You are building a 3-foottall dresser. You want the volume to be 42 cubic feet.a. What should the area of the base be?b. Give a possible length & width of the base.c. Make a hand drawn sketch of the dresser with the dimensions you chose.

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer:

i think its c in my opionion not sure tho

Answer:

D. 13/36

Step-by-step explanation:

Answer:

im an expert

Step-by-step explanation:

Best approximation of the mass of an African elephant is 8 ×10³kg

In physics, mass is a fundamental property of matter that measures the amount of substance in an object. It is a scalar quantity that describes an object's resistance to acceleration when a force is applied. Mass is usually measured in kilograms (kg) and can be calculated by dividing an object's weight by the acceleration due to gravity.

Given;

Mass of elephant=8139kg

Dividing the mass by 1000 and multiplying it by 10³, we get

Mass of elephant=8.139 ×10³kg

Estimating the mass of elephant, we get

Mass of elephant=8 ×10³kg

hence, best approximation of the mass of an African elephant is 8 ×10³kg.

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the car is approximately 22.4 meters away from the tower.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

we can write:

tan(55 degrees) = 32 / d

To solve for "d", we can rearrange the equation:

d = 32 / tan(55 degrees)

Using a calculator, we can evaluate the tangent of 55 degrees:

tan(55 degrees) = 1.428

d = 22.4 meters

Therefore, the car is approximately 22.4 meters away from the tower.

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:863040

Step-by-step explanation:

Rewrite 32! as 32 x 31 x 30 x 29 x 28!

then cancel common factor of 28!

multiply 32 x 31 x 30 x 29

863040

(a) 58 = 2(w + 5 + w)

(b)  I. The width of the rectangle is 12 cm.

II. The length of the rectangle is 17 cm.

III. The area of the rectangle is 204 cm².

Let's solve the problem step by step:

(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:

Perimeter = 2(length + width)

Substituting the values, we have:

58 = 2(w + 5 + w)

Simplifying the equation, we get:

58 = 2(2w + 5)

(b) Now let's solve for the width and length of the rectangle:

I. To find the width, we solve the equation:

58 = 2(2w + 5)

Dividing both sides by 2, we get:

29 = 2w + 5

Subtracting 5 from both sides, we have:

24 = 2w

Dividing both sides by 2, we find:

w = 12 cm

Therefore, the width of the rectangle is 12 cm.

II. To find the length, we substitute the value of the width into the equation:

Length = w + 5 = 12 + 5 = 17 cm

Therefore, the length of the rectangle is 17 cm.

III. The area of the rectangle can be calculated using the formula:

Area = length × width

Substituting the values, we have:

Area = 17 cm × 12 cm = 204 cm²

Therefore, the area of the rectangle is 204 cm².

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We are given the equations of four lines and we are asked to determine which ones are parallel. To do that we need to remember that two lines are parallel if they have the same slope. To determine the slope the line equations must be written in the form:

Where "m" is the slope.

The first equation is:

Therefore, the slope of the first equation is:

The second equation is:

We need to rewrite the equation to the wished form in order to know the slope, therefore we need to solve for "y". We do that first by applying the distributive property on the right sides:

Now we add 7 to both sides:

Therefore, the slope of this line is:

For the third equation we have:

The slope of this equation is:

For the fourth equation we have:

Now we solve for "y", first we subtract "x" from both sides:

Now we multiply both sides by "3/4":

Therefore, the slope of the fourth line is:

Since we have:

Then lines 1 and 4 are parallel.

Answer:

GCF (10,70) = 10

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

8

Step-by-step explanation:

You have to set up a proportion for this!

Because ABC and PAQ are similar triangles (same angles and PQ || BC), you can assume that all the equivalent sides are proportional!

If you solve the proportion for x:

\(\frac{x}{40} =\frac{7}{35}\)

x = 8

Answer:

Slope of line g = \(1\frac{1}{3}\)

Step-by-step explanation:

* Mathematics rule: If two lines are perpendicular to each other, then the product of their slopes is equal to -1 .

∴ \(-\frac{3}{4}\) × slope of line g = -1

Slope of line g = -1 ÷ \(-\frac{3}{4}\) = 4/3 = \(1\frac{1}{3}\)

Answer:

\(f(x) = \dfrac14(x + 1)^2(x + 3)(x -2)( x - 3)\)

Tia is correct

Step-by-step explanation:

From inspection of the graph, we can say that the leading coefficient of the function is positive as:

\(f(x) \rightarrow - \infty, \textsf { as } \ x \rightarrow - \infty\\f(x) \rightarrow +\infty, \textsf { as } \ x \rightarrow + \infty\)

From inspection of the graph, we can see that the curve intercepts the x-axis at x = -3, x = 2, x = 3

As the curve touches the x-axis at (-1, 0) then this means that the root x = -1 has multiplicity 2

Therefore, \(f(x) = a(x + 1)^2(x + 3)(x -2)( x - 3)\) where \(a\) is some positive constant.

