Jay is letting her bread dough rise. After three hours, her bread dough is \dfrac{11}{5} 5 11 ​ start fraction, 11, divided by, 5, end fraction of its original size.

Answer:

The percentage of blue candies is equal to 28​%.

Step-by-step explanation:

Sample size = n = 1000

21​% of them are blue

So, No. of blue candies = [tex]21\% \times 100 =\frac{21}{100} \times 100=21[/tex]

Claim : The percentage of blue candies is equal to 28​%.

[tex]H_0:\mu = 0.28\\H_a:\mu \neq 0.28[/tex]

We will use one sample proportion test  

[tex]\widehat{p}=\frac{x}{n}[/tex]

[tex]\widehat{p}=\frac{21}{100}[/tex]

[tex]\widehat{p}=0.21[/tex]

Formula of test statistic =[tex]\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

                                       =[tex]\frac{0.21-0.28}{\sqrt{\frac{0.28(1-0.28)}{100}}}[/tex]

                                       =−1.55

Now refer the p value from the z table

p value =0.0606

α =0.05

So, p value >  α

So, we failed to reject null hypothesis

So, the percentage of blue candies is equal to 28​%.

Given the problem, first, we denote the sample size, observed proportion of blue candies, claimed proportion of blue candies, and significance level as:

- n = 100
- p_observed = 0.21
- p_claimed = 0.28
- significance_level = 0.05

Our first step in the hypothesis testing process is to calculate the standard error. We do this using the formula:

 standard_error = sqrt((p_claimed*(1 - p_claimed))/n)

which gives us a standard error of approximately 0.0449. The standard error measures the variability or dispersion of our sample proportion from the claimed proportion.

Next, we will calculate the z-score, which measures the number of standard deviations an observation (or in this case, the sample proportion) is away from the mean, or the claimed proportion. We do this using the formula:

 z = (p_observed - p_claimed)/standard_error

which gives us a z-score of approximately -1.559. The negative sign indicates that the observed proportion is less than the hypothesized proportion.

Then, we need to calculate the p-value. The p-value is the probability of getting a sample as extreme, or more extreme, than the one we have, assuming the null hypothesis is true. In other words, it is the likelihood of observing our sample data if the candy company's claim of 28% blue candies is accurate.

As the observed proportion is less than the hypothesized proportion, we calculate the cumulative probability up to the z-score. Doing this gives us a p-value of approximately 0.0595.

Finally, we need to determine whether to accept or reject the null hypothesis based on the p-value and the significance level.

Here, we can see our p-value is slightly larger than the given significance level (0.0595 > 0.05), thus, we do not reject the null hypothesis. This means there is not enough evidence at the 5% significance level to reject the candy company's claim that 28% of their candies are blue.

In conclusion, given our sample and the given significance level, our analysis does not provide sufficient evidence to say with 95% confidence that the company's claim is false. Our data does not contradict the company's claimed proportion of 28%.

Answer:

(D) xy/(x + y)

Step-by-step explanation:

To find r in terms of x and y

Given,

Then,

1/r = 1/x + 1/y

1/r = (y + x)/xy

Find the reciprocal of both sides

r = xy/(x + y)

The right answer is option (D)  xy/(x + y)

Answer:

  9 and 23

Step-by-step explanation:

You can adjust the problem a little bit and make it easier to solve.

Subtracting 5 from the larger number makes it twice the smaller, and their sum be 32-5 = 27. So 27 is 3 times the smaller number, 9, and the larger is 32-9 = 23, which is 5 more than two times 9.

The two numbers are 9 and 23.

_____

You can let x represent "the other number". Then "one number" is 2x+5, and their sum is ...

  (x) +(2x+5) = 32

  3x +5 = 32

  3x = 27 . . . . . subtract 5

  x = 9 . . . . . . . divide by 3

(This working out should look familiar if you followed the above verbal solution.)

"One number" is 27 and "the other number" is 9.

Answer:

Output value for the following function is 4

Step-by-step explanation:

Given:

The input value are the value of x

[tex]y = 3x + 1[/tex]

Input value is 1

We substitute the value 1 for the input variable x in the given function.

[tex]y = 3x + 1[/tex]

[tex]y = 3(1) + 1[/tex]

[tex]y = 3 + 1[/tex]

[tex]y = 4[/tex]

The output value are the value of y

Therefore, for an input of 1, we have an output of 4.

