An Economist consultant needs to forecast the unit cost of a product for the next year. He notes

that each unit of the product requires 10 labor hours and 5 kg of raw material. In addition, each

unit of the product is assigned an overhead cost of ETB 200. He estimates that the cost of a labor

hour next year will be normally distributed with an expected value of ETB 45 and a standard

de useviation of ETB 2; the cost of raw material will be normally distributed with an expected value

of ETB 60 and a standard deviation of ETB 3.

A. Find the distribution of the unit cost of the product.

B. Find its expected value and variance.​

When a test is two-sided and one-sided: We will reject the null hypothesis at the = X 0.01 0.050. 10 significance level if the value of interest falls outside a 95% confidence interval. If the value of interest falls outside a 99% confidence interval, the null hypothesis will be rejected at the = 0.010.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used. The confidence interval is the range of values within which you expect your estimate to fall a certain percentage of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

When a test is two-sided and one-sided: If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = X 0.01 0.050. 10 significance level. The null hypothesis will be rejected at = 0.010 if the value of interest falls outside a 99% confidence interval.

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Answer:

two sided.

.05

.01

Step-by-step explanation:

The lowest corresponding fraction of the integer is its simplest form. so we get the answer is 0.96.

A method is considered efficient if it can generate an answer quickly and without needing a page of computations. A successful strategy is one that solves every issue of a certain class (i.e., one that is generalizable to many problems using the same operation).

The lowest corresponding fraction of the integer is its simplest form.

Take the denominator's LCM as the first step. Step 2: Multiply the numerator and the denominator by the same number to convert the denominators to the LCM Value. Step 3: Subtract the numerator once the denominator is equal. Step 4: If required, simplify the resultant fraction.

5-3 a simpler problem. Then subtract.7 /10

5 / 3 - 7 / 10 =

50 - 21 / 30 = 29 / 30 = 0.96 .

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Fully factor the numerator and denominator of each rational expression. Write as one fraction by multiplying the numerators together and multiplying the denominators together.

Multiplication:

Step 1: Factor both the numerator and the denominator.

Step 2: Write as one fraction.  Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.

Step 3: Simplify the rational expression.

Step 4: Multiply any remaining factors in the numerator and/or denominator.

Multiplying Rational Expressions Involving Quadratics with Leading Coefficients of 1

Step 1: Fully factor the numerator and denominator of each rational expression.

Step 2: Write as one fraction by multiplying the numerators together and multiplying the denominators together.

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Answer:

12x^4y^7

Step-by-step explanation:

base(b)=8x^3y^5

height(h) =3xy^2

Area= (b x h)/2 =12x^4y^7

Answer:

[tex]A = 12x^4y^7[/tex]

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]A = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of the triangle's height.

In this problem, we are given the length of the base of the triangle as [tex]8x^3y^5[/tex] and the length of the height of the triangle as [tex]3xy^2[/tex].

Thus, the area of the given triangle is:

[tex]A = \dfrac{1}{2} \cdot 8x^3y^5 \cdot 3xy^2[/tex]

We can simplify this by combining like terms and using the exponent addition rule ([tex]x^a \cdot x^b = x^{a+b}[/tex]).

[tex]A =\left(\dfrac{1}{2} \cdot 8 \cdot 3 \right)(x^3 \cdot x)(y^5 \cdot y^2)[/tex]

[tex]A = (4 \cdot 3)(x^{3 + 1})(y^{5+2})[/tex]

[tex]A = 12x^4y^7[/tex]

The required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the definition of congruent angles, ∠ EOF ≅ ∠ BOC. Therefore, m ∠ BOC = 66 ∘ . In the addition, m ∠ AOC = 108 ∘ , and by definition of the straight angle, m ∠ AOC + m ∠ COD = 180 ∘ . After application of the subtraction of the angle, m ∠ COD = 72 ∘ .

Thus, the required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

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Answer:

It is given that m∠AOB = 42º and m∠EOF = 66º. By the vertical angles theorem, ∠EOF ≅ ∠BOC. By the angle addition postulate, m∠AOC = 108º, and by the linear pair theorem, m∠AOC + m∠COD = 108º. After the application of the subtraction property of equality, m∠ COD = 72º.

Step - by - step

first box: vertical angles theorem

second box: angle addition postulate

third box:  linear pair theorem

fourth box: subtraction property of equality

Answer:

next person to answer give them the brainly crow

Step-by-step explanation:

Answer:

The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). 2nd Option B

Step-by-step explanation: I saw it in another one so id like to help

The x-intercept of the line is (-1, 0). And the y-intercept of the line is not there.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the line is parallel to the y-axis, then the equation of the line parallel to the y-axis will be given as,

x = c

From the equation, the line is passing through (-1, 0), then we have

- 1 = c

c = - 1

Then the equation of the line is x = -1. Then the x-intercept of the line is (-1, 0). And the y-intercept of the line is not there.

