Maria solved an equation as shown below. 3 (x + 6) = 5 (x minus 4). 3 x + 18 = 5 x minus 20. 38 = 2 x. 19 = x.

Check the picture below, so the lines look more or less like so, so the shape that we'll be getting will be the shape of a bowl with a hole in it, thus we'll use the washer method.

the way I use to get the larger Radius is simply using the "area under the curve" method, namely f(x) - g(x), where g(x) in this case is the axis of rotation.

so to get "R" and "r" we can get it by

\(\stackrel{y = 1}{(1)}~~ - ~~\stackrel{\stackrel{\textit{axis of rotation}}{y = -3}}{(-3)}\implies 1+3\implies \stackrel{R}{4} \\\\\\ \stackrel{y = \ln(x)}{\ln(x)}~~ - ~~\stackrel{\stackrel{\textit{axis of rotation}}{y = -3}}{(-3)}\implies \stackrel{r}{ln(x)+3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{R^2}{(4)^2}~~ - ~~\stackrel{r^2}{[\ln(x)+3]^2}\implies 16~~ - ~~[\ln^2(x)+6\ln(x)+9] \\\\\\ \ln^2(x)+6\ln(x)+7~\hfill \boxed{\displaystyle\int~[\ln^2(x)+6\ln(x)+7]dx}\)

Answer:

The three numbers are 5,6&7

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The expected value of a $2 ticket is $0.63

To calculate the expected value of a $2 ticket, we need to multiply the probability of winning by the value of the prize, then sum those products:

The Probability of winning the grand prize = 1/2000

Product: (1/2000) x $500 = $0.25

The Probability of winning a secondary prize: 3/2000

Product: (3/2000) x $200 = $0.30

The Probability of winning a third level prize: 8/2000

Product: (8/2000) x $20 = $0.08

The sum of the products:

$0.25 + $0.30 + $0.08 = $0.63

So the expected value of a $2 ticket is $0.63, meaning that on average, a person can expect to win $0.63 for every $2 they spend on a ticket.

The charity is expected to make a profit, which is why the answer is negative.

That is -$2 + $0.63 = -$1.37

So the expected profit for the charity per ticket sold is -$1.37, which is approximately the same as the given answer of negative $1.358(rounding off)

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Model B is the most appropriate for the set (-2,3), (-1,-3), (0, -5), (1, -3), (2,3).

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Answer:

Step-by-step explanation:

Given an age difference of 5 years and that Deepika was twice Kanchan's age five years ago, you want their present ages.

The relation five years ago between Deepika's age (d) and Kanchan's age (d-5) was ...

  d = 2(d-5)

  d = 2d -10 . . . eliminate parentheses

  10 = d . . . . . . . add 10-d

  (d -5) = 10 -5 = 5

At present, the ages are ...

  Deepika = 10 +5 = 15

  Kanchan = 5 +5 = 10

__

Additional comment

The age difference always remains the same, so the difference 5 years ago is the same as the difference 5 years later.

Answer:

This is the formula you use for someone investing in money. The formula is actually supposed to be: A=P(1+).

A is the total amount, P is the principal amount (the initial; original), r is percent (%) rate in decimal form, n is frequency, and t is the amount of years.

Step-by-step explanation:

The elements in the sample space obtained from the attached possible Venn diagram created with MS Word indicates;

Venn diagrams visually represent the relationship between sets. Venn diagrams consists of overlapping circular shapes or other shapes, which represents a set of elements.

1. The sample space of the spinner is; S = {0, 1, 2, 3, 5, 6, 7}

2. The set A = {0, 1, 2, 3, 4}

3. The probability of a number less than 5 is the number of elements in the sample space that are less than 5 divided by the total number in the sample space

Number of elements less than 5 = 5

Number of elements in the sample space = 8

4. Set B is; B = {1, 2, 3, 4, 5, 6, 7}

5. The elements that are natural numbers in the sample space are; N = {1, 2, 3, 4, 5, 6, 7}

The probability of spinning a natural number is therefore;

6. The set A and B is the set of elements common to both sets A and B which are; {1, 2, 3, 4}

A and B = {1, 2, 3, 4}

7. The probability of spinning a number that is both a natural number and a number less than 5, P(N and x < 5) can be found as follows;

(N and x < 5)  = {1, 2, 3, 4}

P(N and x < 5) = |{1, 2, 3, 4}|/|S| = 4/8 = 1/2

8. A' and B is the intersection of the complement of the set A and B, which are the elements in set B but not in set A. The Venn diagram indicates that we get;

9. The probability of spinning a number not less than 5 or a natural number, P(A' and B) can be found as follows;

Please find attached of the possible Venn diagram in the question obtained from a similar question on the internet

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The required confidence interval of the random sample of the given data is  (151.5456, 148.4544).