Answer:

The speed of right going rider is 9 mph

The speed of left going rider is 18 mph

Step-by-step explanation:

Given as :

The total distance apart both the riders = 54 miles

Let The speed of right going rider = x mph

and The speed of left going rider = 2 x  mph

The Distance cover by right going rider = D miles

The Distance cover by left going rider = 54 - D  miles

Total time for both = 2 hours

So, Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

Or ,  Distance = speed × Time

For right going rider

       D = x × 2

For left going rider

      54 - D = 2 x × 2

Or, from first equation

     54 - 2 x = 4 x

or, 54 = 4 x + 2 x

or, 6 x = 54

∴   x = [tex]\frac{54}{6}[/tex]

I.e x = 9 mph

So, The speed of right going rider = 9 mph

and The speed of left going rider = 2 × 9 = 18  mph

Hence The speed of right going rider is 9 mph

and The speed of left going rider is 18 mph   answer

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is

y = 2x - 2

Comparing with the slope intercept form,

Slope, m = 2

This means that the slope of the line that is perpendicular to it is -1/2

The given points are (-3, 5)

To determine c,

We will substitute m = -1/2, y = 5 and x = - 3 into the equation, y = mx + c

It becomes

5 = -1/2 × - 3 + c

5 = - 3/2 + c

c = 5 + 3/2

c = 13/2

The equation becomes

y = -x/2 + 13/2

Answer:

$24.20

Step-by-step explanation:

Multiply and add.

Total assets: $3,450

Total liabilities and equity: $3,450

Explanation:

Cash: $2635

Equipment: $815

Total assets: $3,450

Accounts Payable: $185

Owner's Equity: $3,450 - $185 = $3,265

Total liabilities and equity: $3,450

the guy up there didn't understand.

Brainliest?

Question is bit incorrect, Correct question is given below.

Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) she can raise with 10 dark power crystals. How many zombie soldiers can Liliana raise with 10 power crystals?

Answer:

Liliana can raise 35 zombie soldiers.

Step-by-step explanation:

Let the number of zombie soldiers raised by 10 dark power crystals be 'z'.

Zombie raised by 4 power crystals = 14

Since the number of zombie and power crystals are in direct proportion.

Therefore, we get

[tex]\frac{z}{10}=\frac{14}{4}[/tex]

Multiply 10 on both the sides, we get

[tex]z=\frac{14}{4}\times 10 = 35[/tex]

Hence, Liliana can raise 35 zombie soldiers.

Answer:

35  Zombie Soldiers

Step-by-step explanation:

To determine the temperature of an object after a specific time using the given equation T(t) = 69e−0.0174t + 79, you replace t with the desired time in minutes and calculate the result. In case of one and a half hours (90 minutes), the temperature can be found using T(90) = 69e−0.0174*90 + 79.

The subject of this question is mathematics, more specifically an application of exponential decay in the context of temperature change. The equation T(t) = 69e−0.0174t + 79 represents the temperature T of an object after time t in minutes. To find the temperature after one and a half hours, we need to convert this to minutes because the given equation uses time in minutes. One and a half hours is equivalent to 90 minutes. So we will plug t=90 into the equation:
T(90) = 69e−0.0174*90 + 79.

Around this value to the nearest degree will give us the desired temperature in degrees Fahrenheit after one and a half hours.

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The temperature of the object after one and a half hours is approximately [tex]\( {93^\circ} \)[/tex] Fahrenheit.

To find the temperature of the object after one and a half hours, we need to substitute  t = 90 minutes into the equation [tex]\( T(t) = 69e^{-0.0174t} + 79 \)[/tex], since there are 60 minutes in an hour and a half.

Let's calculate:

[tex]\[ T(90) = 69e^{-0.0174 \times 90} + 79 \]\[ T(90) = 69e^{-1.566} + 79 \][/tex]

Using a calculator:

[tex]\[ T(90) \approx 69 \times 0.208 + 79 \]\[ T(90) \approx 14.352 + 79 \]\[ T(90) \approx 93.352 \][/tex]

Answer:

  10,000 ft

Step-by-step explanation:

We can solve the given relation for h:

  [tex]t=\dfrac{\sqrt{h}}{4}\\\\4t=\sqrt{h}\\\\h=16t^2[/tex]

Putting t=25 into this formula, we get ...

  h = 16(25²) = 10,000

With no air resistance the object will take 25 seconds to fall from 10,000 feet.