If we multiply the constants, we can determine the y-intercept:

y-intercept = a x 1² x 3 x -2 x -3 = 18a

Therefore, the y-intercept is at y = 18a

From inspection of the graph, the y-intercept is at y = 4.5

So to determine the value of a:  18a = 4.5 ⇒ a = 1/4

Therefore, the fully factored form of the equation is:

\(f(x) = \dfrac14(x + 1)^2(x + 3)(x -2)( x - 3)\)

Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

16.67

Step-by-step explanation:

2/12

Answer:

33.3%

Step-by-step explanation:

out of all 12 months, there are 3 months with J, January, June, July

100/3=33%

Answer:

right scalene

Step-by-step explanation:

Since all three sides have different lengths , this is a scalene triangle

(isosceles means two sides have the same lengths and equilateral means all three sides have the same length)

We have a right angle indicated by the box in the corner

Answer:

Step-by-step explanation:

Total number of students:

A.

B.

C.

D.

Answer:

5

Step-by-step explanation:

7.25y = 36.25. (after adding 15 on both sides)

Then divide by 7.25 and it should come out to 5. Hope this helps! :D

We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:

GiveN:

As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.

Then,

We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:

\(3x + x + x + 12 = 32\)

Solving it further,

\(5x + 12 = 32\)

Subtracting 12 from both sides,

\(5x + 12 - 12 = 32 - 12\)

\(5x = 20\)

Dividing 5 from both sides,

\( \frac{5x}{5} = \frac{20}{5} \)

\(x = 4\)

Then,

And we are done with the answer !!

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The plant receives a total of 1.08 grams of magnesium in 20 weeks.It's important to note that when performing unit conversions, it's crucial to keep track of the units and ensure that they cancel out correctly. In this case, we converted milligrams to grams and then multiplied by the number of weeks to find the total amount of magnesium in grams.

To calculate the total amount of magnesium the plant receives in 20 weeks, we need to convert the milligrams to grams and then multiply it by the number of weeks.

Given that the plant food contains 54 milligrams of magnesium, we need to convert it to grams. Since there are 1,000 milligrams in 1 gram, we divide 54 by 1,000 to convert milligrams to grams:

54 milligrams ÷ 1,000 = 0.054 grams

Now, we multiply the amount of magnesium received per week (0.054 grams) by the number of weeks (20) to find the total amount of magnesium received in 20 weeks:

0.054 grams/week × 20 weeks = 1.08 grams.

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In linear algebra, a symmetric matrix is a square matrix whose transpose remains unchanged. This indicates that a symmetric matrix is one whose transpose is the same as the matrix itself.

A = 3.75 -1.25 0.25 L = 3.75 -1.75 0.25 -1.75 3.75 -1.25 -1.75 0.25 -1.25 3.75 Now, employing Eigen Vectors, compute the normalized values of V1 as follows: length of V1 = (1)2 + (1)2 + (122 + 422) = 2 Bame as 2 = 3 = 4 Bo the matrix fort= 1 V4 0.5 0.5 0.5 0.5 0.5  -0.5, 0.5, 0.5, 0.5 of the Eigen Values of the Given Matrix A 7,4,3,1 1 Now Rank-2-Approximation GV; & the Bingular Value Mean VT + 62: V2 V₂T

0.50 0.5 0.5 7 [o. 0.50 0.5 0.5 0.50.5 -0.5 +4 0.5-0.5-0.5]

7

50.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 10.25 0.25 0.250.25

0.25 0.25 0.25 0.25

144

16.25 0.25 -0.25 -0.25 0.25 0.25 -0.25 -0.25 10.25 -0.25 0.25 0.25 1-0.25 -0.25 0.25 0.25

= 1.75 1.75 1.75 1.75- 1.75 2.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75

1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 1 1 1 ++

2.75

-0.75 -0.75 2.75 2.75 -0.75 -0.75 2.75 2.75 2.75 -0.75 -0.75

2.75 2.75 -0.75 -0.75.

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Answer:

Let x be the number of employees

50x

Step-by-step explanation:

Answer:

1/20

Step-by-step explanation:

1/5 chance she will wear the blue shirt on the first day and 1/4 chance she will wear a grey shirt on the second day.

1/5 X 1/4 = 1/20

Answer:

i got 1/20 as my answer

The whole number that can be substituted for z is 1.

To order these numbers from least to greatest, we need to first find a value for x that makes the expressions comparable.

1/x can be rewritten as 0.01/x

80% can be written as 0.8

So, the list becomes:

0.01/x, x/3, 0.8

To compare 0.01/x and x/3, we can cross-multiply and simplify:

0.01/x < x/3

0.01*3 < x^2

0.03 < x^2

x > sqrt(0.03)

Since x has to be a whole number, the smallest possible value for x is 1.

So, substituting x = 1, the list becomes:

0.01, 1/3, 0.8

Ordering these from least to greatest, we get:

0.01, 0.8, 1/3

Therefore, the whole number that can be substituted for z is 1.

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Answer:

41

Step-by-step explanation:

we can get this answer because:

3(3)=9

4(8)=32

and u add 32 and 9 together and get 41