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The Mean Value Theorem states that there exists a point c in the interval of the given function such that the derivative of the function at this point is equal to the average rate of change of the function on the interval. In this case, c = 7/2 satisfies the theorem for f(x) = 3x^2 - 5x + 1 on the interval [2, 5].

Using the Mean Value Theorem, we can find c by solving the equation 3c^2 - 5c + 1 = (3(5)^2 - 5(5) + 1 - (3(2)^2 - 5(2) + 1)) / (5 - 2). Simplifying, we get c = 7/2.

The Mean Value Theorem states that there exists a point c in the interval of the given function such that the derivative of the function at this point is equal to the average rate of change of the function on the interval. To find this point c, we must solve the equation

3c^2 - 5c + 1 = (3(5)^2 - 5(5) + 1 - (3(2)^2 - 5(2) + 1)) / (5 - 2).

This simplifies to c = 7/2, which means that this value of c satisfies the conclusion of the Mean Value Theorem for

f(x) = 3x^2 - 5x + 1

on the interval [2, 5]. This means that for any value of x within the interval, the rate of change of the function is always equal to 7/2.

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According to the solving the exponential form of the given number is as follows:

= 6² × 7⁴

= (-104)³

Bases and powers are employed in the exponential form to write numbers. It informs us of the amount of times we must actually multiply a number in order to obtain the answer. When we write the number 125 as 53, for instance, we can see that it is the third power of 5, or the number 125, which looks to be a typical three-digit number when observed.

When a single integer is multiplied by itself a certain number of times, x, the equation y takes on the base component b to the power of x, which is the quantity being multiplied, and is known as the exponential form.

The exponential form of the given number is :

= 6х6х7х7x7x7

= 6² × 7⁴

The exponential form of the given number is :

= -104 x -104 x -104

= (-104)³

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The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².

The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.

The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.

Given that a volume of cylinder = h × r² × π

                         h = 12 in

                          r = 2 in

                       volume = ?

Volume of cylinder = h × r² ×π

                                 = =12 × 3.14×(2)²

                                       =37.68 × 4

                                       =150.796 in³

B). Surface area of cylinder= 2πr² + 2πrh

                                         =2× 3.14 × (2)²+2× 3.14× 2×12

                                          =175.929in²

The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.

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The two cuts that are being roasted for each time-temperature combination are an example of replication.

Option (c) is correct.

What is temperature?

Temperature is a measure of the average thermal energy of the particles in a substance. It is a scalar quantity, meaning it has only a magnitude and not a direction. The most commonly used unit of temperature measurement is the degree Celsius (°C) or the degree Fahrenheit (°F), but it can also be measured in Kelvin (K) in scientific and engineering applications.

Given options are:

(a) The two cuts that are being roasted for each time-temperature combination are an example of conduction

(b) The two cuts that are being roasted for each time-temperature combination are an example of convection

(c) The two cuts that are being roasted for each time-temperature combination are an example of replication

(d) None of the above

(c) The two cuts that are being roasted for each time-temperature combination are an example of replication.

In the question it is given that  From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact sahpe size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparision.

Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.

Option (c) is correct.

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Answer:

see below

Step-by-step explanation:

3²-5 = -5x-3

9-5 =- 5x-3

-5x = 7

so x= -7/5

Answer:

Step-by-step explanation:

d = 6 would not be a solution to the inequality below because it would make the inequality untrue! Plugging in, we get:

13 < d + 3

13 < 6 + 3
13 < 9
We know that 9 is not a solution to the inequality!

To solve, we isolate the d, and from there we can find all values that are a solution to the inequality to the solution!

[tex]13 < d + 3\\\\13 - 3 < d\\\\10 < d[/tex]

Thus, one can say that the solutions to the inequality are: [R, d > 10]!

Answer:

[tex]\frac{7d}{15}[/tex]

Step-by-step explanation:

The plot inverse function g^-1(x) is attached below.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

X           3    4    6   10   18

g^-1(x)    0   1/2   1    3/2   2

In the given table x and g^-1(x) is shown.

Hence, THe plot inverse function g^-1(x) is attached below.

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The model that would explain the utility is U(q) = - 0.02q^2 - 300 + 10q.

The maximum number of workers is 250 and utility is 950

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

The total income as I(q) = 60q - 0.02q^2.

The total cost as C(q) = 300 + 50q.

The utility model can then be calculated as

U(q) = I(q) - C(q)

So, we have

U(q) = 60q - 0.02q^2 - 300 - 50q.

U(q) = - 0.02q^2 - 300 + 10q.

We have

U(q) = - 0.02q^2 - 300 + 10q.

