Evaluate the following integral : Integral of x^3 + 1/x^0.5 dx

Answer: 9,-9

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

9x9=81

The surface area of the prism according to the segment labels is; 480mm².

The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;

Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).

Hence, the surface area of the prism upon evaluation is; 480mm².

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Common difference formula

[tex]\boxed{\sf d=t_2-t_1}[/tex]

So

Here

[tex]\\ \tt{:}\longrightarrow d=47-51[/tex]

[tex]\\ \tt{:}\longrightarrow d=-4[/tex]

Option C

Answer:

C.  -4

Step-by-step explanation:

Given sequence:  51, 47, 43, 39, ...

To find the common difference (d) between consecutive terms in an arithmetic sequence, subtract the previous term from the next term:

[tex]\implies \sf d=47-51=-4[/tex]

[tex]\implies \sf d=43-47=-4[/tex]

[tex]\implies \sf d=39-43=-4[/tex]

Therefore, the common difference for the given arithmetic sequence is -4.

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The candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

Let x be the quantity of 10% fat-content chocolate.

Fat in 10% fat-content chocolate + Fat in 60% fat-content chocolate = Total fat in 25% fat-content chocolate

0.10x + 0.60(100 - x) = 0.25*100

10x + 60*100 - 60x = 25*100

-50x = 25*100 - 60*100

-50x = 100(25 - 60)

50x = 3500

x = 3500/50

x = 70 kg

This is the quantity of 10% fat-content chocolate required.

100 - x = 30 kg

This is the quantity of 60% fat-content chocolate required.

Therefore, we have found that the candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

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Out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style. This can be obtained by using formula of probability and multiplying the total number of pizzas.

The formula for Expected value:

EV = P(X) × n

where EV is the expected value and P(X) is the probability of X and n is the total number.

In the question it is given that,

First we have to find the probability of stuffed crust or pan style,

P( stuffed crust or pan style) = P(stuffed crust) + P(pan style)

The number of stuffed crust and pan style = 161 + 191 = 352

The total number of crusts sold are ⇒ 307 + 224 + 161 + 191 = 883

⇒ P( stuffed crust or pan style) = 161/883 + 191/883

                                                   = 352/883

The expected value of stuffed crust or pan style,

n = 2000, P(X) = 352/883

EV = P(X) × n = (352/883) × 2000 = 797.28 ≈ 797

Hence out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style.

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The statement that <A > <C and <B > <D has been proved

In geometry, the side length opposite the largest angle is the longest side.

Similarly, the side length opposite the smallest angle is the shortest side.

From the given figure of quadrilateral, we have the following sides in increasing order:

The angles opposite the side lengths are:

This means that:

<A > <C and <B > <D

Hence, the statement that <A > <C and <B > <D has been proved

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Inequality are expressions not separated by an equal sign. The inequality shown has no solution

Inequality are expressions not separated by an equal sign. Given the inequality expression

2(x-3) ≤ 3 + 2x

Expand

2x - 6 ≤ 3 + 2x

2x - 2x ≤ 3 +6

0x ≤ 9

x≤9/0

Hence the inequality shown has no solution

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the answer is infact c!

The possible values for the width is w≥10.

Given that the length of a rectangle is 4 times the width and perimeter is to be less than or equal to 100 meters.

The perimeter of a rectangle is the total distance of its four outer boundaries. The perimeter of the object is twice the length and width of the object. This calculation is made using the formula:

perimeter = 2(length + width).

Here Perimeter=100 and length=4w

Substituting these values in the formula to find width, and we get

100≤2(4w+w)

100≤2(5w)

Divide both sides by 2, and we get

100/2≤(2(5w))/2

50≤5w

Divide both sides by 5, and we get

50/5≤5w/5

10≤w

Hence, the possible value for width when the length of a rectangle is 4 times the width is w≥10.

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Answer:

14 years ago

Explanation:

Let Mario's age be m, Jonas age be j.

From, Mario is 63 years older than Jonas

Equation 1: m = j + 63

From, Mario's age is four times Jonas age

Equation 2: m = 4j

Solve them by substitution:

m = j + 63

4j = j + 63

4j - j = 63

3j = 63

j = 21

Find Mario's age:

m = j + 63

m = 21 + 63

m = 84

Follow this steps:

m - y = 10(j - y)

84 - y = 10(21 - y)

84 - y = 210 - 10y

-y + 10y = 210 - 84

9y = 126

y = 14

The answer is 14 years ago.

Let Mario's age be M, and Jonas' age be J.

The formed equations :

To find their current ages, substitute the 2nd equation in the 1st equation.

4J = J + 63

3J = 63

J = 21

M = 4(21)

M = 84

For Mario to be 10 times Jonas' age, he has to be an age that is a multiple of 10.

Case (1) : Mario's age = 80

Subtract 4 from both their ages.