Answer:

  6%

Step-by-step explanation:

The multiplier on George's money is ...

  $708/$600 = 1.18

This value is ...

  1 + rt = 1.18 . . . . . for t = 3

  3r = 0.18 . . . . . . subtract 1; next divide by 3

  r = 0.06 = 6%

The simple interest rate on George's account is 6%.

Answer: V = 0.09L feet^3

Step-by-step explanation:

The tubing has the shape of a cylinder. Formula for determining the volume of a cylinder is

Volume of cylinder = πr^2h

Where π = 22/7 or 3.14

r = the inner radius of the drainage tubing. It is given as 2 inches. We would convert the 2 inches to feets

If 12 inches = 1 foot,

2 inches will be 2/12 inches

h = height of the cylinder and it is replaced by L in feets. L is the length of the cut drainage tubing.

An expression for the volume of L feets of drainage tubing will be

V = πr^2L

= 3.14 × (2/12)^2 × L

= 3.14 × 4/144 × L

V = 0.087L feet^3

V = 0.09L feet^3

Answer:

  40%

Step-by-step explanation:

The amount of income allocated to the items listed totals $744, so there is $496 he can spend on other things. As a percentage of income, that is ...

  496/1240 × 100% = 40%

Malaba can spend 40% of his net income on other things.

Answer: speed of jet A is 704 miles per hour

speed of jet B is 604 miles per hour

Step-by-step explanation:

Let the jets be jet A and jet B

Jet A and Jet B leave an air base at the same time and travel in opposite directions.

Let x = the speed of Jet A

Let y = the speed of jet B

One jet travels 100 miles an hour faster than the other. Let Jet A be the faster Jet. This means that

x = y + 100 - - - - - -1

If the two jets are 3924 miles apart after 3 hours, this means that both Jet A and Jet B travelled a total distance of 3924 miles after 3 hours.

Distance travelled = speed × time

Therefore,

Distance travelled by Jet A in 3 hours will be x × 3 = 3x miles.

Distance travelled by Jet B in 3 hours will be y × 3 = 3y miles.

Therefore, total distance is

3x + 3y = 3924 - - - - - - - -2

Substituting equation 1 into equation 2, it becomes

3(y+100) + 3y = 3924

3y + 300 + 3y = 3924

6y = 3924 - 300 = 3624

y = 3624/6 = 604 miles per hour

x = y + 100 = 604 + 100

x = 704 miles per hour

Answer:

a) dy/dt = ky(1-y)

b) 3:36pm

Step-by-step explanation:

a) Let the number of people who have heard the rumor = p

Let those who have not heard the rumor= q

Total population = p+q

Fraction of those that heard the rumor = p/p+q = y

Fraction of those who did not hear the rumor = q/p+q = 1-y

The rate at which the rumor spreads = dy/dt

dy/dt varies directly to y(1-y)

dy/dt = ky(1-y) where k is a constant

b) Recall that dy/dt = ky(1-y)

y(t) = y/(y+(1-y) e^-kt)

At 8 am , t= 0

y = p/ p+q

y(0) = 280/3500

y(0) = 0.08

By noon(12pm), t = 4

At this time half of the population has heard the rumor

y(4) = 0.5

Recall that y(t) = y/(y+(1-y) e^-kt)

y(t) = y0/(y0+(1-y0) e^-kt)

y(t) = 0.08/(0.08+(1-0.08) e^-kt)

y(t) = 0.08/(0.08+0 92 e^-kt)

To find k, put y(4) = 0.5 into the equation

y(4) = y/(y+(1-y) e^-4k)

0.5 = 0.08/(0.08+0.92e^-4k)

0.08 + 0.92e^-4k = 0.08/0.5

0.92e^-4k = 0.16 - 0.08

0.92e^-4k = 0.08

e^-4k = 0.08/0.92

e^-4k = 0.087

-4k = ln(0.087)

-4k = -2.422

k = -2.422/ -4

k = 0.611

y(t) = 0.08/(0.08+ 0.92 e^-0.611t)