Differentiate and set to 0

-0.04q + 10 = 0

So, we have

-0.04q = -10

This gives

q = 250 --- max workers

Recall that

U(q) = - 0.02q^2 - 300 + 10q.

So, we have

U(250) = - 0.02* 250^2 - 300 + 10 * 250

U(250) = 950 --- amount of utility

See attachment for the graph of I(q)=60q-0.02q^2

On the graph, we have the interpretation to be a maximum income of $45000 at 1500 workers

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The sampling distribution of the sample mean based on samples of size 2 for a population can be approximated by a normal distribution.

The histogram of the sampling distribution would therefore look like a bell-shaped curve. The mean of the sampling distribution is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size (in this case, 2).

Therefore, the formula for the sampling distribution of the sample mean for a population of size 2 is:

Mean = Population Mean

Standard Deviation = Population Standard Deviation / √2

The histogram of the sampling distribution would look like a bell-shaped curve with the mean and standard deviation determined by the formula above.

Therefore, the histogram most likely representing the sampling distribution of the sample mean based on samples of size 2 for the population is a bell-shaped curve with the mean and standard deviation determined by the formula above.

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The value of a and b is -5/4. The value describes the value of each digit in relation to its position in the number.

(a) Mean Value  = [tex]\frac{1}{3-1} \int_1^3 f(x)=\frac{1}{2}-\frac{5}{2}=\frac{5}{4}[/tex]

b) [tex]} \int_3^5 f(x) d x=\int_1^5 f(x) d x-\int_1^3 f(x) d x=10-\frac{5}{2}=\frac{15}{2} \\[/tex]

[tex]& \left.\int_3^5(2 f(x)+6) d x=2 \int_3^5 f(x) d x+6 \int_3^5 d x=2\left(\frac{15}{2}\right)+6 x\right]_3^5=15+6(2)=27 \\[/tex]

c) [tex]} f(x)=a x+b \\[/tex]

[tex]& \left.\int_1^3(a x+b) d x=\frac{a x^2}{2}+b x\right]_{x=1}^3=\frac{9}{2} a+3 b-\frac{a}{2}-b=4 a+2 b=\frac{5}{2} \\[/tex]

Simplifying,

[tex]\left.\int_1^5(a x+b) d x \cdot \frac{a x^2}{2}+b x\right]_{x=1}^5=\frac{25 a}{2}+5 b-\frac{a}{2}-b=12 a+4 b=10 \\[/tex]

[tex]4 a+2 b=5 / 2 \stackrel{n-3}{\rightarrow}-12 a-6 b=-15 / 2[/tex]

Then we get,

[tex]12 a+4 b=10[/tex]

[tex]$ \frac{12 a+4 b=20/2}{ -2 b=5 / 2} b=\frac{-5}{4}[/tex]

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If Jennifer wants to use the money to buy a new bicycle in 2 years, she can spend (future value) $388.54 on the bike as the account earns 13% interest, compounded monthly.

Compound interest is a system of interest computation where interest accumulates on the principal and previously accumulated interests.

Compounding the present value means adding interest to the principal amount when calculating subsequent interests.

N (# of periods) = 24 months (2 years x 12)

I/Y (Interest per year) = 13%

PV (Present Value) = $300

PMT (Periodic Payment) = $0

Results:

Future Value (F) = $388.54

Total Interest = $88.54

Thus, with a deposit of $300, Jennifer can spend $388.54 after earning 13% monthly compounded interest.

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The limit of f(x) as x approaches 0 is 1.

The limit of f of x as x approaches 0 can be calculated using limit theorems. First, we rewrite the function as:

f(x) = (x + 1) / (1 / (x - 1))

Then, we can simplify this by multiplying both the numerator and denominator by (x - 1):

f(x) = (x + 1)(x - 1) / 1

Next, we can apply the limit theorem that states the limit of a product is the product of the limits. Thus, we can calculate the limit as:

lim f(x) = lim (x + 1)(x - 1) / 1

= lim (x + 1) * lim (x - 1) / 1

= 0 + 1 * 0 - 1 / 1

= 1 / 1

= 1

Therefore, the limit of f(x) as x approaches 0 is 1.

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The translated function g(x) can be written as:

g(x) = (x + 2)^2

First, remember that an horizontal shift of N units applied to a function f(x) is:

g(x) = f(x + N)

if N > 0, the shift is to the right.

if N < 0, the shift is to the left.

Here we want a shift of 2 units to the left is:

g(x) = f(x + 2)

Where f(x) = x^3

Then the formula for the function g(x) is:

g(x) = (x + 2)^2

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The linear function in the form is y = 4x + 1.5 to the situation.

What is meant by function?

Initial fee: $4

Per mile: $1.50

Set up an equation where  = the taxi charges

Using y = mx + b form:

y = 4x + 1.5

The linear function in the form is

y = 4x + 1.5

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The account balance after 5 years will be $3935.53.