Statisticians use confidence intervals  to gauge vulnerability in an example variable. For instance, a scientist chooses various examples haphazardly from a similar populace and figures a certainty stretch so that each example might be able to perceive how it might address the genuine worth of the populace variable. The subsequent datasets are different where a few stretches incorporate the genuine populace boundary and others don't.

In an random sample of 60 PCs, the mean fix cost was $150, with the populace standard deviation being $36.

Standard deviationσ = $36, μ = $150 , n = 60

Value of z for 99% confidence interval is 2.576

Then,

Confidence interval =  μ±z(σ/n)

Confidence interval = $150 ± 2.576(36/60)

Confidence interval = $150 ± 1.5456

Confidence interval = $150 +1.5456 , $150 - 1.5456

Confidence interval = 151.5456, 148.4544

Thus, required interval is (151.5456, 148.4544).

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer: 2/5

Step-by-step explanation:

Step-by-step explanation:

The given problem can be solved by using the properties of parabola.

The statements are true about the function and its graph are as follows;

The value of the function when f(-10) is 82.

The value of a is 1/5 which is positive then the parabola opens upward.

The graph contains the point (20, –8)

Given that,

Consider the quadratic function;

\rm f(x) =\dfrac{1}{5}x^2 -5x + 12.f(x)=51x2−5x+12.

We have to determine,

Which statements are true about the function and its graph?

According to the question,

The quadratic function;

\rm f(x) =\dfrac{1}{5}x^2 -5x + 12.f(x)=51x2−5x+12.

1. The value of the function when f(-10) is,

\begin{gathered}\rm f(x) =\dfrac{1}{5}x^2 -5x + 12\\\\f(-10) = \dfrac{1}{5}(-10)^2 -5(-10)+ 12\\\\ f(-10) = \dfrac{1}{5}(100) +50+ 12\\\\ f(-10) =20 +62\\\\ f(-10) = 82\end{gathered}f(x)=51x2−5x+12f(−10)=51(−10)2−5(−10)+12f(−10)=51(100)+50+12f(−10)=20+62f(−10)=82

The value of the function when f(-10) is 82.

2. The graph of the function opens down

.\rm f(x) =\dfrac{1}{5}x^2 -5x + 12.f(x)=51x2−5x+12.

The value of a is 1/5 which is positive then the parabola opens upward.

3.  The graph contains the point f(x) = 20,

\begin{gathered}\rm f(x) =\dfrac{1}{5}x^2 -5x + 12\\\\f(20) =\dfrac{1}{5}(20)^2 -5(20) + 12\\\\f(20) =\dfrac{1}{5}400 -100 + 12\\\\f(20) =80 -100 + 12\\\\f(20)= -20+12\\\\f(20)=-8\end{gathered}f(x)=51x2−5x+12f(20)=51(20)2−5(20)+12f(20)=51400−100+12f(20)=80−100+12f(20)=−20+12f(20)=−8

The graph contains the point (20, –8)

4. The graph contains the point f(x) = 0,

\begin{gathered}\rm f(x) =\dfrac{1}{5}x^2 -5x + 12\\\\f(0) =\dfrac{1}{5}(0)^2 -5(0) + 12\\\\f(0) =\dfrac{1}{5}0 -0 + 12\\\\f(0) =0 -0 + 12\\\\f(0)= 12\end{gathered}f(x)=51x2−5x+12f(0)=51(0)2−5(0)+12f(0)=510−0+12f(0)=0−0+12f(0)=12

The graph contains the point (0, 12).

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Answer:

Slope = 2

Step-by-step explanation:

Rise/run = 2/1 = 2. You can also use slope formula m = (y2-y1)/(x2-x1)

Answer:

640.75

Step-by-step explanation:

2563/4 = 640\(\frac{3}{4}\) = 640.75

Answer:

the result of 2563/4 is 641 with a remainder of 3. We can also express this as a mixed number:

2563/4 = 640 3/4

Answer:

14, sqrt(200), 15

Step-by-step explanation:

14 is the least sqrt(200) equals 14.14 then 15

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Applying the triangle sum theorem, m∠N = 41°

Triangle sum theorem states that the sum of the three interior angles of any triangle equals 180°.

