Write 3 expressions containing exponents so that each expression equals 81

Answer:

-1/2

Step-by-step explanation:

At this point you can guess and try. And it seems that x = -1/2, lets check:

So, this is correct: x= -1/2

Answer:

[tex]\boxed{V=lwh}[/tex]

Step-by-step explanation:

The formula for volume of a cuboid is:

[tex]V=lwh[/tex]

[tex]volume = length \times width \times height[/tex]

Answer:

V = l w h

Step-by-step explanation:

Volume of a Cuboid = Length × Width × Height

Where l = length, w = width and h = height

Answer:

Step-by-step explanation:

[tex]f(x) = 4 {e}^{x} [/tex]

[tex]f(2) = 4 {e}^{2} [/tex]

[tex]f(2) = 4 \times 7.389[/tex]

[tex]f(2) = 29.6[/tex]

( Approximately 30)

Hope this helps..

Good luck on your assignment..

Answer:

approximately 30

Step-by-step explanation:

[tex]f(x)=4e^x[/tex]

Put x as 2 and evaluate.

[tex]f(2)=4e^2[/tex]

[tex]f(2)=4(2.718282)^2[/tex]

[tex]f(2)= 29.556224 \approx 30[/tex]

Answer:

  181.8 yd

Step-by-step explanation:

The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...

  c^2 = a^2 +b^2 -2ab·cos(C)

For the given geometry, this is ...

  c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75

  c ≈ √33037.75 ≈ 181.8 . . . yards

Marsha's ball is about 181.8 yards from the hole.

Answer:

181.8 yds

Step-by-step explanation:

I got it correct on founders edtell

Answer:

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Step-by-step explanation:

(i) probability with 16 success out of 24 = 16/24 = 2/3

(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3

Since the two experiments have the same probability, the observed probabilities are the same.

HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.

Using the binomial distribution,

(i)

p = 1/2

N = 24

x = 16 (number of successes)

P(16,24) = C(24,16) p^16* (1-p)^8

= 735471* (1/65536)*(1/256)

= 0.0438

(ii)

p = 1/2

N = 12

x = 8 (number of successes)

P(8,12) = C(12,8) p^8* (1-p)^4

= 495*1/256*1/16

= 0.1208

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Note: It would help to mention the topic you're on so answers will correspond to what is expected.  Here we cover probability and binomial distribution.

Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

The graph which shows the solution to the system of inequalities is attached in the picture below :

Given the inequalities :

y ≥ 2x + 1

y ≤ 2x - 2

From y ≥ 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y ≥ 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 ≥ 2(0) + 1

0 ≥ 0 + 1

0 ≥ 1

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

From : y ≤ 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y ≤ 2x - 2

Graph the line y ≤ 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y ≤ 2x - 2:

0 ≤ 2(0) - 2

0 ≤ 0 - 2

0 ≤ - 2

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

Learn more : https://brainly.com/question/19670553

Answer:

Its graph B on edge 2022

Step-by-step explanation:

Answer:

[tex]z = \frac{x}{y} [/tex]

Step-by-step explanation:

Let x be the price of carton of ice cream

Let y be the number of grams in carton

Let z be price per gram.

[tex]z = \frac{x}{y} [/tex]

Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.

Hope this helps ;) ❤❤❤

Answer:

r=$14,400

The hotel should charge $120

Step-by-step explanation:

Revenue (r)= p * n

where,

p = price per item

n = number of items sold

A change in price leads to a change in number sold

A variable to measure the change in p and n needs to be introduced

Let the variable=x

Such that

p + x means a one dollar price increase

p - x means a one dollar price decrease

n + x means a one item number-sold increase

n - x means a one item number-sold decrease

for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)

know that at $60 per room, the hotel rents 210 rooms

r = (60 + 2x) * (210 - 3x)

=12,600-180x+420x-6x^2

=12,600+240x-6x^2

r=2100+40x-x^2

= -x^2 +40x+2100=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a= -1

b=40

c=2100

x= -b +or- √b^2-4ac / 2a

= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)

= -40 +or- √1600-(-8400) / -2

= -40 +or- √ 1600+8400 / -2

= -40 +or- √10,000 / -2

= -40 +or- 100 / -2

x= -40+100/-2 OR -40-100/-2

=60/-2 OR -140/-2

= -30 OR 70

x=70

The quadratic equation has a maximum at x=70

p+2x

=60+2(30)

=60+60

=$120

r= (60 + 2x) * (210 - 3x)

={60+2(30)}*{(210-3(30)}

r=(60+60)*(210-90)

=120*120

=$14,400

Answer:

[tex] -3n - 7 [/tex]

Step-by-step explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]

[tex] m = \frac{-13 + 10}{1} [/tex]

[tex] m = \frac{-3}{1} [/tex]

[tex] m = -3 [/tex]

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

[tex] y = mx + b [/tex]

[tex] -10 = -3(1) + b [/tex]

[tex] -10 = -3 + b [/tex]

Add 3 to both sides:

[tex] -10 + 3 = -3 + b + 3 [/tex]

[tex] -7 = b [/tex]

[tex] b = -7 [/tex]

The equation of the given linear function can be written as:

[tex] y = -3x - 7 [/tex]

Or

[tex] f(x) = -3x - 7 [/tex]

Therefore, if the input is n, the output would be:

[tex] f(n) = -3n - 7 [/tex]

Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Answer:

0.078

Step-by-step explanation:

The probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question;

There are two events;

(i) Drawing a first card which is a king: Let the event be X. The probability is given by;

P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]

Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.