Compound interest is interest that is paid on both principal and interest at regular intervals. The first year of compound interest is similar to the first year of simple interest, but the difference begins in the second year.

Continuously compounded interest means that an account balance is constantly earning interest and reinvesting that interest so that it, too, earns interest.

Given that Jessica invests $3,065 in a savings account with an annual interest rate of 5% compounded continuously.

The account balance after 5 years will be calculated as:-

[tex]P(t) = P_oe^{rt}\\P(t) = 3065\times e^{0.05\times 5}\\P(t) = \$3935.53[/tex]

Therefore, the balance in the account after 5 years will be $3935.53.

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Using the equation

Since Pat is the CEO of Pat's Pickle-Packing Plant, but can still pack 18 jars of pickles per hour. Kim, a rising star in the industry, packs 24 jars per hour. Kim arrived at work at 9:00 am one day to find that Pat had been packing pickles since

7:30 am. Later that day, Kim had packed exactly the same number of jars as Pat.To find the time and number of jars picked, we solve an equation.

An equation is a mathematical expression that shows the relationship between two variables.

Let

Since Pat picks at a rate of 18 jars of pickles per hour, the number of jars Pat picks is n = 18t

Also, Kim picks at a rate of 24 jars per hour, 1.5 hours later the number of jars Kim picks is n' = 24(t + 1.5)

Since n = n', we have that

18t = 24(t - 1.5)

18t = 24t - 36

18t - 24t = -36

-6t = -36

t = -36/-6

t = 6 hours

Since Kim's time is t - 1.5 = 6 - 1.5 = 4.5 hours

To find the number of jars each picked, substitute t = 6 into n. so, we have that

n = 18t

= 18(6)

= 108 jars

So,

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Answer: 5

Step-by-step explanation:

The area of the square with side length [tex]5x[/tex] is [tex]25x^2[/tex].

The area of the square with side length [tex]2x[/tex] is [tex]4x^2[/tex].

The area of the triangle is [tex]\frac{1}{2}(2x)(5x)=5x^2[/tex].

It follows that [tex]25x^2 +4x^2 +5x^2=850 \implies x=5[/tex]. Note that we reject [tex]x=-5[/tex] since the length cannot be negative.

If the sum of the squares on its other two sides equals the square of its greatest side.

Given:

AB = 9 cm CB = 40 cm AC = 41 cm

The Pythagorean Theorem states that

If the largest side's square is equal to the sum of the squares on the other two sides, the triangle will have a right angle.

AB = 9 cm CB = 40 cm AC = 41 cm

The Pythagorean Theorem states that

AC 2 =BC² +AB ²

41²=40²+9²

41 ²=40 ² +9 ²

1681 = 1600 + 81

1681 = 1681

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The question is incomplete

Show that the triangle ABC is a right-angled triangle; if:

AB = 9 cm, BC = 40 cm, and AC = 41 cm.

if b is the span of the given vectors, so we can express b as the linear combination of the other given two vector.

given that,

[tex]a_{1} =\left[\begin{array}{ccc}-1&\\3&\\-1\end{array}\right] , a_{2} =\left[\begin{array}{ccc}-2\\-3\\6\end{array}\right] , b=\left[\begin{array}{ccc}-6\\9\\2\end{array}\right] \\\\\\\\\\\\\\\\\\\\\\\\[/tex]

We have determined that b is span of given vector a1 and a2.

we can write.   [tex]a_{1} =(-1,-3,-1) ,a_{2}=(-2,-3,6) , b=(-6,9,2)[/tex] .

A vector is a quantity that has magnitude and direction.

if x,y,z...., v are vectors and a,b,c....k are scalars then the linear combination is ax+by+cz+......+kv  

The set of linear combinations is called span for set of vectors.

So, b is span of given vector.

[tex]b=(c)a_{1} +(d)a_{2}[/tex]   ...... equation (A)

where c and d are scalars.

Now,

[tex](-6,9,2)=c(-1,3,-1)+d(-2,-3,6)\\(-6,9,2)=(-c,3c,-c)+(-2d,-3d,6d)\\(-6,9,2)=(-c-2d,3c-3d,-c+6d)\\[/tex]

equating the equations,

[tex]-c-2d=-6\\3c-3d=9\\-c+6d=2\\[/tex]

now we shall solve the above linear equations.[tex]subtract \\-c-2d-(-c+6d) = -6-2\\-8d=-8\\d=1\\now, \-c=-6+2d\\c=6-2=4\\c=4[/tex]

So, value of scalars c, d satisfied equation A,

thus, b is span of given vector a1 and a2.

The complete question is.

Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. a1=[-1 3 -1], a2=[-2 -3 6]= [-6 9 2]

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