The time by which 90% of the population would have heard the rumor is

0.9 = 0.08/(0.08+0.92e^-0.611t)

0.08 + 0.92e^-0.611t = 0.08/0.9

0.92e^-0.611t= (0.08/0.9) - 0.08

e^-0.611t = [(0.08/0.9)-0.08] / 0.92

e^-0.611t = 0.00966

-0.611t = ln(0.00966)

-0.611t = -4.640

t = -4.640/ -0.611

t = 7.6hrs

t = 7 hrs + (0.6*60)mins

t= 7 hrs + 36mins

t = 7hrs 36 mins

Therefore 8 am + 7 hrs 36 mins = 3:36pm

The time by which 90% of the rumor spreads = 3:36pm

The differential equation for the spread of a rumor, given the rate is proportional to the product of the fraction of the population who have heard the rumor and the fraction that has not, is dy/dt = k * y * (1 - y). To solve when 90% will have heard it, we find k using initial conditions and integrate to find the time.

To create a differential equation for the spread of the rumor we can say that the rate of spread, which is the derivative of the fraction of the population that has heard the rumor with respect to time (dy/dt), is proportional to the product of the fraction of the population that has heard the rumor (y) and the fraction that has not heard the rumor (1 - y). This gives us the differential equation dy/dt = k * y * (1 - y), where k is the proportionality constant.

To solve the problem for when 90% of the population will hear the rumor, we must first find the value of k using the initial conditions provided. At 8 AM, y(0) = 280/3500 and at noon, which is 4 hours later, y(4) = 0.5. Using this information, we can integrate the differential equation to find k and then use it to determine when 90% (i.e., y(t) = 0.9) of the population will have heard the rumor, applying appropriate integration and exponential growth techniques.

The selling price will be $232 if he applies a 45% markup.

Step-by-step explanation:

Cost of each stereo = $160

Mark up = 45%

Amount of mark up = [tex]\frac{45}{100}*160[/tex]

Amount of mark up = [tex]\frac{7200}{100} = \$72[/tex]

Selling price = Cost of stereo + mark up

Selling price = 160 + 72 = $232

The selling price will be $232 if he applies a 45% markup.

Keywords: addition, markup

Learn more about addition at:

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Answer:

b

Step-by-step explanation:

you first got twerk and this is workable because my wife left me for this reason

Answer:

  3.  25/45

Step-by-step explanation:

[tex]\dfrac{5}{9}=\dfrac{5\cdot 5}{5\cdot 9}=\bf{\dfrac{25}{45}}[/tex]

Answer:

OPTION C: 60%

Step-by-step explanation:

Chances of raining the next day + Chances that it will not rain = 100%

One of them should definitely be true.

So, if the chance of it raining tomorrow is 40% then there is 60% chance that it will not rain tomorrow.

This can also seen as follows:

Probability of rain tomorrow + Probability of no rain = 1

Given Probability of rain tomorrow = 40% = [tex]$ \frac{40}{100} = \frac{2}{5} $[/tex]

Probability of no rain tomorrow = 1 - Probability of rain tomorrow

⇒ Probability of no rain = 1 - [tex]$ \frac{2}{5} $[/tex]

⇒ Probability of no rain = [tex]$ \frac{3}{5} $[/tex]

Expressing it as percentage: [tex]$ \frac{3}{5} \times 100 $[/tex] = 60%.

The statements mostly describe properties of an unbiased estimator in statistics, which typically involves large sample sizes, the mean of the sampling distribution being equivalent to the population mean, and the distribution of sample means approaching a normal distribution. One incorrect statement suggests that each individual sample mean will be equivalent to the population mean.

This question pertains to the concept of statistical estimation. The statements reflect the properties of an unbiased estimator in a simple random sample from the population. Let's analyze each choice:

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The sample mean is an unbiased estimator of the population mean when the sample is a simple random sample; the mean of the sampling distribution of the sample mean will equal the population mean.

The student's question relates to the concept of an unbiased estimator in statistics, particularly the sample mean as an unbiased estimator of the population mean. The correct statement that defines an unbiased estimator is:

This means that if you were to take many samples from the population and calculate the mean of each sample, the average of all these sample means would be equal to the population mean. This property is fundamental in inferential statistics for making generalizations about a population from a sample.

