\\ \)

Intersection of a set are the values which are common to all the given sets.

The union of M and F is MUF = {b, d, e, h, j}

The intersection of M and F is MnF = {d}

Given the following sets:

The union of both sets is the combination of the elements in both sets. Hence;

MUF = {b, d, e, h, j}

The intersection of both sets is the element(s) common to both sets. Therefore;

MuF = {d}

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Answer:

7

Step-by-step explanation:

а>12-6

The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units

The radius of the base = 4 units

The length of the side of the square = 2x

The area of the square = a^2

Where a is side of the square

The area of the square = (2x)^2

= 4x^2

The equation of the circle is

x^2 + y^2 = 16

x^2 = 16 - y^2

The area = 4(16 - y^2 )

= 64 - 4y^2

The volume of the square

V = \(\int\limits^a_b {A(y)} \, dy\)

= \(\int\limits^4_0 {64-4y^{2} } \, dy\)

= 64×4 - 4×(4^3/3)

= 256 - 256/3

= 512/3 cubic units

Therefore, the volume of the solid is 512/3 cubic units

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The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).

The length of the  rectangle is:

l = 3.5 - (-3.5)

l = 3.5 + 3.5

l = 7

The width of the rectangle is:

w = 3-(-3)

w = 3 + 3

w = 6

The perimeter of the rectangle is given by:

P = 2 (l +w)

P = 2(7 + 6)

P = 26

The area of the rectangle is:
A = l × w

A = 7 × 6

A = 42

Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

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Answer:

Two lines are perpendicular if the product of their slopes equals -1.

In general form, this means that you reverse the coefficients of x and y and negate one of the two.

So the general form of this perpendicular line becomes: 12x + 3y + C = 0, or simplified: 4x + y + C’ = 0.

Now fill in the desired point to find C’: 4*(-2)+5+C’=0 so C’= 3.

The general form of the line becomes 4x + y + 3 = 0

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

Answer:

1/12

THIS DESERVES BRAINLISTTT

Step-by-step explanation:

There are 12 possible outcomes, 6 for the die for each of the 2 for the coin. Only one comprises a 5 and a tail so the probability, assuming a fair coin and die, is 1/12.

A die has 6 sides. A coin has two.

The probability of rolling a 5 on the die is 1/6.

The probability of getting tails is 1/2.

To get the combined probability, we must multiply the two together. This gives us a total probability of 1/12.

The probability of rolling a 5 and getting tails is 1/12.

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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Answer:

-34/100 is the fraction in simplest form

Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

\(w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\\)

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

--------------------

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

--------------------

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

x^3 - 1 = (x-1)(x^2 + x + 1)

--------------------

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

Answer:

d. At least 75%

Step-by-step explanation:

Since nothing is known about the distribution, we use the Chebyshev Theorem.

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by \(100(1 - \frac{1}{k^{2}})\).

In this problem, we have that:

Mean = 80, standard deviation = 5.

What percentage of test-takers scored better than the trainee who scored 70?

70 = 80 - 2*5

So 70 is two standard deviations below the mean.

Due to the Chebyshev Theorem, we know that at least 75% of the measures are within 2 standard deviations of the mean, between 70 and 90, which means that this percentage is at least 75%, and the correct answer is given by option d.

Answer:

The answer is 10,000

Step-by-step explanation:

So the answer is not there so it is none of the above

Answer:

a. P(A∪B)=0.85

b. P(A∩C)=0

c. P(A/B)=0

d. P(B∪C)= 0.70

Step-by-step explanation:

Events are said to be mutually exclusive when both cannot occur simultaneously in the result of experimentation. They are also known as incompatible events.

Being P(A)=0.30,  P(B)= 0.55 and P(C)= 0.15

Let A and B be any two events, P (A) and P (B) the probability of occurrence of events A or B, is known as the probability of union [denoted as P (A U B)]:

P(A∪B)=P(A) + P(B) - P(A∩B)

Mutually exclusive events are results of an event that cannot occur at the same time. So:

P(A∩B)=0 That is, there is no chance that both events will occur.

So: P(A∪B)=P(A) + P(B)

In this case: P(A∪B)=P(A) + P(B)= 0.30 + 0.55 → P(A∪B)=0.85

As mentioned, if two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then: P(A∩C)=0

The probability that event A will occur if event B has occurred is called the conditional probability and is defined:

P(A/B)=P(A∩B)÷P(B) being P(B)≠0

Since A and B are mutually exclusive, P (A∩B) = 0. So:

P(A/B)=P(A∩B)÷P(B)=0÷0.55 → P(A/B)=0

Finally, P(B∪C)=P(B) + P(C) - P(B∩C)

Since A and B are mutually exclusive, P (B∩C) = 0. So:

P(B∪C)=P(B) + P(C)= 0.55 + 0.15 → P(B∪C)= 0.70

Answer:

3 x 21.50= 64.50

3 x 7.96= 23.88

3 x 14.99= 44.97

Altogether equals  133.35

400-133.35= 266.65

Answer:

3 x 21.50= 64.50

3 x 7.96= 23.88

3 x 14.99= 44.97

Altogether equals  133.35

400-133.35= 266.65

The limits lim x→ −4 f(x) is 5

The method is substitution method

From the question, we have the following parameters that can be used in our computation:

−5x − 15 ≤ f(x) ≤ x² + 3x + 1

The limits is given as

lim x→ −4 f(x)

By direct substitution, we have

−5(-4) − 15 ≤ f(x) ≤ (-4)² + 3(-4) + 1

Evaluate the exponents and the products

20 − 15 ≤ f(x) ≤ 16 - 12 + 1

Evaluate the difference

5 ≤ f(x) ≤ 5

This means that

f(x) = 5

So, we have

lim x→ −4 f(x) = 5

The method used is the direct substitution method

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Answer:

A. 2/3

Opposite Sides of a Parallelogram

The two pairs of sides in a parallelogram are parallel to each other.

Parallel lines have the same slope.

The slope of the opposite sides of a parallelogram are congruent (equal in measure).

Given:

Slope of PQ = 2/3

Slope of QR = -1/2

For PQRS to be a parallelogram, the slope of SR must be same as the slope of PQ.

This implies that: Slope of SR = Slope of PQ = 2/3.

Therefore, based on the properties of a parallelogram, the slope of SR for PQRS to be a parallelogram would be: 2/3.

Answer:

Andrew 50

todd 30

Step-by-step explanation:

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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Answer:

C 1.1 mph

Step-by-step explanation:

Divide 2 3/4 by 2 1/2 to get 1.1

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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