Use the graph of y = ex to evaluate the expression e1.5. Round the solution to the nearest tenth if necessary.

Answer:

z = -17.67 + i3.43

Step-by-step explanation:

Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -

z = 18( cos169 + isin169 ),

z = r(cos Ф + i sin Ф)

Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -

sin169 is positive, while cos169 is negative, thus -

a = -17.6692893021...,

b = 3.43456191678...

Rectangular Form, z = -17.67 + i3.43

Hope that helps!

Answer:

[tex]\large \boxed{\text{-1.8$^{\circ}$F/1000 ft}}[/tex]

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

[tex]\begin{array}{cccc}\textbf{Alt/1000 ft} & \textbf{B.p.$/^{\circ}$F} & \Delta\textbf{B. p}& \Delta\textbf{B.p/1000 ft}\\0 & 212.0 & & \\& &-0.9 & -1.8\\0.5 & 211.1 & & \\& &-0.9 & -1.8\\1.0 & 210.2 & & \\& &-1.8 & -1.8\\2.0 & 208.4 & & \\& &-1.8 & -1.8\\3.0 & 206.6 & & \\& &-1.8 & -1.8\\4.0 & 204.8 & & \\& &-0.9 & -1.8\\4.5 & 203.9 & & \\\end{array}[/tex]

[tex]\text{ The change in boiling point per thousand feet of altitude is $\large \boxed{\textbf{-1.8$^{\circ}$F/1000 ft}}$}[/tex]

Answer:

Answer:

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

Step-by-step explanation:

Hey there! :)

Answer:

16p + 6.

Step-by-step explanation:

Add the two binomials together by combining like terms:

12p + 9 + 4p - 3

12p + 4p + 9 - 3

16p + 6.

Answer:

16p+6

Step-by-step explanation:

You combine like terms you do not multiply.

Answer:

all squares are quadrilaterals

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.

Answer:

6 x 10⁶ or 6,000,000

Step-by-step explanation:

100 × (200 × 300)

100 x 60,000 → 6,000,000

6,000,000 → 6 x 10⁶

Hope this helps! :)

Answer:

x = 5 and y = -4

Step-by-step explanation:

y = - 3x + 11 ______(1)

5x + y = 21______(2)

Substitute (1) into (2).

5x + (-3x + 11) = 21

5x - 3x + 11 = 21

2x = 21-11

2x = 10

x = 10/2

x = 5

Now substitute x = 5 into (1).

y = -3(5) + 11

y = -15 + 11

y = -4

Hence, x = 5 and y = -4

Answer:  x = 4

4x - 6=10

4x = 10 + 6

4x = 16

[tex]x = \frac{16}{4}[/tex]

x = 4  ←  the missing value

Therefore the the solution is (4,-6) of the equation 4x+y=10 .

Hope this helped You!

Answer: 52.8

Step-by-step explanation: it’s on khan ,

Answer:

B

Step-by-step explanation:

area of top on triangle=1/2×4×3=6m²

area of four top triangles=6×4=24 m²

area of bottom square=4×4=16 m²

area of four side rectangles=4×(4×5)=80 m²

Total area= 24+16+80=120m²

Answer:

In improper form your solution will be [tex]\frac{90}{7}[/tex]. As a mixed fraction it will be [tex]12\frac{6}{7}[/tex].

Step-by-step explanation:

The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,

[tex]\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\:[/tex] - Apply exponential rule " [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] "

= [tex]81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}}[/tex] - Combine fractions [tex]\frac{2}{7}[/tex] and [tex]\frac{3}{7}[/tex]

= [tex]81\cdot \frac{2}{9}x^{\frac{5}{7}}[/tex] - Multiply the fractions, and simplify further

= [tex]\frac{162x^{\frac{5}{7}}}{9}[/tex] = [tex]18x^{\frac{5}{7}}[/tex] - This is out simplified expression

Now that we have this simplified expression, we can see that a = [tex]18[/tex], and b = [tex]\frac{5}{7}[/tex]. Therefore, multiplying the two we should receive the improper fraction as follows,

[tex]18 * \frac{5}{7}[/tex] = [tex]\frac{90}{7}[/tex] - Note that this is in improper form. If you want your solution in a mixed fraction, it will be [tex]12\frac{6}{7}[/tex].

Answer:

1. Point estimate M (sample mean): 83.33

2. The lower bound is $73.36 and the upper bound is $93.30. One can be______% confident that the mean travel tax for all cities is between these values.

3. A. The researcher could decrease the level of confidence.

Step-by-step explanation:

A point esimate for the population mean travel tax can be done with the sample mean.

We can calculate the sample mean as:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(67.85+78.62+70.28+84.03+79.28+87.72+101.54+97.28)\\\\\\M=\dfrac{666.6}{8}\\\\\\M=83.33\\\\\\[/tex]

2. We have to calculate a 95% confidence interval for the mean.

The sample mean is M=83.33.

