Which numbers could be a solution to the inequality? -6 < 3x+ 9 <21

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

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If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

First step: Simplify everything

\(2(10-a) + 4a + 4a+7 = 48\)

Next: Distribute required values

\(20-2a+4a+4a+7=48\)

Next: Time to add like terms

\(6a = 21\)

Final Step: Divide 6 on both sides to isolate variable

\(a = \frac{21}{6}\)

Thus, the value "a" = \(\frac{21}{6}\)

Hope this helps :)

Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2

Answer:

2x + 30° = 40°

4x + 30° = 50°

Step-by-step explanation:

2x + 30° and 4x + 30° are complementary angles.

Complementary angles sum up to give 90°.

Therefore,

2x + 30° + 4x + 30° = 90°

Add like terms

6x + 60 = 90

6x = 90 - 60

6x = 30

6x/6 = 30/6

x = 5

✔️2x + 30°

Plug in the value of x

2(5) + 30

10 + 30

= 40°

✔️4x + 30°

4(5) + 30°

20 + 30

= 50°

Answer:

B

Step-by-step explanation:

Center of the distributions -> mean/median (preferably mean)

The option with range is eliminated

Median might not be accurate as median is the center person, not the center result.

Based on the graphs, identify the graph with the intervals of greatest frequency.

For North Heights -> between 30 and 32 (right-skewed, some higher values)

For Southview -> between 28 and 30 (most concentrated there)

Hence, mean of Southview is lower than North Heights.

Answer:

the answer is-116

Step-by-step explanation:

I calculated all and it gave me the answer

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Given:

\(\dfrac{dr}{dt}=1.4\text{ in/s}\)

\(\dfrac{dh}{dt}=-2.1\text{ in/s}\)

To find:

The rate of change in volume at \(r=120\text{ in. and }175\text{ in.}\)

Solution:

We know that, volume of a cone is

\(V=\dfrac{1}{3}\pi r^2h\)

Differentiate with respect to t.

\(\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]\)

Substitute the given values.

\(\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]\)

\(\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]\)

\(\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560\)

\(\dfrac{dV}{dt}=29920\)

Therefore, the volume of decreased by 29920 cubic inches per second.

Answer: \(1\dfrac{11}{12}\text{ pounds}\)

Step-by-step explanation:

The complete question is provided in the attachment.

Given, Amount blueberry jelly beans= \(1\dfrac{1}{4}\) pounds

\(=\dfrac{5}{4}\) pounds.

Amount lemon jelly beans = \(2\dfrac{1}{3}\)pounds

\(=\dfrac{7}{2}\) pounds

Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans

\(=(\dfrac{5}{4}+\dfrac{7}{3})\) pounds

\(=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}\)

Amount of jelly beans she gave away = \(1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}\)

Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away

=\(\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}\)

She has left \(1\dfrac{11}{12}\text{ pounds}\) of jelly beans.

Answer:

The top left

Step-by-step explanation:

Answer:

the first one... maybe called "A" ...

Step-by-step explanation:

the range is all reals greater or equal to 1

the low point is when x=3. so (3,1) is the pivot point

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)

so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)

Options:

A. Players at school 1 typically spent more time in the weight room than players at school 2.

B. The middle half of the data for school 1 has more variability than the middle half of the data for school 2.

C. The median hours spent in the weight room for school 1 is less than the median for school 2 and the interquartile ranges for both schools are equal.

D. The total number of hours spent in the weight room for players at school 2 is greater than the total number of hours for players at school 1.

(See attachment for the box plots)

Answer:

C. The median hours spent in the weight room for school 1 is less than the median for school 2 and the interquartile ranges for both schools are equal.

Step-by-step explanation:

The median for school 1 is the value at the vertical line that divides the box of the box plot display of for school 1, which is 8

School 2 has a median of 9.

As we can see, the median for school 1 is less than the median of school 2.

Interquartile range is the range of the box.

Interquartile range for school 1 = 10 - 4 = 6

Interquartile range for school 2 = 13 - 6 = 6

As we can also see, the interquartile range for school 1 and that of school 2 are equal.

The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.

The total number of visitors is 105 + 41 + 8 = 154.

The number of visitors who purchased one or more costumes is 41 + 8 = 49.

So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.

Answer: 1280 fluid ounces.

