Write each of the following expressions as a^n or a^n b^m,

Step-by-step explanation:

2) 8,6,5,3 ,57 7,4,2/8

=92/8

mean =11.5

Arrange the terms in ascending order

2,3, 4, 5, 6, 7, 8, 57

the median of the ascending set= 5.5

3) 72 75 85 82 37 108/ 6

459/6

mean =76.5

Arrange the terms in ascending order

37, 72, 75, 82, 85, 108

the median of the ascending set= 78.5

4) 10 students were asked because there were 10 data values in the list.

5) it should be 55/10 =5.5

so its false

6) Sum first and find the mean number

5+4+3+2+1/5

=3

we know the angle is between 90° and 180°, 90° < θ < 180°, that means the angle is in the II Quadrant, where the sine is positive and the cosine is negative, with that info, let's find check a few things

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - 3^2}=a\implies \pm\sqrt{16}=a\implies \pm 4 = a\implies \stackrel{II~Quadrant}{-4=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}} \\\\\\ tan\left(\cfrac{\theta}{2}\right)\implies \cfrac{sin(\theta)}{1+cos(\theta)}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies 3[/tex]

Answer:

here is your answer

Step-by-step explanation:

cross multiplication

divide

Answer:

[tex]b = 2[/tex].

Step-by-step explanation:

By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].

Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:

[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].

Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:

[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].

Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:

[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].

[tex]b = 2[/tex].

Answer:

Step-by-step explanation:

Let the number of 1-point shots is x and 2-points shots is y.

The system as per question is

Solve it by elimination, subtract the first equation from the second

Find the value of x

Answer:

Y less than or equal to zero

Step-by-step explanation:

The graph shows that its moving downwards, therefore the Y value is decreasing..

Step-by-step explanation:

[tex]y - y_1 = m.(x - x_1)[/tex]

[tex]y - ( - 9) = 8.(x - ( - 2))[/tex]

[tex]y = 8x + 16 - 9[/tex]

[tex]y = 8x + 7[/tex]

Answer:

y = 8x + 7

Step-by-step explanation:

We are given that a line contains the point (-2, -9), and a slope of 8

We want to write the equation of this line

There are multiple ways to write the equation of the line:

The most common of these 3 methods is slope-intercept form, so let's write our equation this way

As we are already given the slope, we can immediately plug that into our formula for m

Replace m with 8:

y=8x+b

Now we need to find b

As the equation passes through (-2, -9), we can use its values to help solve for b

Substitute -2 as x and -9 as y:

-9 = 8(-2) + b

Multiply

-9 = -16 + b

Add 16 to both sides

7 = b

Substitute 7 as b.

y = 8x + 7

Topic: finding the equation of the line

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The price that John would pay for the new laptop after accounting for the sales, price coupon and the sales tax is  0.72p.

After the sales price and coupon is applied, the price of the laptop would reduce.

Price after the sales price = (1 - 0.2) x p = 0.8p

Price after the coupon = (1 - 0.15) x 0.8p

0.85 x 0.8p = 0.68p

A tax increases the price of the laptop.

Price after the tax = (1 + 0.06) x 0.68p = 1.06 x 0.68p = 0.72p

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Answer:

Domain: all real numbers (all reals)

Range: y> OR EQUAL TO -2

Step-by-step explanation:

Hope this helps! ;-)

Answer:

55

Step-by-step explanation:

Answer:

[tex]144^{90}[/tex]

Step-by-step explanation:

sqrt (144^180)   =    (144^180 )^1/2  = 144^90

Answer:

0.4714, a simplified 47%

Step-by-step explanation:

:)

Answer:

D. t < -4 or t > 5

Step-by-step explanation:

Inequality 1

Inequality 2

⇒ t < -4 or t > 5

⇒ Option D

Graph

Answer:

[tex]\sf D. \quad t < -4, t > 5[/tex]

Step-by-step explanation:

Given system of inequalities:

[tex]\begin{cases}5t-1 < -21\\4t+2 > 22\end{cases}[/tex]

Solve the inequalities by isolating t.

Inequality 1

[tex]\sf \implies 5t-1 < -21[/tex]

[tex]\implies \sf 5t-1+1 < -21+1[/tex]

[tex]\sf \implies 5t < -20[/tex]

[tex]\sf \implies 5t \div 5 < -20 \div 5[/tex]

[tex]\sf \implies t < -4[/tex]

Inequality 2

[tex]\sf \implies 4t+2 > 22[/tex]

[tex]\sf \implies 4t+2-2 > 22-2[/tex]

[tex]\sf \implies 4t > 20[/tex]

[tex]\sf \implies 4t \div 4 > 20 \div 4[/tex]

[tex]\sf \implies t > 5[/tex]

Therefore, the solution to the system of inequities is:

[tex]\sf t < -4, t > 5[/tex]

When graphing inequalities:

Therefore, to graph the given system of inequalities:

(Refer to attachment for the graph).