Answer:

4.8 hours

Step-by-step explanation:

Let the time taken to hike uphill be T

Let the time taken taken to hike downhill = 8 -T

The average speed of walking up = 2 mph

Average speed of walking down = 3mph

Distance hiked uphill = Distance hiked downhill

Speed = distance /time

Distance = Speed * Time

2T = 3(8 -T)

2T = 24 - 3T

2T + 3T = 24

5T = 24

T = 24/5

T= 4.8 hours

Time taken to hike uphill = 4.8hours

Answer:

Option a, 0.10

Step-by-step explanation:

Given that of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.

i.e. out of 500 customers 50 customers purchased

Hence probability for any random customer to purchase = [tex]\frac{50}{500} =0.10[/tex]

Thus we find that if the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is

Option a)

0.10

This is based on the assumption that the past pattern of purchase determines the probabiltiy

Answer:

Part 1) Option A. The graph of g(x) has the lesser y-intercept

Part 2) Option B. (2,4)

Part 3) Option B. 62.5 miles per hour

Part 4) Option A. The functions will intersect at x=-2 and at x=1

Step-by-step explanation:

Part 1)

Let

x ----->the number of years

g(x) ----> the expected value in dollars of televisions

we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

In the function g(x)

The slope is

[tex]m=-\$90\ per\ year[/tex] ---> is negative because is a decreasing function

The y-intercept is

[tex]b=\$360[/tex]

substitute

[tex]g(x)=-90x+360[/tex]

Find the x-intercept (value of x when the value of the function is equal to zero)

For g(x)=0

[tex]0=-90x+360[/tex]

[tex]x=4[/tex]

The x-intercept is the point (4,0)

The y-intercept is the point (0,360)

Function f(x)

we have

[tex]f(x)=100(-x+4)[/tex]

[tex]f(x)=-100x+400[/tex]

Find the x-intercept (value of x when the value of the function is equal to zero)

For f(x)=0

[tex]0=-100x+400[/tex]

[tex]x=4[/tex]

The x-intercept is the point (4,0)

The y-intercept is the point (0,400) (value of f(x) when the value of x is zero)

Compare the intercepts both functions

The y-intercept is the same in both functions

The y-intercept is greater in the function f(x)

therefore

The graph of g(x) has the lesser y-intercept

Part 2) we have the equation of the line

[tex]4x-3y=-4[/tex]

Remember that

If a ordered pair is on the given line, then the ordered pair must satisfy the given line

Verify each case

a) (4,4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(4)-3(4)=-4[/tex]

[tex]4=-4[/tex] ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

b) (2,4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(2)-3(4)=-4[/tex]

[tex]-4=-4[/tex] ---> is true

so

the ordered pair satisfy the equation

therefore

the ordered pair is on the line

c) (2,-4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(2)-3(-4)=-4[/tex]

[tex]20=-4[/tex] ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

d) (4,-4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(4)-3(-4)=-4[/tex]

[tex]28=-4[/tex] ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

Part 3) we know that

The formula to calculate the average rate of change using the graph is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

In this problem we have

[tex]f(a)=f(2)=75\ mi[/tex]  

[tex]f(b)=f(4)=200\ mi[/tex]

[tex]a=2\ h[/tex]

[tex]b=4\ h[/tex]

Substitute

[tex]\frac{200-75}{4-2}=125/2=62.5 mi/h[/tex]

Part 4) we know that

The solution of the equation

f(x)=g(x)

are the x-coordinates of the intersection points both graphs

In this problem

If the solutions are x=-2 and x=1

then

The functions will intersect at x=-2 and at x=1

Final answer:

Joelle would earn $322.50 for a week in which she works 42 hours.

Explanation:

To calculate Joelle's earnings for a week in which she works 42 hours, we need to determine the regular pay for the first 40 hours and the overtime pay for the additional 2 hours.

Regular pay for 40 hours = $7.50/hour x 40 hours = $300

Overtime pay for 2 hours = 1.5 x $7.50/hour x 2 hours = $22.50

Therefore, Joelle's total earnings for a week of 42 hours would be $300 (regular pay) + $22.50 (overtime pay) = $322.50.

The correct answer is C. $322.50.  Joelle earns $322.50 for a week in which she works 42 hours.