Given the following interior angles of ΔMNO:

m∠M = (6x+1)°

m∠N = (3x-10)°

m∠O = (x+19)°

Find the value of x:

m∠M + m∠N + m∠O = 180°

6x+1 + 3x-10 + x+19 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

x = 17

m∠N = (3x-10)°

m∠N = 3(17) - 10

m∠N = 41°

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Answer:

60 problems

Step-by-step explanation:

Find how many he got correct by multiplying 80 by 0.75:

80(0.75)

= 60

So, Bill got 60 problems correct

Answer:

1, -4, -9, -14, -19, -24, -29, -34, -39, -44, -49, -54 = -318

Step-by-step explanation:

Answer:

The Answer is -318.

Step-by-step explanation:

1 + (-4) + (-9) + (-14) + (-19) + (-24) + (-29) + (-34) + (-39) + (-44) + (-49) + (-54)

Answer:

Step-by-step explanation:

372 Millimeters

Answer:

2,300 millimeters

Step-by-step explanation:

when you convert 30 centimeters it’s 300 millimeters. When you convert 2 meters it’s 2,000 millimeters so…. That is the correct answer plus I just did the quiz and got it correct with that answer.

Answer:

2.6

Step-by-step explanation:

Could you mark this the brainlist

Answer:

2.5 or 2 1/2 ft is the width

Step-by-step explanation:

Area of rectangle = length × width

(13 3/4 can also be written as 13.75)

(5 1/2 can also be written as 5.5)

Area = l × w

13.75 = 5.5 × w

13.75 ÷ 5.5 = w

2.5 = w

Answer:

140

Step-by-step explanation:

First you have to solve for x

20x + 60 = 30x + 20

so you would subtract 20x from both sides

60 = 10x + 20

then subtract 20 from both sides

40 = 10x

then divide both sides by 10

4 = x

then you would put 4 in for x in the equation for angle 1

20(4) + 60

80 + 60

140

Answer:

angle 1=20(4)+60=140 degrees

Step-by-step explanation:

theory : If two parallel lines are cut by a transversal, the corresponding angles are congruent.

so angle 1 and angle 3 are equal:

20x+60=30x+20

60-20=30x-20x

40=10x

x=40/10=4

angle 1 = 20(x)+60

angle 1=20(4)+60=140 degrees

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

B. A teacher compares the pre-test and post-test scores of students

Step-by-step explanation:

the answer is true, because it is a good example to compare the tests between students, we know that a matching pair design is a random model and is used when the experiment allows grouping subjects in pairs based on a variable and each pair will receive randomly a different handling, the answer A is not true because in the example all students are uniformly averaged and the variable is not correlated with subgroups, option c is incorrect because the variable was not randomized and generates classification bias and the option d is incorrect because the teacher compares a small sample as her class with a score of a total sample, but does not intervene on her students when selecting the corresponding group

Matched pair design describes an experimental technique whereby subjects having certain variable or characteristic are paired or matched based on that variable, usually called the key variable. Hence, an example of a matched pair design is "a teacher compares the pre-test and post-test scores of students."

Hence, the most appropriate option is A.

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The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be  fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

The well-knοwn straightfοrward apprοach, actual variables, and any relevant infοrmatiοn frοm the initial and specialist questiοns can all be used tο finish the assignment. Custοmers may be given anοther chance tο try the gοοds in respοnse. If nοt, significant expressiοn in οur understanding οf prοgrams will be lοst.

Here,

We must figure οut hοw many pairs οf sunglasses must be sοld tο cοver the fixed and variable cοsts in οrder tο reach the break-even pοint.

Assume that X sunglasses must be sοld tο break even.

Fixed cοst plus variable cοst equals tοtal cοst.

Selling price x Number οf units sοld equals tοtal revenue.

The tοtal revenue and entire expense are equal at the break-even pοint.

Thus, we can cοnstruct the equatiοn:

Fixed cοst plus variable cοst multiplied by the selling price equals the quantity sοld.

=>  $9.44 X = $748,374 + $2.19 X

=>  $9.44 X - $2.19 X = $748,374

=>  $7.25 X = $748,374

=>  X = $748,374 / $7.25

=>   X = 103,184

Therefοre, fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

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The restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.

Sale refers to the transfer of ownership of goods or services from one person to another in exchange for money or other consideration.

The total purchase price of the franchise naming rights and physical property was $1,250,000.

To calculate the amount paid for each individual element of the sale, the total purchase price must be divided by the two elements.

The total purchase price of $1,250,000 divided by two elements equals $625,000.

This means that the restaurant chain paid $625,000 for the franchise naming rights and $625,000 for the physical property.

The amount of money paid for the franchise naming rights (four times the cost of buying the physical property) can be calculated by multiplying the cost of the physical property, which is

$625,000/4 .

When the cost of the physical property is multiplied by four, the result is $2,500,000.

This means that the restaurant chain paid $2,500,000 for the franchise naming rights.

In summary, the restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.

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Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²