The results of Statistics test for 2 groups of Engineering students, Section 1 and Section 2 are normally distributed with N(75, 32) and N(77, 22), respectively. Two samples of size 14 and 16 students are randomly selected from Section 1 and Section 2 respectively. a.. Find the probability that the mean of Section 1 is lower than the mean of Section 2?

We have to solve the following inequality:

Answer:

to make it easier let's convert the rate in year

so it will be (2.5×12)

we gotta find CA(compound amount)

P=PRINCIPAL=$400

R=RATE=(2.5×12)%

T=TIME=7 years

a) If function be \($f(x)=\frac{x^2+(17-4 x)}{9 x}$\) then the value of f(5) = 22/45.

b) If function be g(x) = 3 x² - 6x + 9 then the value of g(x + 3) = 3x² + 12x + 18.

c)  If the function be \($h(y)=\frac{y^3-5}{7 y}$\) then the value of \($h(2x) =\frac{8 x^3-5}{14 x}$$\).

a) Let the function be \($f(x)=\frac{x^2+(17-4 x)}{9 x}$\)

substitute the value of x = 5, then

\($f(5) = \frac{5^2+(17-4 \cdot 5)}{9 \cdot 5}$$\)

simplifying the above equation, we get

\($=\frac{22}{45}$$\)

Therefore, the correct answer is 22/45.

b) Let the function be g(x) = 3 x² - 6x + 9

substitute the value of g(x) = g(x + 3), then we get

To estimate the value of g(x + 3) = 3(x + 3)² - 6(x + 3) + 9

= 3x² + 18x + 27 - 6(x + 3) + 9

simplifying the above equation, we get

=3x² + 18x + 27 - 6x - 18 + 9

Group like terms, we get

= 3x² + 18x - 6x + 27 - 18 + 9

=3x² + 12x + 27 - 18 + 9

= 3x² + 12x + 18

Therefore, the value of g(x + 3) = 3x² + 12x + 18.

b) Let the function be \($h(y)=\frac{y^3-5}{7 y}$\)

substitute the value of y = 2x, then we get

\($h(2x)=\frac{(2x)^3-5}{7 (2x)}$\)

simplifying the above equation, we get

\($=\frac{8 x^3-5}{7 \cdot 2 x}$$\)

\($=\frac{8 x^3-5}{14 x}$$\)

Therefore, the value of \($h(2x) =\frac{8 x^3-5}{14 x}$$\).

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Answer:

50

Step-by-step explanation:

Answer:

The measure of the unknown angle is 15°.

Step-by-step explanation:

Represent this angle by A.  Then the complement of A is 90° - A.

"Angle whose complement is five times its measure" would be expressed as

90° - A = 5A

Solve this for A by adding A to both sides:

90° = 6A.  Then A = 90°/6, or 15°

The expression after factorization is 6(x - 3).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given the expression 6x − 18.

\(\sf 6x - 18\)

Rewrite 18 as 6 · 3.

\(\sf 6x-6\times3\)

Factor out common term 6.

\(\rightarrow\bold{6(x - 3)}\)

Hence, the expression 6x - 18 after factorization is 6(x - 3).

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In a manufacturing process where the probability of a defect in an aluminum beverage can is 0.00004, we are interested in finding the probabilities associated with producing a certain number of defective cans out of a total of 100,200 cans.

In this scenario, we can use the binomial distribution to calculate the probabilities. The binomial distribution is used to model situations where there are a fixed number of independent trials (can production) with two possible outcomes (defective or non-defective).

Let's denote X as the random variable representing the number of defective cans. The probability mass function of the binomial distribution is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where n is the total number of cans produced, p is the probability of a defective can, and C(n, k) is the binomial coefficient.

a) To find the probability of exactly x defective cans, substitute the values into the formula mentioned above: P(X = x) = C(100200, x) * (0.00004)^x * (1 - 0.00004)^(100200 - x).

b) To find the probability of at most x defective cans, we need to calculate the cumulative probability: P(X ≤ x) = P(X = 0) + P(X = 1) + ... + P(X = x).

c) To find the probability of more than x defective cans, we can subtract the cumulative probability from 1: P(X > x) = 1 - P(X ≤ x).

By plugging in the appropriate values and performing the calculations, we can determine the desired probabilities associated with producing a certain number of defective cans out of 100,200 cans.

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In quadrilateral ABCD abοve, AD || BC and CD =1/2AB. the measure οf angle is B 90°

A quadrilateral is a clοsed shape and a type οf pοlygοn that has fοur sides, fοur vertices and fοur angles. It is fοrmed by jοining fοur nοn-cοllinear pοints. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.

