I really don't understand this ​

It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.

To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have

[tex]21^1 + 9 = 21 + 9 = 30[/tex]

and of course 30 = 5×6 is divisible by 5.

Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write

[tex]21^k + 9 = 5\ell[/tex]

Now the induction step: when [tex]n=k+1[/tex], we have

[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]

which is divisible by 5. QED

Answer:

A= 16

P=16

Step-by-step explanation:

A=h^bxb/ 2

P= side+base+side

Answer:

Step-by-step explanation:

The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.

In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers

Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.

Answer:The radius is √16.

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Answer:

9 songs

Step-by-step explanation:

a quarter is basically a fourth of a number so you need to just divide the number by four

Answer:

C. 9

Step-by-step explanation:

The cubed root of 729 is the number that is multiplied 3 times to get 729. In this case, it's 9.

9*9*9 = 81*9

81*9 = 729

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 wonderful waffle cone holds more ice cream than super sundae cone.

In this question,

The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.

Volume of ice cream cone = volume of hemisphere + volume of cone

Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]

Volume of super sundae cone:

Radius of hemisphere = height of hemisphere = 0.5 in

Depth of the ice cream cone = 4 in

Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]

⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]

⇒ 0.2616+1.0466

⇒ 1.3082 ≈ 1.31 cubic in.

Volume of wonderful waffle cone:

Radius of hemisphere = height of hemisphere = 0.9 in

Depth of the ice cream cone = 3 in

Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]

⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]

⇒ 1.526+2.5434

⇒ 4.0694 ≈ 4.07 cubic in.

Thus volume of wonderful waffle cone > volume of super sundae cone.

Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.

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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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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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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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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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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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Answer:

{x:x is a real number}

Since any value can replace x to give an integer.

{x:x is a real number}

[tex]f(x) = 3(x + 2)(x - 5)[/tex]

[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]

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 number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of the parabola passing through (0, 0), (-3, 9) and (3, 9) is y = x²

The equation of the parabola with vertex at (4, 22) passing through (0, 6), (8, 6) and (3, 9) is y < -x² + 8x + 6

The solution to the system of equation is the darker region and it contains the point (-1, 6)

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Answer:

(2,9)

Step-by-step explanation:

Got it on FlVS

❄ 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]

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

❄

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 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 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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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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What is one major limitation of the Social Readjustment Rating Scale?

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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.

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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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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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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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

The laterals surface area of the given hexagonal prism is: 250 cm².

Lateral surface area = 5ah, where:

Given the following:

a = 5 cm

h = 10 cm

Lateral surface area of the hexagonal prism = 5ah =  5(5)(10)

Lateral surface area of the hexagonal prism = 250 cm²

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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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