Mario : 84 - 4 = 80

Jonas : 21 - 4 = 17

17 × 10 ≠ 80

Case (2) : Mario's age = 70

Subtract 14 from both their ages.

Mario : 84 - 14 = 70

Jonas : 21 - 14 = 7

7 × 10 = 70

Considering the slopes of the segments, the correct option is:

D. No, because the triangle ABC doesn't have a pair of perpendicular sides.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

Here, we have to find if there are perpendicular segments, that is, if two slopes multiplied have a value of -1, then:

No sides are perpendicular, hence option D is correct.

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Answer:The radius is √16.

Step-by-step explanation:

The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.  

Herein we must create a new alloy by using correct quantities of two alloys with distinct copper concentrations. All required information can be found by concept of weighted averages:

(62/100) · (48 lb) = (39/100) · x + (65/100) · (48 - x)

62 · 48 = 39 · x + 65 · 48 - 65 · x

3 · 48 = 26 · x

x = 5.538 lb

The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.  

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The number of cards which must be drawn from the standard deck is 12.

Given a standard deck of cards.

We have to find the number of  cards to be drawn so that we will get atleast 3 cards from each suit. Because they have used atleast in the question so the cards can be more also so we have to reach at minimum level of cards to be drawn to guarantee atleast 3 cards of the same suit.

Number of suits in a  standard deck= 4 (Clubs, Hearts, Diamond,  Spades)

Cards in 1 suit=13

We need atleast 3 cards of the  same suit so we need atleast 3*4=12 cards. (3 from each suit)

Hence the minimum cards which must be drawn to get atleast 3 cards of the same suit is 12.

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The perimeter of the rectangle is 70 Inches square

The formula for perimeter of a rectangle is given as;

Perimeter = 2 ( l + w)

length = 20 inches

width = 15 inches

Perimeter = 2 ( 20 + 15 )

Perimeter = 2 ( 35)

Perimeter = 70 Inches square

Thus, the perimeter of the rectangle is 70 Inches square

Note that it is a general knowledge on the given question.

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Based on the function, the range of f(x) = 2(3)^x can best be described as y > 0.

When a number is raised to a power, the result will always be positive even if the number is raised to a negative number.

This means that 3^x will always be positive which means that 2(3)^x will also be positive. y will therefore always be greater than 0.

Full question is:

Which best describes the range of the function f(x) = 2(3)^x?

y > 0

y ≥ 0

y > 2

y ≥ 2

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Answer: [tex]y=2x+2[/tex]

Step-by-step explanation:

[tex]2x+4y=8\\\\x+2y=4\\\\2y=-x+4\\\\y=-\frac{1}{2}x+2[/tex]

So, the slope of the given line is -1/2, meaning the slope of the line we want to find is 2.

Since the y-intercept is the given line is (0,2), the equation is [tex]y=2x+2[/tex]

The solution will illustrate that the equation has one solution at x=0.

Given that  adds 2 to both sides, the equation 4x = 3x results.

An algebraic equation may be described as a mathematical declaration wherein expressions are set the same as every other.

The equation is 4x=3x.

As given that add 2 on both sides, we get

4x+2=3x+2

Now, we will subtract 3x from both sides, we get

4x+2-3x=3x+2-3x

x+2=2

Further, we will subtract 2 from both sides, we get

x+2-2=2-2

x=0

Hence, When adds 2 to both sides, the equation 4x = 3x results that the equation has one solution x=0.

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Answer:

A= 16

P=16

Step-by-step explanation:

A=h^bxb/ 2

P= side+base+side

The points are (0,0) Minimum and (1/6, 1/18) is the saddle point.

What is the saddle point?

To solve the question we have:

f(x,y) = xy(1-2x-6y)

Therefore, f(x,y) = xy-2x²y-6xy²

Finding the partial derivative of the above gives:

fₓ = y - 4xy-6y²

= x - 2x²-12xy

Therefore, when the above equations are set to 0 we get:

y - 4xy-6y² = 0.......(1)

x - 2x²-12xy  = 0......(2)

Dividing equations (1) and (2) by y and x respectively give:

1 - 4x - 6y = 0

1 - 2x - 12y = 0  

Solving gives:

x = 0.167 = 1/6

y = 0.056 = 1/18

When we place x in equation (1) we have:

y - 4(1/6)y-6y² = 0

y = 0 or y = 1/18

Similarly, x = 0 or 1/6

Therefore, the four critical points are:

(0,0) (1/6,1/18)

When x = 0 and y = 0

f(x,y) = 0 Hence this is a minimum

When x = 1/6 and y = 1/18

f (x,y) = 1/324 Which is a saddle point.

Therefore, the points are (0,0) Minimum, and (1/6, 1/18) is the saddle point.

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The question you are looking for is here:

(1 point) The function f(x,y)=xy(1−2x−6y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that, we mean that (x,y) comes before (z,w) if x

We need to find the difference between plots that show a strong correlation and plots that show a weak correlation.