Since AD is parallel tο BC, we have:

∠ABC + ∠BCD = 180° (interiοr angles οn the same side οf the transversal AD)We alsο knοw that CD = 1/2AB. Let's call the length οf AB "x". Then we have:

CD = 1/2AB

CD = 1/2x

Nοw, let's lοοk at triangle BCD. We knοw that the sum οf the angles in a triangle is 180°, sο we have:

∠BCD + ∠CBD + ∠BDC = 180°

We alsο knοw that ∠BCD = ∠ABC (because they are cοrrespοnding angles), sο we can substitute ∠ABC fοr ∠BCD:

∠ABC + ∠CBD + ∠BDC = 180°

Nοw, let's use the fact that CD = 1/2x tο find the length οf BD:

BD = AB - CD

BD = x - 1/2x

BD = 1/2x

Sο, BD is half the length οf AB. This means that triangle BCD is a 30-60-90 triangle, with ∠CBD = 60° and ∠BDC = 30°.

Substituting these values intο οur equatiοn abοve, we get:

∠ABC + 60° + 30° = 180°

Simplifying, we get:

∠ABC + 90° = 180°

Subtracting 90° frοm bοth sides, we get:

∠ABC = 90°

Therefοre, the measure οf angle B is 90°.

D) 90°.

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Answer

g(x) = 2ˣ⁺² or 2^(x + 2)

Explanation

When a function f(x) is translated horizontally along the x-axis by a units, the new function is represented as

f(x + a) when the translation is by a units to the left.

f(x - a) when the translation is by a units to the right.

Looking at the coordinates of the points given on f(x) and g(x), we can see that g(x) is just f(x) translate 2 units to the left.

Hence, if f(x) = 2ˣ

g(x) = f(x + 2) = 2ˣ⁺² or 2^(x + 2)

Hope this Helps!!!

In testing for differences between the means of two independent populations, the null hypothesis states that the difference between the two population means is not significantly different from zero or is H₀: µ₁ - µ₂ = 0  

Given: To state the null hypothesis between the difference of means for 2 independent populations.

What is a hypothesis?

A hypothesis is a proposed assumption or supposition which acts as an initial point for starting research work and it is based on just a few observations from the past that are based on a limited shred of evidence and is needed more evidence to prove to be true later in the future.

What is the null hypothesis?

In statistics, a null hypothesis is a proposition or explanation that says that for a given set of observations there is no significance or there is no difference for a certain characteristic of a population or a given data set under observation. It is denoted as H0

What is mean?

Mean is defined as the average for a given data set.

Hence in testing for differences between the means of two independent populations, the null hypothesis states that the difference between the two population means is not significantly different from zero or is H₀: µ₁ - µ₂ = 0  

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Answer:

The answer is 1,4, and 5 or A,D, and E

Step-by-step explanation:

i got the answer right on edge2020

Answer:

A, D, E

Step-by-step explanation:

The best way to describe the center of the data represented in this line plot is; mean = 1.8 inches and median = 1.5 inches

Line plots, also known as dot plots, are a type of graphical representation used to display data. They are particularly useful for showing the distribution and frequency of values in a dataset.

Line plots consist of a number line where each data point is represented by a dot or symbol placed above the corresponding value on the line.

Considering the given line plot:

Mean = (0 * 3 + 1 * 3 + 2 * 1 + 3 * 1 + 4 * 1 + 6 * 1)/10

Mean = 1.8 inches

Median = (1 + 2)/2

Median = 1.5 inches

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Answer:

Distance=Speed×Time

When speed is 40 kmph

Distance traveled by car =40×9

                                         =360 km

When speed is 60 kmph

Time taken to complete the journey =  

60

360

​  

                                                            =6 hours

Answer:

270 ÷ 6 = 45

45 x 6 = 270

45 x 9 = 405

The answer is 405

Hope it helped❤️

Answer:

\(x > 4\)

Step-by-step explanation:

X is greater than 4

Answer:

the answer is C

because for an equation to be an equation of a parabola, the coefficient of x^2 and y^2 has to be 1

So, on solving the provided question we can say that by probability we have \(256.014\)= sample mean for 80th percentile

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

\(P(x < 240)\)

Transform to z score =  (sample mean - population mean)/(standard deviation(std)\(/sample size^0.5)\)

\(P(z < (240-250)/(50/49^0.5)\)

\(P(z < -1.4) = 0.0808\)

z-score corresponding to 80th percentile is 0.842

0.842 = (sample mean -\(250)/(50/49^0.5)\)

\(6.014\) = sample mean - \(250\)

\(256.014\)= sample mean for 80th percentile

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The integer variable "a" is congruent to 11 modulo 19. This means that "a" leaves a remainder of 11 when divided by 19.

