3. Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value. You can find it if you know the number of trials and the probability of success for an individual trial. Use the formula μx = np to find the expected value.

Answer:

Yes

Step-by-step explanation:

no. of squares able to fit length=800/40=20

no. of squares able to fit breadth= 120/40=3

total no. of squares able to fit entire rectangle=20×3=60

cost of squares=60×4.50=270

Yes, he has enough money to buy all the paving stones.

The p-value is 0.0062  and we reject the null hypothesis

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

n = 200, pi = 0.28; n2 = 300, p2 = 0.18

The p value is calculated as

Z = (p1 - p2) - (d0 /√(p * (1 - p) * (1/n1 + 1/n2)))

Where

d0 = 0.28 - 0.18 = 0.10.

So, we have

Z = (0.28 - 0.18) - (0.10 / √(0.23 * (1 - 0.23) * (1/200 + 1/300)))

Evaluate

Z = -2.50

Uisng the z-score table, we have

p = 0.0062

We reject the null hypothesis that the population proportions are equal

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Answer:

y = 36

Step-by-step explanation:

Because the problem says y is proportional to the square root of x, we can assume that it is directly proportional.

The general formula for direct proportionality is

[tex]y=kx[/tex], where k is the constant of proportionality.

Taking into account the square root of x, we can use the following formula to find k by plugging in x and y:

[tex]y=k\sqrt{x}\\ 21=k\sqrt{49}\\ 21=7k\\3=k[/tex]

Since we found k, we can now use this value and the x we're given for the second part of the problem to find y:

[tex]y=3\sqrt{x} \\y=3\sqrt{144}\\ y=3*12\\y=36[/tex]

Answer:

Step-by-step explanation:

5+2/3-3-2/3

5+93439535309573092

The values of the composite functions, obtained by evaluating the functions at a specified x value input are presented as follows;

1. f(h(-3)) = 14

2. g(h(-9)) = 110

3. f(g(x)) = 9 - x² - x

A composite funtion is a function that is applied to the output of another function.

The functions are; F(x) = 9 - x, g(x) = x² + x, h(x) = x - 2

The composite functions, which are functions that have a function as an input, aere evaluated as follows

1. h(-3) = (-3) - 2 = -5

f(h(-3)) = f(-5), therefore;

f(-5) = 9 - (-5) = 9 + 5 = 14

f(-5) = 14

f(h(-3)) = 14

2. h(-9) = -9 - 2 = -11

g(h(-9)) = g(-11)

g(-11) = (-11)² + (-11) = 121 - 11 = 110

g(-11) = 110

Therefore; g(h(-9)) = g(-11) = 110

g(h(-9)) = 110

3. g(x) = x² + x

f(x) = 9 - x

Therefore, f(g(x)) = f(x² + x) = 9 - (x² + x) = 9 - x² - x

f(g(x)) = 9 - x² - x

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Therefore, the solutions to the equation are (0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), and (-3, 9).

In arithmetic equations, the exact symbol (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.

Here,

We can plug in some arbitrary values for y to find the corresponding values of x:

y x

0 0

1 1

-1 1

2 4

-2 4

3 9

-3 9

Therefore, the solutions to the equation are (0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), and (-3, 9).

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Therefore , the solution of the given problem of equation comes out to be value of b = 0 , as it is parallel to y axis.

The identical symbol (=) is used in arithmetic equations to signify the equality of two statements. It is shown that it is possible to evaluate various numerical factors using mathematical techniques, which have served as manifestations of reality. In actuality, even though the solution is y + 6 = 12, the equal sign divides the figure 12 into two distinct parts. How many characters are also present along either end of such a character can be calculated. Conflicting sign readings are common.

Here,

Given :

=> equation  y = 15x + b

Comparing to y = mx+ b

Where b is said to be intercept.

So , value of b = 0 , as it is parallel to y axis.

Therefore , the solution of the given problem of equation comes out to be value of b = 0 , as it is parallel to y axis.

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Answer: A) T = 63 - 3.8A (where T is the temperature in °F, A is the altitude in thousands of feet)

(B) To find the altitude when the temperature is 9.8°F, we can substitute 9.8 for T and solve for A:

9.8 = 63 - 3.8A

3.8A = 63 - 9.8

3.8A = 53.2

A = 14

Step-by-step explanation:

a. (f + g) (0) = 0

b. (f/g) (3) = 2/3

This can be solved by function method.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

(a) (f + g) (0) = .........

g(0) = 0, f(0) = 0

(f + g) (0) = f(0) + g(0)

(f + g) (0) = 0 + 0

(f + g) (0) = 0

(b)

(f/g) (3) = ............

f(3) = 2, g(1/3) = 1

(f/g) (3) = f(3) × g(1/3)

(f/g) (3) = 2 × (1/3)

(f/g) (3) = 2/3

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Answer:

I'm sorry but your question is not clear. Can you please provide more context or clarify what you are asking?