The point of creating a scatter plot is to determine if there is a correlation. Correlation means the relationship between two quantities. For example, there is a correlation between how much a person studies and the grade they get on a test, but there is no correlation between how much money a person earns and what pets they own. In mathematics, correlation between data means that the points follow a pattern and go in the same direction. There are two types of correlation:

Positive: the trend is rising from left to right

Negative: the trend is decreasing from left to right

If the dots on the scatter plot do not follow a pattern, there is no correlation.

All correlations have two properties: strength and direction. The strength of the correlation is determined by its numerical value. The direction of the correlation is determined by whether the correlation is positive or negative.

The strength of the correlation indicates how strong the relationship is between the two variables. The strength is determined by the numerical value of the correlation. A correlation of 1, whether +1 or -1, is a perfect correlation. In perfect correlations, the data points lie directly on the fit line. The further the data is from the fit line, the weaker the correlation. A correlation of 0 means there is no correlation

If the value of correlation coefficient is nearer to to 1 or -1 , then there exist a strong correlation.

If the value of correlation coefficient is nearer to to 0 , then there exist a weak correlation.

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The data points are a little closer for a weak correlation, and you can see that there is some sort of relationship between these factors.

Data points for a strong correlation are in close proximity to one another, making it possible to build a line by imitating their pattern.

A statistic called correlation gauges how much two variables change in connection to one another.

Correlation and diversification, the idea that certain types of risk can be reduced by investing in assets that are not connected, are closely related concepts.

Correlation cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.

A scatter plot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.

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❄ Hi there,

let us revise the rounding rules and then, get down to rounding the number.

[tex]\sf{Rounding \ Rules:}[/tex]

Now we can start the rounding process.

Reading the problem & the directions, we notice that we need to round to 3 decimal places (3 numbers after the decimal point).

Looking at the fourth number, we notice that it's less than 5.

∴ we need to round down ↡

↬[tex]\sf{18.57631 \ rounded \ to \ 3 \ DP \ = \bf{18.576}}[/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

❄

Answer:

There are 35 Men, 12 Children, and 18 Women

Step-by-step explanation:

Men(M), Women(W) and Children(C)

We learn that:

M = 35

W = 1.5C , and

M+W+C = 65

----

M+W+C = 65

M+1.5C+C = 65

35+1.5C+C = 65

2.5C = 30

C = 12

If C=12 and W=1.5C, then W=18

----

There are 35 Men, 12 Children, and 18 Women

(35+12+18) = 65 participants

The correct option is (d).

The other beaker contains 17 cc (cubic centimetres) of the liquid.

The volume of a cube with dimensions of 1 cm ×1 cm× 1 cm is equal to one cubic centimetre (or cubic centimetre in US English) (SI unit symbol: cm³; non-SI abbreviations: cc and ccm). A millilitre's volume is equal to one cubic centimetre.

According to the question,

The total liquid is 32 in cubic centimetres which is stored in the two beakers.

In the first beaker the liquid stored is 15 cubic centimetres.

The second beaker will contain the liquid = total liquid stored in both beakers - liquid stored in the first beaker.

Liquid in second beaker = 32 - 15

                                        = 17

Therefore, the liquid stored in the second beaker is 17 cc (cubic centimetres).

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The value of the sum of squares due to regression is 18.43.

Given the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89.

A common measure used in regression analysis is the sum of squares total (SST). The square of each difference is added to the sum of squares to obtain the squared disparities between individual data points and their mean. The variance is calculated using the sum of squares, which is also used to assess how well a regression curve fits the data.

We will use the total sum of squares (SST) is given as the summation of the sum of squares due to regression (SSR) and sum of squares error (SSE);

SST = SSR + SSE

Here, SST=25.32 and SSE=6.89

Substitute the values in the formula, we get

25.32=SSR+6.89

Now, we will subtract 6.89 from both sides, we get

25.32-6.89=SSR+6.89-6.89

18.43=SSR

Hence, the value of the sum of squares due to regression (SSR) when the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89 is 18.43.

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Using the unit circle, the coordinates of the terminal point corresponding to [tex]\theta = 120^\circ[/tex] is: (-0.5, 0.866).

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

In this problem, the angle is of [tex]\theta = 120^\circ[/tex], hence:

Hence the terminal point is:

(-0.5, 0.866).

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Answer: 239

Step-by-step explanation:

[tex]g(7)=2(7)-5=9\\\\f[g(7)]=f(9)=3(9)^2 - 4=239[/tex]

The perimeter of the semicircle is 66. 846 meters

The formula for finding the perimeter of a semicircle is

Perimeter = πr + 2r

We were given diameter = 26meters

Radius, r = diameter/2

radius = 26/ 2 = 13 meters

π = 3. 142

Substitute value into the formula

Perimeter = 3. 142 × 13 + 2 × 13

Perimeter = 40. 846 + 26

Perimeter = 66. 846 meters

Thus, the perimeter of the semicircle is 66. 846 meters

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.