Also, the total number of sample space = 52, since there are 52 cards in total.

P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;

P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]

Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4

But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.

P(Y) = [tex]\frac{4}{51}[/tex]

Therefore, the probability of selecting a first card as king and a second card as queen is;

P(X and Y) = P(X) x P(Y)

= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078

Therefore the probability is 0.078

Answer:

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Step-by-step explanation:

To identify outliers the interquartile range of the dataset can be used

Outliers can be identified as data values that are

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Using the interquartile range concept, it is found that:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

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

[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]

Thus:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

A similar problem is given at https://brainly.com/question/14683936

Answer:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]

here;

m = 5

n = 9

r = 0.5

Then:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]

For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,

the responses are;

(1) The number of terms are 9

(2) The value of the sum is approximately 0.374

The given geometric series is presented as follows;

3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³

(1) The number of terms in the series = 13 - 4 = 9

Therefore;

(2) The value of the sum can be found as follows;

The common ratio, r = 0.5

The sum of the first n terms of a geometric progression is presented as follows;

[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]

The sum of the first 4 terms are therefore;

[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]

The sum of the first 13 terms is found as follows;

[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]

Which gives;

The sum of the 5th to the 13th term = S₁₃ - S₄

Therefore;

[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]

Learn more about geometric series here:

https://brainly.com/question/12471913

Answer:

False

Step-by-step explanation:

To find <A, we can do 5x - 80 = 3x + 20.

As we simplify, we will get 2x = 100, which is x = 50

Therefore, <A will be 50 degrees and not 45 degrees.

Also, if you need y, you can do:

3y - 7 = y + 7

2y = 14

y = 7

Answer:

Hey there!

Jimmy has 15-7, or 8 apples left.

Hope this helps :)

Answer:

36

Step-by-step explanation:

You did not attach a picture, so I just assumed where the lengths of 15 and 39 were.

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

Answer:

The  90%  confidence interval for population mean is   [tex]14.7 < \mu < 19.1[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 16.9[/tex]

    The confidence level is  [tex]C = 0.90[/tex]

     The sample size is  [tex]n = 45[/tex]

     The standard deviation

Now given that the confidence level is  0.90 the  level of significance is mathematically evaluated as

       [tex]\alpha = 1-0.90[/tex]

       [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex]  from the standardized normal distribution table. The values is  [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The  reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex]  instead of  that of  [tex]\alpha[/tex]  is because [tex]\alpha[/tex]  represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%)  did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex]  is just considering the area of one tail which is what we required calculate the margin of error

  Generally the margin of error is mathematically evaluated as

        [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]

         [tex]MOE = 2.207[/tex]

The  90%  confidence level interval is mathematically represented as

      [tex]\= x - MOE < \mu < \= x + MOE[/tex]

substituting values

     [tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]

    [tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]

     [tex]14.7 < \mu < 19.1[/tex]

Answer:

-∞<x<∞

Step-by-step explanation:

volume of a cube=s^3

the domain is (-∞,∞) the domain is all the real number of s

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

Answer:

[tex]x \geq -91/2[/tex]

Step-by-step explanation:

[tex]6(x+8) \geq -43 + 4x[/tex]

Resolving Parenthesis

[tex]6x+48 \geq -43 + 4x[/tex]

Collecting like terms

[tex]6x - 4 x \geq -43-48[/tex]

[tex]2x \geq -91[/tex]

Dividing both sides by 2

[tex]x \geq -91/2[/tex]

Answer:

x ≥ - 91 / 2

Step-by-step explanation:

In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.

Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]

[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,

[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,

[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,

[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.

Answer:

[tex]79591.8872 in^3/s[/tex]

Step-by-step explanation:

we know that the volume of a right circular cone is give as

[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]

Therefore differentiating partially  with respect to  r and h we have

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]

Answer:-95 1/7 feet

Step-by-step explanation:

-120 4/7+25 3/7=-95 1/7 feet

Answer:

8/5

Step-by-step explanation:

w = k / √x

4 = k / √4

k = 8

w = 8 / √x

w = 8 / √25

w = 8/5

Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

[tex]T_A=4.225+1.375+3=8.6[/tex]

The total sales tax for Florida is:

[tex]T_F=6.5+1+1.625=9.125[/tex]

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

Answer:

The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.

Step-by-step explanation:

There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.

Answer:  D. y = (x - 3)² + 2

Step-by-step explanation:

Inverse is when you swap the x's and y's and solve for y.

               y = [tex]\sqrt{x-2}[/tex] + 3

Swap:      x = [tex]\sqrt{y-2}[/tex] + 3

Solve:  x - 3 = [tex]\sqrt{y-2}[/tex]

           (x - 3)² = [tex](\sqrt{y-2})^2[/tex]

           (x - 3)² = y - 2

    (x - 3)² + 2 = y