Step-by-step explanation:

Answer:

(a) \(Area = 232.23\ cm^2\)

(b) \(Area = 52.78\ cm^2\)

(c) \(Area = 373.06cm^2\)

Step-by-step explanation:

The area of a circle:

\(Area = \pi r^2\)

Where

\(\pi = 3.14\)

Solving (a):

\(r = 8.6cm\)

\(Area = \pi r^2\)

\(Area = 3.14 * (8.6cm)^2\)

\(Area = 3.14 * 73.96cm^2\)

\(Area = 232.2344cm^2\)

\(Area = 232.23\ cm^2\) --- Approximated

Solving (b):

\(r = 4.1cm\)

\(Area = \pi r^2\)

\(Area = 3.14 * (4.1cm)^2\)

\(Area = 3.14 * 16.81cm^2\)

\(Area = 52.7834cm^2\)

\(Area = 52.78\ cm^2\) --- Approximated

Solving (c):

\(r = 10.9cm\)

\(Area = \pi r^2\)

\(Area = 3.14 * (10.9cm)^2\)

\(Area = 3.14 * 118.81cm^2\)

\(Area = 373.0634cm^2\)

\(Area = 373.06cm^2\) --- Approximated

A student is chosen at random from a class ,The student is a woman.

lacking a clear goal, plan, or pattern. : created, completed, or picked at random. read a few pages of the book at random. : referring to, containing, or being elements or occurrences that have a known likelihood of occurring.

Known as an entropy source, a TRNG is a function or apparatus that uses randomness to produce non-deterministic data (such as a series of numbers) to seed security algorithms.

As synonyms for random, the words casual and haphazard are frequently used.

straightforward random sampling Choosing a sample with simple random sampling necessitates the use of randomly generated numbers.

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Answer:

Approximately 23.6

Step-by-step explanation:

So first find the fraction of the whole circumference the arc is.

270 ÷ 360 = 0.75

The circumference is 10π

0.75 * 10π = 7.5π

7.5π = 23.5619449019 ≈ 23.6

order to determine the rate of change of the given function, use the following formula:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) and (x2,y2) are any two points of the line.

Use, for example:

(x1,y1) = (0,250)

(x2,y2) = (20,500)

replace the previous values of the coordinates into the expression for m:

m = (500 - 250)/(20 - 0)

m = 250/20

m = 12.5

Hence, the correctstament is:

C. After her raise, Natasha makes $12.50 an hour.

\({ \boxed{ \purple{ \sf{ \frac{dy}{dx} = \frac{3}{1 + {x}^{2}}}}}} \)

Step-by-step explanation:

Given question is, \({ \red{ \sf{y = {tan}^{ - 1}( \frac{3x - {x}^{3} }{1 - 3 {x}^{2} })}}}\)

Put \({ \tt{x = \tan \theta }}\) then,

\({ \tt{ \theta = { \tan}^{ - 1} x}}\)

\({ \red{ \sf{y = { \tan}^{ - 1}( \frac{3 \: tan \theta - { \tan}^{3} \theta}{1 - 3 { \tan}^{2} \theta})}}}\)

But \({ \green{ \sf{ \tan3 \theta = \frac{3 \: \tan \theta - { \tan}^{3} \theta }{1 - 3 \: { \tan}^{2} \theta}}}} \)

\({ \red{ \sf{y = { \tan}^{ - 1} ( \tan3 \theta)}}}\)

\({ \red{ \sf{y = 3 \theta}}}\)

\({ \red{ \sf{y = 3}}}{ \tt{ { \tan}^{ - 1} x}}\)

\({ \red{ \sf{ \frac{dy}{dx} = 3 \times }}}{ \tt{ \frac{1}{ {1 + x}^{2}}}} \)

•°•\({ \green{ \boxed{ \red{ \sf{ \frac{dy}{dx} = \frac{3}{1 + {x}^{2}}}}}}} \)

Answer:

6.40

Hope this helped somehow

Answer:

x-intercept= (4.265,0)

y-intercept= (0,-534)

Step-by-step explanation:

the simplest fοrm οf the given expressiοn is - (1+3/ 2ˣ).

Using variables and cοefficients, pοlynοmials are algebraic expressiοns. The term "indeterminates" is sοmetimes used tο describe variables. The terms Pοly and Nοminal, which tοgether signify "many" and "terms," make up the wοrd pοlynοmial.

When expοnents, cοnstants, and variables are cοmbined using mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn, the result is a pοlynοmial (Nο divisiοn οperatiοn by a variable). The expressiοn is categοrized as a mοnοmial, binοmial, οr trinοmial based οn the number οf terms it cοntains.

\(2^x +3 /-2^x\)

divide by  \(2^x\)

(1+3/ 2ˣ)  /  (1)

- (1+3/ 2ˣ).

Hence the simplest form of the given expression is - (1+3/ 2ˣ).

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Answer:

Step-by-step explanation:

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

Answer:

I believe 15 is one ahaha