To calculate Joelle's earnings for the week, we need to consider both her regular pay for the first 40 hours and her overtime pay for the additional hours worked beyond 40 hours.

First, let's calculate her regular pay for 40 hours:

Joelle's regular pay rate is $7.50 per hour. Therefore, for 40 hours, her regular pay is calculated as:

Regular pay = Hourly pay rate × Number of regular hours

Regular pay = $7.50/hour ×40 hours

Regular pay = $300.00

Next, we calculate her overtime pay for the 2 hours of overtime work. Joelle earns 1 1/2 times her regular pay rate for overtime hours. So her overtime pay rate is:

Overtime pay rate = 1 1/2 × Regular pay rate

Overtime pay rate = 1.5 × $7.50/hour

Overtime pay rate = $11.25/hour

Now, we calculate her overtime pay for the 2 hours of overtime work:

Overtime pay = Overtime pay rate × Number of overtime hours

Overtime pay = $11.25/hour × 2 hours

Overtime pay = $22.50

Finally, we add her regular pay and overtime pay to find her total earnings for the week:

Total earnings = Regular pay + Overtime pay

Total earnings = $300.00 + $22.50

Total earnings = $322.50

Therefore, Joelle earns $322.50 for a week in which she works 42 hours.

Answer: E. 1200

Step-by-step explanation:

Given : A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts.

i.e. No. of choices for different salads= 8  -----(1)

No. of choices for different main courses = 5  ----(2)

No. of choices for different desserts = 6

When we choose two different desserts then we use permutation(repeatition not allowed) :

[tex]^6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6\times5\times4!}{4!}=6\times5=30[/tex]----(3)

[∵ No. of ways to choose r things out of n =[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex] ]

If customers choose one salad, one main course and two different desserts for their meal , then By Fundamental principle of counting (Multiply (1) , (2) and (3)), the number of  different meals are possible :-

[tex]8\times5\times30\\\\=1200[/tex]

Hence, the correct answer is E. 1200 .

Answer:

Q = 1.84

Step-by-step explanation:

If we poured  0,5 gallon of mixture A with 0.5 gallon of mixture B we will get a gallon of:

   ( 15 + 50 )/ 2  =  32.5 %

Now by ule of three

        If       with     0, 5 gl    of A     we get    32.5 %

                                ?? x                                   30

x  =  (0.5)*(0.3)/ 0.325

x = 0,462 gl  t get a mixture of 30%

Then for 4 gl

Q = 4 * 0.462

Q = 1.84

Answer:

162.5 meters

Step-by-step explanation:

With respect to the angle given, the side from Meg to Store (150m) is the side that is "opposite" to the angle.

The side from Store to Bank is the side that is "adjacent" to the angle.

So, we have Opposite side and want to know the Adjacent side.

Which trigonometric ratio relates "opposite" to "adjacent"??

Yes, it is Tan!

We write the trig equation and solve for the distance (letting it be x):

[tex]Tan(42.71)=\frac{Opposite}{Adjacent}=\frac{150}{x}\\x=\frac{150}{Tan(42.71)}\\x=162.49[/tex]

Rounding the answer to 1 decimal place, it is:

162.5 meters

Answer:

0.2907

Step-by-step explanation:

Given that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on.

Since each topic is independent we find that probability for success in each topic = constant = 1/50 = 0.02

X no of topics that match is binomial with n = 17 and p = 0.02

Required probability

= Probability to find that you match on at least one of them

=[tex]P(X\geq 1)\\=1-P(X=0)\\=1-(1-0.02)^{17} \\=0.2907[/tex]

It would not be surprising as probability is reasonably large.

Answer: a) $80 b)$1900

Step-by-step explanation:

a) change in Yolanda total pay y, for each 'English is fun' sold x, i.e ∆y/∆x = dy/dx

y = 1900+80x

differentiating the equation above

dy/dx = 80

Therefore, dy/dx = $80

change in Yolanda total pay y, for each 'English is fun' sold x, is $80

b) if she doesn't sell any copy of ' English is fun ',x=0

Therefore,

y = 1900 + 80x

Substituting x = 0, into the equation above

y = 1900 = $1900

Therefore her total pay is $1900 if she did not sell any ' English is fun'