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Answer:

It’s If I do not stay home from the concert then it is not raining.

Step-by-step explanation:

it’s the answer that I have because in the question it’s asking what is the same but I guess opposite. Which is why I chose the first answer as my answer since if it’s not raining then they would go to the concert.

Answer:

Median = 19

IQR = 11

Third quartile = 25

Step-by-step explanation:

Just caculate it...

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

Speed of Carmen = 40km/h

and speed of Carmella = 60km/h

Step-by-step explanation:

Let the speed of Carmen = x km/h

Carmella speed will be (x + 20)km/h

Distance = 120 km

Time between Carmen and Carmella = 1 hour

[tex] \sf Time= \frac{distance}{speed} [/tex]

Let the time taken by Carmen be T1

and Carmella be T2

[tex] \sf So \: T_1 = \frac{120}{x} \: and \: T_2 = \frac{120}{x + 20} [/tex]

As there is 1 hour difference so

[tex] \sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies \frac{120}{x } - \frac{120}{x + 20} = 1 \\ \\ \\ \sf \implies \frac{120(x + 20) - 120x}{x(x + 20)} = 1 \\ \\ \\ \sf \implies 120x + 2400 - 120x = {x}^{2} + 20x \\ \\ \\ \sf \implies 2400 = {x}^{2} + 20x \\ \\ \\ \sf \implies 0 = {x}^{2} + 20x - 2400 \\ \\ \\ \sf \implies 0 = {x}^{2} + 60x - 40x - 2400 \\ \\ \\ \sf \implies0 = x(x + 60) - 40(x + 60) \\ \\ \\ \sf \implies 0 = (x + 60)(x - 40) \\ \\ \\ \sf \implies \red{\boxed{x = 40km}}[/tex]

We have not considered 60 as it will become negative value and negative value is not possible in distance

Speed of Carmen = 40km/h

Speed of Carmella = 40 + 20 = 60km/h

The final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns in mathematics.

The calculation of the given matrix is as follows:-

[tex]\rm D-C= \left[\begin{array}{ccc}13&2&-5\\6&-4&0\\\end{array}\right] - \left[\begin{array}{ccc}1&4&-8\\3&-5&2\\\end{array}\right] \\[/tex]

[tex]\rm D-C= \left[\begin{array}{ccc}(13-1)&(2-4)&(-5+8)\\(6-3)&(-4+5)&(0-2)\\\end{array}\right][/tex]

[tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

Hence the final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

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If the equation is y = - 11sin(4x - 8). Then amplitude will be 11, the time period is 4, and the phase difference is 8.

It is a function that repeats itself in a particular time interval.

The sinusoidal function is given as

y= |A| sin(ωx - Φ) ...1

Where A is amplitude, ω is the time period, and Φ is the phase difference.

The equation is given below.

y =  -11 sin(4x - 8) ...2

Comparing the equations 1 and 2, then we have

Amplitude will be 11, the time period is 4, and the phase difference is 8.

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Answer:

59.5 miles

Step-by-step explanation:

1 in = 7 mi

7 x 8.5 = 59.5

Answer:

x + 7 = 5

Step-by-step explanation:

I think this should be an equation I’m in 7th and I am learning these again so it should be an equation.

Answer:  0.3 feet

Work Shown:

(1 ft)/(150 ft) = (x ft)/(40 ft)

1/150 = x/40

1*40 = 150*x

40 = 150x

x = 40/150

x = 4/15

x = 0.2667 approximately

x = 0.3

Note: 0.3 ft = 0.3*12 = 3.6 inches

Answer:

Step-by-step explanation:

In the question, it is given that a right cone has a diameter of 12 units and volume of 168π units³ and we have to find the height of the cone.

[tex] \: [/tex]

To Find the height of the cone, we must know this formula :

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi r^2h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]

Where,

Now, we will substitute the values in the formula :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times (6)^2 \times h = 168 \pi}}}}}}} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times 36 \times h = 168 \cancel\pi}}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \ \times 36 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{36}{3} \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = \frac{168}{12} }}}}}}} \\ \\[/tex]

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\[/tex]

Therefore,

Answer:

x=8

Step-by-step explanation:

Let's say this mystery number is x.

6 times this x is 16 less than the square of x so we can write this as:

[tex]6x = x^2 - 16[/tex]

We can then re-arrange this into a quadratic and simplify it so:

[tex]x^2 -6x-16 =0[/tex]

[tex](x-8)(x+2)[/tex]

x=8, x=-2

And since the question is asking for the positive solution,
x=8

Here's the link to the answer:

https://riverside.rocks/index.php

Answer:

130 cm³

Step-by-step explanation:

Volume of the pyramid = 1/3 × base area × height

Calculating base area;

Area = length × width

= 8 × 7

= 56 cm²

Now, Volume = ⅓ × 56 × 7

= ⅓ × 392

= 130.6 cm³.

Answer:

A

Step-by-step explanation:

Please see attached, I have colour coded for your convenience