The linear Equation in the form of p(n)=mn+b is p(n) = -0.005n + 999.85.

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

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $20 .

p = price

n = number of shirts

m = slope of the line   (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

so, the slope is

= (20- 30)/ (3000 - 1000)

= -10 / 2000

= -0.005

and, the equation is

p - 1000 = -0.005 ( n- 30)

p- 1000 = -0.005n + 0.15

p(n) = -0.005n + 999.85

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Answer:

Step-by-step explanation:

You need to order 2 36" bulbs and 4 24" bulbs in order to keep twenty of each size in stock.

The stock is a type of security that represents ownership in a company. It is a financial asset that can be traded, and the price of the stock is determined by the supply and demand of the market. When a company issues stock, the stockholders gain a share of the company’s ownership.

36" bulbs:

First storage closet: 5 boxes with 2 in each box = 10

Second storage closet: 3 boxes with 4 in each box = 12

Total = 10 + 12 = 22

Need to order = 20 - 22 = 2

24" bulbs:

First storage closet: 4 boxes with 4 in each box = 16

Total = 16

Need to order = 20 - 16 = 4  

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The height of the top of the tree from the ground is h = a * b / (a / b) = a * b

Let's call the height of the tree "h". Then, using trigonometry, we can write two equations to describe the two angles of elevation:

tan(a) = h / a

tan(ß) = h / b

Dividing these two equations, we get:

tan(a) / tan(ß) = h / a * b

Since tan(a) / tan(ß) = a / b, we can substitute this and simplify:

h = a * b / (a / b) = a * b

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PART A) The height of the base is 10cm

PART B) Aproximate amount of cardboard to make the candy box is 860cm. You add all of the totals from each side to get the grand total of 860cm.

In this configuration, the number of circles that can be packed is already at its maximum of 10,000.

What is Equilateral triangle?

All sides of an equilateral triangle are the same length. That is, all of the triangle's angles will be congruent.

It is not possible to add more circles in this configuration because the centers of the tangent circles already form an equilateral triangle, which is the most efficient way to pack circles.

In this configuration, the number of circles that can be packed is already at its maximum of 10,000.

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By adding the two given fractions we can see that Josiah ate 17/24 of his orange.

We know that first, Josiah ate 3/8 of his orange.

Then at this point, the remaining amount is 5/8 of the orange.

Then he ates 1/3 of the orange (the total orange, not the remaining amount)

Then the total fraction of the orange that he ate is:

3/8 + 1/3

Finding a common denominator we will get:

9/24 + 8/24 = 17/24

We conclude that Josiah ate 17/24 of his orange.

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For the given relation, the domain is  [0,70] and the range is   [0,500].

What is meant by relation?

In mathematics, a relation describes the connection between two distinct sets of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their items. The relationship between two or more sets of values is called a relation.

Assume that there are two sets of ordered pairs, x and y. If set x and set y are related, then the values of set x are referred to as the domain while the values of set y are referred to as the range.

W can also determine domain and range from graphs.

Also, note that the given graph is continuous so the domain and range values all all values in an interval.

The domain represents all the input values which are on the x-axis.

From the given graph, we can see that the domain values are in the interval  [0,70].

The range represents all output values which are on the y-axis.

From the graph, the range values are in the interval [0,500].

Therefore for the given relation, the domain is  [0,70] and the range is   [0,500].

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Answer:true

61.5 km = 61.5 x 1000 =61.500 m

The value of m∠C in  the triangle  is 42.77°

The sine rule is a mathematical formula used in trigonometry to find the length of a side or the size of an angle in a triangle when two sides and one of the angles opposite to those sides are known. It states that:

a/sin A = b/sin B = c/sin C

Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite to those sides.

m∠A = 47°, a = 28, c = 26.

a/sin A = c/sin C

28/sin 47° = 26/sin C

sin C = (26 sin 47°)/28

sin C = 0.6791

C = arcsin(0.6791)

C = 42.77°

Thus, m∠C = 42.77°

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Answer:

The equation to calculate the balance in the account after "x" months would be: y = 100 + 25x

And after 6 months, Alexa would have $250 in his retirement account, and after 12 months, he would have $400 in his account.