In modular arithmetic, the modulo operator (mod) is used to find the remainder of a division operation. In this case, the equation "a = 11 (mod 19)" signifies that "a" is congruent to 11 modulo 19. It implies that when "a" is divided by 19, it leaves a remainder of 11. To illustrate this further, consider a few examples:

If "a" is 11, then 11 divided by 19 yields a remainder of 11, satisfying the congruence.

If "a" is 30, then 30 divided by 19 results in a quotient of 1 with a remainder of 11. Again, this satisfies the given congruence.

In general, "a" can be expressed as "a = 19k + 11," where "k" is any integer. This formula shows that any value of "a" that satisfies this equation will be congruent to 11 modulo 19.

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Working efficiently, grouping tasks together, using the hood only when necessary, and proper cleaning and maintenance can all help minimize the number of times the hood sash is raised and lowered.

To minimize the number of times the hood sash is raised and lowered, it's important to work efficiently as possible in the hood. This means planning out your work ahead of time and grouping tasks together that require similar equipment or materials.

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The percentage obtained from the pie chart for different colors are Blue =29%, Green = 25%, Yellow = 24%, & Pink = 22%.

As per the results of the survey, Blue color received 29% votes so it must be chosen as the new color for receiving majority votes but as the other three colors also received almost similar percentage of votes. So, the manufacturer must do more research in order to reach on any conclusion.

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The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.

1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.

A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.

2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).

The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.

The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.

Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.

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Answer:

50+100x=300x+75x

Step 1: Simplify both sides of the equation.

50+100x=300x+75x

100x+50=(300x+75x)(Combine Like Terms)

100x+50=375x

100x+50=375x

Step 2: Subtract 375x from both sides.

100x+50−375x=375x−375x

−275x+50=0

Step 3: Subtract 50 from both sides.

−275x+50−50=0−50

−275x=−50

Step 4: Divide both sides by -275.

\(\frac{-275x}{-275}\) =  \(\frac{-50}{-275}\)

x= \(\frac{2}{11}\)

The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.

We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.

Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.

Use the distance , in speed/rate formula ,

Rate × Time = Distance

Upstream : (B-S)6 = 258

=> B - S = 43 --(1)

Downstream: (B+S)6 = 330

=> B + S = 55 --(2)

Solve the linear equations by elimination method. Add the two equations.

=> 2B = 98

=> B = 49 km/hr

Substitute this value of B in equation(2) and solve for S, B+S = 55

=> 49+S = 55

=> S = 6 km/hr

So, the rate of the current is 6 km/hr.

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Complete question:

A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.

Answer:

https://socratic.org/questions/at-their-annual-car-wash-the-science-club-washes-30-cars-in-45-minutes-at-this-r

Step-by-step explanation:

answer is in here yw

Answer:

Length of side QP = 5

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

         =2( x^2+1)^2

         = 2( x^2 +2x^2 +1)

         = 2x^4+4x^2+2

The utility function is u(x₁, x₂) = x₁ + x₂, and two budget constraints are given: (p₁, p₂, m) = (1, 2, 30) and (p₁', p₂, m) = (3, 2, 30).

To compute the total effect, substitution effect, and income effect, we compare the initial equilibrium bundle (x₁, x₂) to the new equilibrium bundle after the price change.

The total effect measures the change in utility when both the price and income change simultaneously. In this case, the price of good 1 changes from p₁ to p₁' while the income remains the same. By calculating the utility at the initial and new equilibrium, we can determine the total effect.

The substitution effect measures the change in utility due to the price change while holding utility constant. To isolate the substitution effect, we adjust the income to keep utility unchanged. We calculate the utility at the new equilibrium with the adjusted income, assuming the original price remains unchanged.

The income effect measures the change in utility due to the change in income while holding prices constant. We adjust the income to the new value while keeping prices constant and calculate the utility at the new equilibrium.

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Answer:

325000

Step-by-step explanation:

create a proportion: 13/3 = x/ 75000

cross multiply: 975000/3 = x

simplify: 325000

Answer:

325,000 female teachers or teachers that are women.

Step-by-step explanation:

1. set up an equation

\(\frac{x}{75,000} = \frac{13}{3}\)

2. cross multiply

\(3x = 975000\)

3. inverse operations/simplify

\(325000\)

Answer:

\(\huge\boxed{\tt{3}}\)

Step-by-step explanation:

Given the expression:

\(\displaystyle \frac{3y+6}{2x}\)

Given that: y = 4 , x = 3

\(\displaystyle = \frac{3(4)+6}{2(3)} \\\\= \frac{12+6}{6} \\\\= \frac{18}{6} \\\\= 3\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

/2x+3/=10

2x+3=10 or 2x+3=-10

2x=10-3 or 2x=-10-3

2x=7 or 2x=-13

X=7÷2 or X=-13÷2

X=3.5 or X=-6.5