The sample size is N=8.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

We calculate the sample standard deviation as:

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((67.85-83.33)^2+(78.62-83.33)^2+(70.28-83.33)^2+. . . +(97.28-83.33)^2)}\\\\\\s=\sqrt{\dfrac{994.49}{7}}\\\\\\s=\sqrt{142.07}=11.92\\\\\\[/tex]

The standard error is:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{11.92}{\sqrt{8}}=\dfrac{11.92}{2.828}=4.214[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=8-1=7[/tex]

The t-value for a 95% confidence interval and 7 degrees of freedom is t=2.36.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.36 \cdot 4.214=9.97[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 83.33-9.97=73.36\\\\UL=M+t \cdot s_M = 83.33+9.97=93.30[/tex]

The 95% confidence interval for the mean travel tax is (73.36, 93.30).

We can be 95% confident that the true mean travel tax is within this interval.

3.. If we have no access to additional data, we can not decrease the standard deviation or increase the sample size.

The only way to have a narrower confidence interval is decreasing its level of confidence. With the same sample information, the lower the confidence, the narrower is the interval.

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]

1) Calculating the first derivative

[tex]f'(x)=2x[/tex]

2) Now, let's work to find the critical points

Set this

[tex]2x=0\\x=0[/tex]    

0, belongs to the interval. Plug it in the original function

[tex]f(0)=(0)^2+8\\f(0)=8[/tex]

3)  Making a table x, f(x) then compare

x|  f(x)

-1 | f(-1)=9  

0 | f(0)=8   Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.    

Answer:

84%

Step-by-step explanation:

The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.

If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:

[tex]P_1 = 20\% * 60\% = 12\%[/tex]

If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:

[tex]P_2 = 80\% * 90\% = 72\%[/tex]

To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:

[tex]P = P_1 + P_2[/tex]

[tex]P = 12\% + 72\% = 84\%[/tex]

Answer:

Step-by-step explanation:

opp=x,hyp=16

sin 51°=[tex]\frac{x}{16}[/tex]

cross multiply

sin 51° x 16 =x

0.7771 x 16=x

12.4=x

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.

Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.

Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

Learn more about horizontal asymptotes here -

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Answer:

c

Step-by-step explanation:

Answer:

  134 degrees

Step-by-step explanation:

Right so far. To find the numerical measure of the angle, you need to use x=7 in your expression for the angle measure:

  m∠STU = -27 +23(7) = 134 . . . degrees

Answer:

I think its

             T

 R--------Q----------A

             U

Step-by-step explanation:

Because RA as a line bisects TU

Answer:

if m is supposed to be the equals (=) sign then x = 25

Step-by-step explanation:

45 = (2x-5)

+5         +5

50 = (2x)

÷2     ÷2

25 = x

Answer: 70

Step-by-step explanation:

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:

Prime number

Step-by-step explanation:

A prime number has 2 factors.

A composite number has more than 2 factors.

47 has the factors 1 and 47.

47 is a prime number.

Answer:

47 is prime.

Step-by-step explanation:

Its factors are 1 and 47.

If a number has only 2 factors, then it's prime.

Answer:

Step-by-step explanation:

The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.

There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.

  C(1, 1), D(4, 1)

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

The general term is

Sn = -(-2)ⁿ.3¹⁻ⁿ

step by step Explanation:

we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

Total distance= 15.055 unit

Step-by-step explanation:

Distance between the first journey i.e from her office to the supermarket is calculated as follows given the coordinates.

(-5,-7) and (4,-6)

The distance between those tow points

Is

= √((4-(-5))² +( (-6)-(-7))²)

= √(9²+1²)

= √ 81+1

= √ 82

= 9.055

Noe the distance between the second journey traveled i.e from the supermarket to her house is calculated as follows given the coordinates.

(4,-6) and (-2,-6)

Distance= √((4--2)² +( -6--6)12

Distance = √(4+2)² + 0

Distance = √ 6²

Distance = 6

Total distance= 9.055 + 6

Total distance= 15.055

Answer:

x = 5, AB=5, BC = 15

Step-by-step explanation:

AC = AB + BC (Segment Addition)

AC= 20, AB =x Bc = 3x,

20= x+3x 20=4x

x=5

AB=x, AB =5

BC=3x BC= 15

The segment addition postulate states gives the value of x as 5, given

that the sum of x and 3·x is 20.

Responses:

From the given diagram, we have;

[tex]\overline{AB}[/tex] = x

[tex]\overline{BC}[/tex] = 3·x

According to segment addition postulate we have;

[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches

Which gives;

x + 3·x = 20

Therefore;

4·x = 20

[tex]x = \dfrac{20}{4} = 5[/tex]

[tex]\mathbf{\overline{BC}}[/tex] = 3·x  

[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15

Learn more about segment addition postulate here:

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Answer:

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Step-by-step explanation:

Confidence interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 290, \pi = \frac{261}{290} = 0.9[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]

Percentage:

Proportion multplied by 100.

0.8546*100 = 85.46%

0.9454*100 = 94.54%

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Based on the​ result, does the method appear to be​ effective?

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Step-by-step explanation:

[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

The quadratic formula is honestly the most straightforward way of solving here.

Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:

1) a=1, b=0, c=8

This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)

2) a=-9, b=4, c=-10

This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.

3) a=1, b=8, c=17

This reduces to x=(-4+i), (-4-i)

So those are the answers for each.

Please Refer to the screenshot. Hope this helps!