Step-by-step explanation:

Let's call the balance in Alexa's retirement account after "x" months "y".

The equation to calculate the balance in the account after "x" months would be:

y = 100 + 25x

After 6 months, Alexa would have added 6 * $25 = $150 to the original balance of $100, so the balance would be:

y = 100 + 25 * 6 = 100 + 150 = $250

After 12 months, Alexa would have added 12 * $25 = $300 to the original balance of $100, so the balance would be:

y = 100 + 25 * 12 = 100 + 300 = $400

So, after 6 months, Alexa would have $250 in his retirement account, and after 12 months, he would have $400 in his account.

The area of the shaded portion of the given figure is 84 sq. units.

What is meant by area?

The size of a region on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a structure or planar lamina.

From the figure, we can conclude that,

Area of the shaded portion = Area of the square - Area of the four congruent parallelograms.

Now we have to find the area of square and parallelograms separately.

Area of square

Side length l = 12

Area = l *l = 12 * 12 = 144 sq. units

Area of parallelograms

Base b = 5

Height h = 3

Area of 1 parallelogram = b.h = 5 * 3 = 15 sq. units

Since all the parallelograms are congruent,

Area of all 4 parallelograms = 15 * 4 = 60 sq. units

Hence the area of the shaded portion of the given figure = 144 - 60

                                                                                          = 84 sq. units

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The function graphed above is:

Increasing on interval: (-3 0.5),

Decreasing on interval(s): (-∞ -3) and (0.5 ∞)

Real number intervals with growing and decreasing real-valued functions are referred to as increasing and decreasing intervals.

We apply the first-order derivative test to examine the sign of the derivative in each interval and identify the growing and decreasing intervals.

For the graph attached, the decreasing interval is

While the increasing interval is from -3 to 0.5

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the average time of 27 minutes is not an accurate representation of the friends' actual times, so the example describes neither accuracy nor precision.

Precision refers to how close multiple measurements are to each other. In this example, the three friends' times are all close to each other (20 minutes, 21 minutes, and 21 minutes), so the measurements are precise.

Accuracy refers to how close a measurement is to the true or correct value. In this example, the average time of the three friends running a 5K is 27 minutes, but the actual average time should be 20.33 minutes (20 + 21 + 21 / 3). So, the measurement is not accurate.

However, the average time of 27 minutes is not an accurate representation of the friends' actual times, so the example describes neither accuracy nor precision.

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The minimum point of a function f(x) is obtained as follows:

There are two requirements such that a value of x = a is a minimum point of a function f(x):

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Answer:

Part A: Yes, there is a correlation between the number of employees in the plant and the number of products produced monthly. This is because as the number of employees increases, the number of products produced also increases in a linear fashion.

Part B: The function that best fits this data is y = 8x + 120, where x is the number of employees and y is the number of products.

Part C: The slope of this plot indicates that for every additional employee, there is an increase of 8 products produced monthly. The y-intercept of this plot is 120, which is the number of products that would be produced if there were no employees.

we can see that Rule 2 has a higher probability of accepting a shipment containing 20% defectives. Therefore, Rule 2 has a smaller probability of accepting a shipment containing 20% defectives.

To compare the probabilities of acceptance of a shipment containing 20% defectives for the two rules, we can calculate the probabilities for both rules and compare the results.

For Rule 1, the probability of accepting a shipment containing 20% defectives is given by the probability of having 0 defectives in a sample of 10 components. This can be calculated as

P(Accept | 20% defectives) = (0.8)¹⁰

= 0.107374

For Rule 2, the probability of accepting a shipment containing 20% defectives is given by the probability of having 0 or 1 defectives in a sample of 20 components. This can be calculated as:

P(Accept | 20% defectives) = (0.8)²⁰ + ²⁰C₁ * (0.8)¹⁹ * (0.2)

= 0.276

Comparing the two probabilities, we can see that Rule 2 has a higher probability of accepting a shipment containing 20% defectives. Therefore, Rule 2 has a smaller probability of accepting a shipment containing 20% defectives.

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Refer to the attached images.

Answer: 25%

Step-by-step explanation:

Divide 17/68 = .25

Move decimal 2 places over = 25%

The fifth letter, Diego will type, is 'a'.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

Han types the letters a, s, d, f.

And repeats the over and over.

That means,

a, s, d, f, a, s, d, f, a, s, d, f, ....

Here, the fifth letter is 'a'.

So, the Diego will type 'a'.

Hence, the fifth letter is 'a'.

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